**Determining Economic Security of a Business Based on Valuation of Intangible Assets according to the International Valuation Standards (IVS)**

#### **Dmitrii Rodionov, Olesya Perepechko and Olga Nadezhina \***

Graduate School of Industrial Economics, Peter the Great St. Petersburg Polytechnic University, 195251 Saint-Petersburg, Russia; rodionov\_dm@spbstu.ru (D.R.); po.olesya9@gmail.com (O.P.) **\*** Correspondence: nadezhina\_os@spbstu.ru; Tel.: +7-911-252-8637

Received: 25 August 2020; Accepted: 8 October 2020; Published: 20 October 2020

**Abstract:** This work considered the economic security of an enterprise with regard to the valuation of intangible assets according to the International Valuation Standards (IVS). This study is essential due to a growing number of companies with intangible assets (trademarks, patents, know-how, etc.) as their main value. This study included analysis of the impact created by the value of intangible assets and intellectual property on company capitalization and economic security plus a regression model. An algorithm was developed to determine the economic security of a business based on the valuation of intangible assets according to the IVS. The suggested algorithm can allow a company to manage its intangible assets effectively using the IVS, which, in turn, will provide the required level of economic security for further development and achievement of strategic goals by the business entity.

**Keywords:** economic security of companies; valuation of intangible assets and intellectual property; International Valuation Standards (IVS); legal disputes over intellectual rights

#### **1. Introduction**

The issues of providing business entities with economic security in a time when multiple internal and external threats are being faced are of top priority today. According to the World Intellectual Property Organization (WIPO), intellectual property accounts for over 75% of all earnings in the world economy (World Intellectual Property Organization 2017).

Companies are always investing in intangible assets and intellectual property in attempts to outrun their competitors (World Intellectual Property Organization 2017).

A considerable growth in the number of cases on the rights for intangible assets and intellectual property heard by the Court of Intellectual Rights of the Russian Federation is evidence of growing losses caused by the violation of rights in this sphere. According to the latest survey of the cases related to settling disputes on intellectual rights, 742 cases of this category were considered in 2018 in Russia, with 710 of them being about providing or terminating legal protection of the results of intellectual activity and means of identification. The growth rates as of the first six month of 2019 amounted to 14.5% against the same period of the previous year (Superior Court of Arbitration 2018).

According to the statistics of the United States District Courts, the total number of cases on copyright, patents, or trademarks was 12,268 in 2019, while in 1990 the number of cases was 5700 (Courts 2019).

This is due to the fact that the internal structure of economic security of any business entity includes three primary components: economic independence, economic resilience and self-development (Radyukova and Shamaev 2011).

At present, there are many different approaches that are based on the assessment of individual components of the security of a company's activities, and there is no structured methodology that includes intangible assets and intellectual property.

The purpose of the study was to develop an algorithm to determine the economic security of businesses based on valuation of intangible assets in accordance with the IVS.

In order to accomplish the purpose of the study, the following objectives were set:


The paper is structured as follows: literature review, description of the applied models and methods, substantiation of the applied data, specification of the research results and reliability analysis of the calculated research results. The paper also details an algorithm for determining the economic security of businesses based on the valuation of intangible assets according to the IVS, along with discussion of the results and conclusion.

#### **2. Literature Review**

A universal algorithm for determining the economic security of enterprises based on intellectual property has not been developed so far. Starting from the 1980s, foreign scholars conducted major scientific research on the whole range of questions related to the role of intellectual capital for business development. They note a considerable effect produced by intangible assets on company security (Barth et al. 2001). American economists V. Andonova and Ruíz-Pava highlight that companies are highly dependent on their intangible assets. The authors also conclude that intangible assets are a major factor in the productivity of enterprises and determine their competitive advantages in the external environment (Andonova and Guillermo 2016). According to the International Valuation Standards 2020, section IVS 210, an intangible asset is defined as: "a non-monetary asset that manifests itself by its economic properties. It does not have physical substance but grants rights and/or economic benefits to its owner".

Tsai et al. (2016) present a study that is based on comparison of various types of machine learning for intangible assets. Clausen and Hirth (2016) in their work introduce a profit indicator, related to the value of intangible assets based on the productivity of intangible assets. Gu and Li (2015) in their study investigate the matters related to investing in companies based on intangible assets. Vasconcelos et al. (2019) presented work aimed at studying the relationship between the intangible assets, macroeconomic environment and market value of public companies in Germany, the UK and Portugal. They also investigated the impact of intangible assets on the market value of companies using sensitivity tests. In their research, the authors Montresor and Vezzani (2016) highlight the innovative impact of intangible investments and claim that via intangible investments companies acquire knowledge assets that increase their innovativeness. Matos et al. (2018) formulated a hypothesis that future results of many companies will depend on intangible assets. They carried out analysis of intangible assets for a number of European Union countries.

The research by Basso et al. (2015) shows the contribution of intangible assets in the creation of the value of companies using the methodology suggested by Gu and Li.

In his research, Nejati (2016) explains the main components of intangible assets, namely human capital, structural capital and relational capital.

Russell (2016) considers the intangible assets of pharmaceutical companies and compares the value of these assets in terms of their significance.

In their research, Pastor et al. (2017), Bontis (2001), Bouteiller and Karyotis (2010) and Pastor et al. (2017) carried out analysis and review of the literature dedicated to intangible assets and their valuation as well as the examples of methods that can be used to evaluate individual intangible assets. The work by Plaskova et al. (2019) carried out analysis, based on which a clear definition of an innovative asset as an element of an organization's intangible assets was given. Proposals were made to create a solid business image and investment attractiveness of an organization. Authors Boj et al. (2014) look at intangible assets and intellectual capital as the key drivers creating value and competitive advantages for organizations (Rodionov et al. 2018a) They suggest methodology for defining, measuring and managing the relevance of intangible assets in achieving the strategic goals of an organization (Bouteiller and Karyotis 2010).

In the method described by Kaplan and Norton (2004), a firm initiates the most important processes and determines human, information and organizational capital necessary for these processes (Rodionov et al. 2018b).

Del Giudice and Paola (2017) consider intangible assets and intellectual property from the perspective of the fact that they ensure competitiveness, prosperity and growth of the enterprise.

Based on the literature review it can be concluded that the issues concerning the impact created by intangible assets on economic security of companies have not been extensively studied to date. Moreover, not enough attention is paid to economic security on the basis of intangible assets.

According to the data presented in the survey conducted by Brand Finance GIFT, the Top 100 Companies by Total Intangible Value, among 100 large companies, more than 50 have intangible assets exceeding 90% of the value of the entire business. Examples of these companies are Johnson & Johnson, Visa Inc., The Procter & Gamble Co., Anheuser-Busch InBev., Comcast Corp., Mastercard Inc., Novartis AG, Amazon.com Inc., and Microsoft Corp. (Brand Finance 2019). Thus, many business entities carry out their activities only because they have trademarks, patents, new technologies, intangible assets and intellectual property (Chernogorsky 2018).

Accordingly, new R&D, advanced technologies and know-how are becoming more and more actively involved in business processes, which increases the importance of intellectual property and intangible assets, so determining economic security in this field is becoming increasingly important. At the same time, it was observed that to date no algorithm has been developed for determining the economic security of a business based on valuation of intangible assets in accordance with the IVS.

At present, there are many different approaches that are based on the assessment of individual components of the security of a company's activities.

In addition, it should be noted that the presented approaches do not have a structured methodology. Some proposed methods have the following disadvantages:


Accordingly, a distinctive feature of this study is the special attention paid to intangible assets and intellectual property and their impact on the economic security of companies.

#### **3. Models and Methods**

In the course of the study, we identified the parameters that could be used to judge the factors that affect the value and economic security of business entities.

The indicators of companies that are not interdependent act as factor characteristics, X. These characteristics include revenue, intangible assets, intellectual property, fixed assets, assets under construction, financial investments, current assets and long-term and short-term liabilities.

Capitalization or the value of business entities (the resulting characteristic, Y) is understood as the product of the market value of one company's share (share price) and the number of shares in circulation.

The imbedded Excel package "Data Analysis" and statistics data analysis package "Stata" were used for modeling.

In the course of the study it was established that there is a ratio between the resulting indicator and variables. Its direction was defined, as well as the correlation ratio and adequacy of the model obtained, which implies the degree to which the theoretical model that was built to describe the relationship between the characteristics reflects the actual dependence between these characteristics, i.e., whether the model is practically admissible.

In order to check the presence of heteroscedasticity of random errors in the regression model obtained according to the initial values of the characteristics in logarithmic form, the White test was used. The test is based on checking a time series for heteroscedasticity.

An important accompanying problem is to verify the causal link between the time series of the factor and resulting characteristic, which was settled using the Granger causality test. The test can be used to answer the question: Is it true that change in the value of intangible assets and intellectual property (*X*) will entail change in the company capitalization (*Y*)? It was checked using a linear regression model of *Y* values on previous *X* and *Y* values.

In other words, *Y* values are presented in the following form:

$$Y\_i = u\_i + \sum a\_k y\_{i-k} + \sum b\_k x\_{i-k} + E\_i \tag{1}$$

*Yi* is the value of variable *Y* at time *i*;

*Xi* is the value of variable *X* at time *i*;

*k* is the time delay (in our case, a lag).

If in the regression obtained coefficients *k* of the formula can be neglected, it is believed that the previous *X* values do not help to predict *Y* and, consequently, *X* is not the cause of *Y* according to the Granger causality test.

Based on the model obtained, an algorithm determining the economic security of businesses was suggested. The uniqueness of the algorithm is in the fact that it unites all the basic functions of intangible assets and intellectual property that provide economic security. In addition, the algorithm is versatile and can be used by companies operating in different industries.

#### **4. Data**

The largest companies were chosen as objects of the research, since they are clearly indicative representatives of the oil industry among Russian companies whose shares are listed on the stock market and that represent 90% of the market in the sector.

The analytical data posted on the official websites of Russian organizations formed the information basis for the research. The financial and economic indicators of the Russian companies whose shares are listed on the OJSC Moscow Stock Exchange and the Russian Trading System (RTS) were the empirical basis of the research.

In addition, the totality of indicators was determined from the existing indicators of the financial statements of the business entities over the last seven years for each company operating in the oil sector.

#### **5. Results**

The results of the calculations and the regression model built for the oil industry are presented below.

#### *5.1. Adequacy Analysis of the Calculated Research Results*

The indicators of companies, which are not interdependent among themselves, are used as factor signs "*x*". These features are revenue, intangible assets, intellectual property, fixed assets, construction in progress, financial investments, current assets and long-term and short-term liabilities. By capitalization or the value of business entities (resultant attribute "*Y*") we mean the market value of one share of the company (share price) per the number of shares in circulation. Data from financial statements for the last five years were used for calculations. For this study, annual data were used.

The tightness of the relationship between linearly dependent features was determined using a linear correlation coefficient (r), the calculation of which is automated using statistical data analysis packages. The linear model of pair regression between the value of intangible assets and company capitalization has the following form:

$$\begin{aligned} \text{Y} &= -1.946987 \text{x}\_1 + 307.4673 \text{x}\_2 - 0.4629237 \text{x}\_3 - 2.445406 \text{x}\_4 - 0.4796452 \text{x}\_5 \\ &+ 6.288961 \text{x}\_6 - 0.1429317 \text{x}\_7 - 103000000 \end{aligned} \tag{2}$$

The regression coefficient under *x* shows that if the value of intangible assets and intellectual property increases, the market capitalization of the company increases too. Input data for the computational model are presented in Appendix A.

The model was checked for adequacy. The results presented in the Tables 1–4.

**Table 1.** Regression analysis data of the relationship between the value of intangible assets (*x*2) and the capitalization of Russian companies.


Thus, the result of 0.004 means that the hypothesis is confirmed as the result was less than 0.134.

**Table 2.** Regression analysis data of the relationship between the value of intangible assets and the capitalization of Russian companies.


Since the significance level ap (*p*-value), calculated for coefficients a0 and a1 is lower than the set significance level a = 0.01, both these coefficients are recognized as non-random (i.e., typical for the general population).

The value of the determination index R2 (R-squared in the table) is equally 0.9971. This value is over 0.5, which is evidence of the good approximation of the source (actual) data using the built linear function of relation.

**Table 3.** The regression output *p*-value of each variable.


The adequacy of the regression model to the actual data was also established by Fisher's ratio test, which evaluates the statistical significance (non-randomness) of the determination index as typical, so the linear model of relation between characteristics X and Y is to a greater degree applicable to the general population of enterprises as a whole. Then, a heteroscedasticity test was used. The presence of heteroscedasticity leads to the following negative effects: the estimations of the standard errors of regression coefficients are displaced, the estimations of regression coefficients using the method of least squares are ineffective and *t*-statistics of regression coefficients are inadequate.


**Table 4.** The results of the heteroscedasticity test.

As a result of the test, it was revealed that in the majority of cases heteroscedasticity is satisfactory, so general statistical methods can be used.

According to the results of the test, it was concluded that the *p*-value is higher than the significance level chosen as 5% (0.3336 > 0.05), so hypothesis zero about the lack of heteroscedasticity was not rejected, i.e., the random disturbance dispersion does not depend on X and the regression model (3) detailed above is homoscedastic. This proves the adequacy of the statistical valuations of the quality of the linear regression model. Calculations were made according to the Granger test for the period from 2013 to 2019 with the time lag being 1.

To study the directions of the causal relationships between the intangible assets and capitalization, the Granger test was used, where *x*1 is the intangible assets of the company. If it is > 0.05, it cannot be claimed that the hypothesis "A is NOT the Granger cause of B" is true. Thus, capitalization is dependent on intangible assets, since the coefficient is 0.224 and 0.997.

Typically, the Granger test tests two null hypotheses: "*x* is not the cause of y by Granger" and "(Y is not the cause of *X* by Granger". The p-values are small, so we accept the hypothesis that X1 is the Granger cause of Y1. Further, when the situation is reversed, p-values are greater than 0.05; therefore, we reject the hypothesis that Y1 is the Granger cause for X1.

According to the above information it can be concluded that despite industry specific features, which affect the quantitative values of intangible assets and intellectual property, the value of business entities and their level of economic security are affected.

#### *5.2. Algorithm to Determine Economic Security of a Business Based on Valuation of Intangible Assets According to the IVS*

According to the results of the study, an algorithm was developed to determine the economic security of businesses. This algorithm is based on a multi-stage comprehensive analysis of intangible assets and intellectual property.

As an example, one of the large oil companies represented on the Russian market was considered. At the first stage the company performance was preliminarily analyzed considering the specifics of the sector where it operates. The performance analysis was carried out on the example of the Neft Y company, for which indicators for the period 2017–2019 were analyzed. The main indicators of the financial status and performance of Neft Y were selected and grouped according to the qualitative characteristics in the period analyzed.

The company performance is defined by the following indicators:

• The net assets exceed the equity capital, and an increase in the net assets was observed during the analyzed period;


Based on the above analysis, it can be concluded that positive dynamics of the main indicators (revenue, net profit) are observed in the performance of Neft Y. The company actively involves intangible assets in its operations.

At the second stage, more profound analysis of the indicators was carried out.

Firstly, in Block 1 we analyzed the existing intangible assets, including the rights for the results of intellectual activity that are not accounted for in books, as well as the efficiency of the intangible assets management system of the business entity. According to the conducted analysis, Neft Y has the following intangible assets: a license for exploration and production of raw hydrocarbons and a patent. Thus, intangible assets are applied in the operations of the company, which allows it to use new technologies and explore deposits for producing raw hydrocarbons.

In Block 2, investments were calculated.

In this block, investments in intangible assets and intellectual property were calculated. The value of intangible assets and intellectual property was calculated according to the IVS to achieve a high quality of calculations along with transparency and reliability. Since Neft Y acquired a new license for exploration and production of raw hydrocarbons, the value of the required investments was estimated, as detailed in Section 5.

In Block 3 the sources of the effect were analyzed.

In order to determine the source of the effect (benefits, profits) from using intangible assets and intellectual property, it is important to carry out a comprehensive study, which represents a legal and engineering study.

The legal study includes defining the title documents based on which the rights for intellectual property are vested.

In the engineering study, the quantitative and qualitative technological and engineering characteristics and parameters of the goods produced due to the presence of intellectual property are established.

When the sources of the effect were analyzed, the following intangible assets were identified for Neft Y: a license for exploration and production of raw hydrocarbons and a patent for a gravel filter. The patent is a title document. The invention is specific to the oil and gas industry and can be used to install gravel filters and to overhaul boreholes. The validity period of the patent is 20 years. Neft Y has a registered trademark, which is not accounted for in books. Thus, the trademark of Neft Y can be accounted for in books according to the market value.

Stage 3.1. Using intangible assets in business activities (calculating the annual income from using them). In this case it is assumed that the business entity is the holder of exclusive rights due to which the business entity has a right to produce unique goods and services.

Stage 3.2. Using intangible assets in commercial turnover, license for intangible assets. According to the license contract, the holder of the exclusive right (licensor) grants the other party (licensee) the right to use the intellectual property. The transfer of non-exclusive rights is another source of income from applying intellectual property.

Neft Y has not made license contracts so far but plans to consider the possibility of granting non-exclusive rights for the use of the patent for the gravel filter.

Stage 3.3. Using intangible assets when exclusive rights belong to three parties. In this case the business entity uses intangible assets in its activities that belong to the right of use of a non-exclusive license. Prior to making a license contract, a feasibility study has to be conducted to make sure it is reasonable to conclude this contract and to adequately calculate the price of the right of use.

Neft Y lacks such contracts, so no analysis was performed at this stage.

Stage 3.4. Using intangible assets as a collateral for attracting investments.

A mandatory condition for collateral is the state registration of the above list of assets. In order to obtain the collateral, the market value of the asset has to be defined. In this case, special attention must be paid to the quality of the valuation report, which will be used as a basis for taking a decision about the collateral. It is the IVS that ensure the quality, transparency, fairness and reliability of the valuation. This is extremely important for taking investment decisions and for the purposes of collateral. The registered trademark and the patent for the gravel filter can be the subject of collateral for the Neft Y company.

Stage 3.5. Using intangible assets to make a payment in the business entity's equity capital.

Exclusive rights for intangible assets can be introduced into the company's equity capital. All intangible assets are introduced into the equity capital of the business entity at market value calculated in the valuation report that is prepared according to the IVS. Increasing the equity capital helps to attract investments for the activities of the company.

In Block 4 the current expenses of the business entity were analyzed.

Stage 4.1. Analysis and calculation of patent taxes to maintain the patent in force.

Stage 4.2. Tax analysis and calculation.

Periodic (current) payments for the use of rights for the results of intellectual activity and rights for individualization means (in particular, the rights emerging from patents for inventions, useful models, industrial samples) are included in the composition of the company's expenses. Thus, due to an increase in expenses, the size of the profit tax goes down.

In addition to the income obtained by business entities due to intangible assets, it is reasonable to account for the tax benefits for the rights holder.

Tax benefits include reduction in the amounts of taxes and an effective increase in the cash flow of the business entity. For some objectives of valuation, such as financial statements, the tax benefit from depreciation should be included in the valuation when applying the income approach to intangible assets (International Valuation Standards 2020).

Thus, intangible assets give the company real tax benefits due to depreciation, which is in many tax jurisdictions. The calculation of results are presented in the Table 5.


**Table 5.** The profit tax calculated prior to and after the intangible assets were accounted for and depreciated.

Compiled by the authors.

Thus, the profit tax due to the depreciation of the business entity's intangible assets can be 18,973 thousand rubles lower per year.

Stage 4.3. Analyzing and calculating royalty fees.

The company paying royalty fees to the authors for using intellectual property is one of the most important issues. Royalty fees were not calculated in this study because the company lacks patents wherein the authors have the right to receive royalty fees.

Stage 4.4. Analyzing and calculating payments under license contracts.

Payments under license contracts can be defined by one of the following options: royalties (payments represent a percentage of the licensee's revenue from the products sold), a lump sum payment (a single payment, which represents a fixed amount) and a combined payment (part of the amount is paid in one installment, and the second part represents payments in form of royalties).

Stage 4.5. Expenses related to risks in the sphere of intellectual rights (legal expenses).

Legal expenses in the sphere of patent disputes can amount to substantial costs that business entities bear in case of litigation. These expenses arise if legal disputes are dealt with.

Stage 4.6. Expenses related to loan payments in case intangible assets are used as collateral.

In this case, expenses related to payment interest on loans arise only if the business entity has a loan and occur according to the terms of the contract.

In Block 5 the value of the effect was calculated.

The effect from intangible assets and intellectual property can be expressed in the ways described below.

Stage 5.1. Calculating the market value of intangible assets. The market value of the asset is determined according to the IVS. The calculation of the market value of the license for production of raw hydrocarbons is presented as an example in Section 6 and Table 7.

Stage 5.2. Calculating the profits from using intangible assets and intellectual property.

Earnings from the use of intangible assets and intellectual property can be formed by regular royalty payments, depreciation deductions of intangible assets, tax benefits and collateral benefits.

Receiving regular royalty fees is possible in case a license contract is made to transfer non-exclusive right of use of the patent for the gravel filter. In case the license contract is concluded, Neft Y can receive annual income amounting to, on average, 1.91% from the earnings formed with the application of the above patent. Thus, if a medium company in the oil and gas sector applies the patent, it can bring the holder of the exclusive ownership rights 612,350 thousand rubles, on average, with the average earnings being 32,103,215 thousand rubles and the average value of the royalty rate being 1.91%.

Below is given the calculation of the amount of license fee for use of the patent for one year Table 6.


**Table 6.** The calculated royalty rate (annual payment).

Compiled by the authors.

#### **6. Valuation of Intangible Assets According to the IVS**

In order to implement the algorithm determining the economic security of a business at the investment stage, it is necessary to appraise the investments required for acquiring or creating intellectual property and intangible assets.

The market value of the intellectual property and intangible assets is determined according to the IVS. The IVS are key guidelines for carrying out qualitative valuation all over the world. Applying the IVS gives us a high quality, reliable assessment which is internationally recognized (IVSC 2020).

The market value of the license for the right to produce raw hydrocarbons for Neft Y based on IVS 210 Intangible Assets (IVS 210 Intangible Assets) was calculated using a comparative approach.

According to the IVS, corrections were introduced into the calculations to reflect the specific features of the intangible assets that were evaluated. The method of comparative transactions was used in terms of the comparative approach according to IVS 210 (IVS 210).

In order to estimate the interest discount of Urals oil price to Brent oil price on the markets of Western Europe and the USA, the average level of oil prices for the period 2012 through 2018 was used. The average value according to agency Platts was 1.2%. The average oil prices were according to the source https://ru.investing.com.

The average value of the specific indicator of the resource value (price of the license/recoverable resources) was calculated based on the results of the tenders and auctions for obtaining licenses for exploration and production of raw hydrocarbons (www.torgi.gov.ru). The average Urals oil price on the world market as of the tender/auction date was used in the calculations.

After the calculations were made, the corrected value of the stock was 85.957 rub./t. The calculation of results are presented in the Table 7.


**Table 7.** The results of the calculated market value of the license.

Source: data of the customer, authors' own calculations.

An algorithm for determining the value of intangible assets according to the IVS is presented above. It was considered on the example of Neft Y and represents a sequence of actions to be taken to determine the value of the license for production of raw hydrocarbons. This structure is part of the algorithm for determining economic security of a business, because intangible assets are one of the major components that provide economic security of economic entities.

#### **7. Discussion and Conclusions**

This study analyzed the impact that the value of intangible assets and intellectual property has on capitalization of companies and their level of economic security, based on calculated values. The study relies on pair correlation relationships between the factor and performance characteristics. The impact of revenue, intangible assets, intellectual property, fixed assets, assets under construction, financial investments, current assets and long-term and short-term liabilities was analyzed.

The calculated results of the study are presented for the example of the oil and gas sector. The effect of intangible assets and intellectual property on the company value and economic security were determined.

An algorithm was developed to determine economic security based on valuation of intangible assets according to the IVS. It includes the entire cycle of the enterprise's use of intangible assets and intellectual property to calculate economic security. The algorithm includes analysis of the business entity's activities, which consists of two stages (preliminary analysis and in-depth analysis of indicators). Five interrelated blocks are presented: 1—analysis of the intangible assets and intellectual property existing in the enterprise; 2—calculation of the investments necessary for intangible assets and intellectual property; 3—analysis of the sources of the effect (possible earnings from the intangible assets and intellectual property are identified as well as the ways they can be used to attract investments in the company and increase the value of the company's assets); 4—possible expenses of the business entity, as well as the possible options for reducing them. This section presents possible benefits in terms of profit tax due to depreciation deductions on the company's intangible assets. Thus, in the presented algorithm, qualitative assessment of the value of intangible assets and intellectual property according to the IVS is the major component revealing the economic security of business entities.

The multiple stages of the suggested algorithm make it versatile and suitable for application by companies that use intangible assets and intellectual property to different extents.

The uniqueness of the presented algorithm is due to the fact that it contains a full set of stages to manage intangible assets and intellectual property within which the values of the assets are defined in accordance with the International Valuation Standards. This is an essential component of the algorithm that determines the economic security of businesses.

The algorithm can be used to evaluate the company's activities in a new way, to prevent risks and use new possibilities related to the application and valuation of intangible assets and intellectual property according to the IVS.

The practical significance of the research is that the results of the study may be used in the operations of modern companies that apply intangible assets and intellectual property in their activities to determine sustainable development and form an effective system for economic security management due to the use of intangible assets.

Further research will involve goodwill accounting and valuation according to the IVS aimed at determining the economic security of companies.

**Author Contributions:** Conceptualization, D.R., O.P.; methodology, D.R., O.P.; software O.P.; validation, O.N., formal analysis, D.R., O.P. and O.N.; investigation, D.R., O.P. and O.N.; data curation and writing–original draft preparation, D.R., O.P. and O.N.; visualization, D.R., O.P.; supervision, D.R., O.P. and O.N.; projectadministration, Dmitrii Rodionov, O.P.; funding acquisition D.R., O.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Academic Excellence Project 5-100 proposed by Peter the Great St. Petersburg Polytechnic University.

**Acknowledgments:** The authors thank everyone who helped to make the research happen.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **Appendix A**

**Table A1.** Research results for the oil and gas industry (annual data, yearly data).



**Table A2.** Research results for the oil and gas industry (annual data, yearly data).

Source of information: Financial statements of companies. Trading results.

**Table A3.** Research results for the oil and gas industry (annual data, yearly data).


**Table A4.** Analysis of indicators of the company (annual data, yearly data).


\* Short-term, or current liabilities, are liabilities that are due within one year or less. They can include payroll expenses, rent, and accounts payable, money owed by a company to its customers.

#### **References**


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## *Article* **Use of Neural Networks to Accommodate Seasonal Fluctuations When Equalizing Time Series for the CZK/RMB Exchange Rate**

#### **Zuzana Rowland 1,\*, George Lazaroiu <sup>2</sup> and Ivana Podhorská <sup>3</sup>**


Received: 18 August 2020; Accepted: 10 October 2020; Published: 22 December 2020

**Abstract:** The global nature of the Czech economy means that quantitative knowledge of the influence of the exchange rate provides useful information for all participants in the international economy. Systematic and academic research show that the issue of estimating the Czech crown/Chinese yuan exchange rate, with consideration for seasonal fluctuations, has yet to be dealt with in detail. The aim of this contribution is to present a methodology based on neural networks that takes into consideration seasonal fluctuations when equalizing time series by using the Czech crown and Chinese yuan as examples. The analysis was conducted using daily information on the Czech crown/Chinese yuan exchange rate over a period of more than nine years. This is the equivalent of 3303 data inputs. Statistica software, version 12 by Dell Inc. was used to process the input data and, subsequently, to generate multi-layer perceptron networks and radial basis function neural networks. Two versions of neural structures were produced for regression purposes, the second of which used seasonal fluctuations as a categorical variable–year, month, day of the month and week—when the value was measured. All the generated and retained networks had the ability to equalize the analyzed time series, although the second variant demonstrated higher efficiency. The results indicate that additional variables help the equalized time series to retain order and precision. Of further interest is the finding that multi-layer perceptron networks are more efficient than radial basis function neural networks.

**Keywords:** time series; prediction; exchange rate; artificial neural networks; radial basis function; multi-layer perceptron; seasonal fluctuations; global economy

#### **1. Introduction**

At the microeconomic level, securing exchange rates has a significant impact on the development of a company´s cost base, profits, and financial viability, whilst on the macroeconomic level, on a country´s balance of trade. Such consequences may be the result of the correct or incorrect use of exchange rates, which is an issue many managers or important politicians will find hard to avoid. In a global economy, despite the current geopolitical and health concerns, exchange rates have a significant impact, particularly on the currencies of small and medium-sized countries, both at the micro- and macroeconomic levels (Vochozka et al. 2020).

Many economists share the view that foreign trade provides the opportunity to expand a country's potential level of consumption. As a result of this growing openness, the global economy is approaching its ideal production capacity curve. Based on the above, it can be argued that foreign trade is a factor that largely affects the stability of economies and economic growth. This is no different for the Czech Republic and the People's Republic of China.

Probably the most important indicator in the international trade environment is the exchange rate, which not only reflects the imports and exports price, but also the currency value. There is no doubt that changeability of exchange rates has a serious impact on the decisions of all entities operating in the international market for goods and services. For this reason, it is essential to set it correctly (Machova and Marecek 2019).

At present, research is focused on the development of methods that are best able to predict exchange rates. Although the scientific literature provides numerous theories and approaches used to estimate exchange rate developments including the factors affecting them, it is very surprising that the issue of seasonal fluctuations in the Czech crown/Chinese yuan exchange rate have not been addressed using artificial intelligence (artificial neural networks).

A number of studies dealing with the topic exist. However, they compare the Chinese yuan with other currencies. Similarly, the Czech crown is compared with those currencies more closely associated with it. This study is therefore unique, with the importance thereof growing with the increasing volume of Chinese investment in the Czech Republic (Foreign Direct Investment 2018–2019) and the growth of the trade balance. The aim of this paper was to present a methodological foundation based on the use of neural networks that takes into consideration the seasonal fluctuations when equalizing time series by using the Czech crown and Chinese yuan as examples.

With regard to the structure of the contribution, the literature review is partially devoted to international trade as a whole, and goes on to describe the results of studies on exchange rates and the prediction thereof using artificial intelligence. The Materials and Methods section includes the calculations for the two sets of neural networks. The results of both experiments are subsequently presented. Furthermore, the discussion provides a comparison of the results of both experiments with each other and also with those of other studies. The paper is concluded with a brief summary of all the important information and puts forward suggestions for further research.

#### **2. Literature Review**

As previously mentioned, according to Vrbka et al. (2019), international trade is considered to be crucial for economic growth, the essence of which consists of the exchange of goods, services, and capital across national borders. Horak and Machova (2019) stated that, in contrast to trade at the domestic level, the implementation of this trade type is a very complex process. On the other hand, Bernard (2004) added that for most countries, international trade plays a key role and represents a significant share of gross domestic product. The author further stated that the existence of foreign trade goes back a very long way, but that its social, political, and economic importance has only grown in recent centuries. Nevertheless, this statement does not change the fact that international trade has always been given due attention and has always been considered as very important. Li et al. (2019) considered international trade as an essential contributor to regional economic development. The authors claimed that those regions experiencing rapid growth in international trade were also those regions developing the most rapidly, as far as the economy is concerned. The issue of exchange rates is also very often discussed in connection with international trade.

Vochozka et al. (2019) stated that the conventional approach to the worldwide economy was based on the fact that exchange rates are seen as the main factor influencing external trade. Since the Czech economy is very closely linked to external trade, a quantitative understanding of the impact of exchange

rates on exports and/or imports represents an essential piece of information for all participants in the field. Hnat and Tlapa (2014) stated that the reasons for the decision by states to open themselves up for international trade differ, depending on the conditions and natural resources of the given country as well as on the differences in consumer habits and tastes.

Cheong et al. (2006) examined, for example, the dynamic relationships between exchange rate uncertainty, international trade, and price competitiveness using the United Kingdom as their example. Results based on the empirical analysis by means of vector autoregressive models (VAR) showed that shocks that stimulate exchange rate volatility have a negative influence on trade volumes and that this negative impact is stronger than the influence on trade price levels.

Budikova et al. (2010) stated that, like most other economic information, exchange rates have certain time dynamics (i.e., they are recorded in the form of time series). There are several possible ways to define time series. Sheikhan et al. (2013) provided a definition of the concept of time series and described them as a sequence of spatially and factually comparable observations that are organized in time. De Baets and Harvey (2018) had a simpler definition; they understood time series as sequences of values of variables arranged in an orderly manner, evenly spaced over time. León-Alvarez et al. (2016) defined time series analysis as a method employing the study of individuals or groups observed at successive moments. These moments represent a particular series of data points presented in chronological order. The author further added that the analysis of time series can also provide us with significant statistics and other essential data characteristics. It can be stated that, without a doubt, forecasting is one of the most important tasks of time series analysis. The reason for this is that with the help of time series prediction, based on previously monitored values, it is possible to predict values for the future. Mai et al. (2018) stated that the analysis and measurement of time series can also be employed primarily for predictions in the future. The author goes on to describe time series as the monitoring of certain data arranged on a time horizon from the past to the present. According to Vochozka and Vrbka (2019), time series provides crucial insights into the entire exchange rate development process. Prediction is considered the most important function of time analysis. The analysis of time series is a field in which neural networks are widely used. Horak (2019) saw their advantage in the fact that in terms of prediction, neural networks worked with big data, therefore guaranteeing a relatively high level of accuracy; neural networks, together with time series, can be used for solving complex problems and predictions. It is, of course, possible to use standard structural exchange rate models or autoregressive conditionally heteroscedasticity (ARCH) and generalized autoregressive conditionally heteroscedasticity (GARCH) models and mutations thereof. These models focus on the assumption of heteroscedasticity. In essence, they form a systematic framework for volatility modeling. Theoretically, they can be employed very successfully to measure the development of and predict the price of exchange rates that meet the above-stated assumptions, as evidenced by Petrica and Stancu (2017), Quaicoe et al. (2015), You and Liu (2020), and Smallwood (2019). However, neural networks are a very suitable alternative that produce very interesting results, and of which the potential has not yet been fully exploited. An artificial neural network is a topological arrangement of individual neurons in a structure with the help of oriented evaluated connections. Each network is therefore characterized by the type of neuron, their topological arrangement, and the strategy of adaptation during network training (Alonso-Monsalve et al. 2020). The great advantage of neural networks is their profitability, whereby the main advantage lies in the ability to learn and capture hidden, even strongly non-linear dependencies. Based on the learned experience, they then estimate a new result (Henriquez and Kristjanpoller 2019). They are able to work with inaccurate data and noise. The principle of neural networks has now been implemented in various fields of human activity and in some analytical and decision-making software products, producing very good results (Parot et al. 2019).

For example, Laily et al. (2018) compared ARCH and GARCH models with the Elman recurrent neural network (ERNN) when analyzing stock prices. They found that the most suitable model in this

case was GARCH, which had the smallest mean squared error (MSE). Ortiz Arango (2017), in turn, used GARCH models and neural network differentials (RND) to predict the future prices of financial assets, specifically the future development of the price of a barrel of oil. He found that neural networks produce better results than the basic GARCH model and are therefore a reliable alternative method for time series analysis. Lu et al. (2016), who predicted the volatility of log-returns in the Chinese energy market using the GARCH model and neural networks, also confirm the better predictive ability of neural networks. Similarly, Arneric et al. (2014), who examined the development of the Croatia stock market (CROBEX) or Mohamed (2013) index price by comparing GARCH models and neural networks for modeling financial returns in the market in the Arab Republic of Egypt, confirmed the better predictive power of neural networks in relation to GARCH models. Due to the findings from these studies, neural networks will be applied in this contribution for exchange rate prediction.

The application of NN (neural networks) for predicting and trading the EUR/USD exchange rate is described by Dunis et al. (2011). Dhamija and Bhalla (2011) found that NNs can be effectively used for forecasting exchange rates and therefore also for business strategy proposals. Guresen et al. (2011) also argued that exchange rate forecasting is an important financial issue, one that is receiving an ever-increasing amount of attention. Over the last few years, a number of neural network models and hybrid models have been put forward to exceed traditional prediction results in an effort to surpass traditional linear and non-linear approaches. Guresen et al. (2011) assessed the effectiveness of neural network models, which are known to be dynamic and effective in financial market forecasting. The analyzed models were multi-layer perceptrons (MLP), dynamic artificial neural networks (DAN2), and hybrid neural networks that use generalized autoregressive conditional heteroscedasticity (GARCH) to extract new input variables.

Sindelarova (2012) also dealt with the application of artificial neural networks (ANN) for the prediction of economic time series. First, she focused on the revision of the basic existing ANN architectures for predicting time series and described their application in predicting the CZK/EUR exchange rate. She also presented a hybrid version of ANN, as did Bielecki et al. (2008), which was based on the same network strategy, but tried to increase the prediction accuracy. The results of the studies are comparisons of the hybrid approach and the accuracy of traditional ANN settings for the CZK/EUR or USD/PLN exchange rates. However, due to the many parameters to be empirically assessed, it is not easy to choose a suitable NN architecture for the prediction of the exchange rate. Researchers frequently do not consider the influence of the neural network parameters on its performance. Zhang and Hu (1998) examined the effect of the number of the input and hidden nodes and the size of the training sample on the performance in and outside the sample. For a detailed examination, the GBP/USD exchange rate (prediction) was used. It was discovered that NNs outclass linear models, especially in the case of a short prediction horizon. Yin and Chen (2016) suggested a method for the application of the exponential generalized autoregressive conditional heteroscedasticity-M (EGARCH-M) model in connection with the Elman NN for predicting the return rate of the USD/CNY exchange rate. The EGARCH-M model captured the volatility asymmetry, plus the correlation between the return, and this one was past volatility; Elman's NN was used so that it corresponded with the non-linear character of the return rate. GBP/CNY and USD/CNY exchange rate predictions were carried out by Liu et al. (2011) using predictions by RBF neural networks and GARCH models. CNY rates can be considered as a financial TS (time series) characterized by a high non-linearity and a change of behavior over time (Cai et al. 2012). CNY has grown from a trading currency to an investment currency and currently has the potential to be a worldwide reserve currency. The development of CNY as an international currency might balance the USD dominated system and add to regional and international financial stability (Ma and Mccauley 2011; Zhang and Sato 2012).

Interestingly, the correlation between the exchange rate and stock market performance was approached by Tian and Ma (2010), who used the autoregressive distributed lag model—ARDL's cointegration approach to examine the impact of financial liberalization on the relationship between

the exchange rate and stock market performance in China. They found that there was a cointegration between the Shanghai stock index and the renminbi (RMB) against the US dollar and the Hong Kong dollar from 2005, the year in which the Chinese exchange regime became a flexible, managed floating system. The authors found that the exchange rate and the money supply affected the share price with a positive correlation. They also showed that the increase in the money supply had been largely due to the huge influx of "hot money" from other countries in recent years.

The prediction of exchange rate changes, their link to other macroeconomic phenomena and possible geopolitical impacts have been the subject of an extremely extensive volume of research. For example, Ilzetzki et al. (2019) dealt with exchange rate arrangements and restrictive measures in 194 countries. Ho and Karim (2012) examined the significant relationship between exchange rates, macroeconomic fundamentals, and international trade in a group of Asian countries from 1980 to 2009. According to them, international trade is essential for developing countries for investment purposes and to attract foreign exchange in this liberalized and globalized world. Regression analyses show that market size and the exchange rate play a very important role in promoting international trade. Population growth has significant negative effects on developed countries like Japan and Singapore, but has positive effects on the Philippines. In addition, inflation rates have a negative impact on the Philippines and India, while financial market developments are only marginally significant in overall trade between Singapore and India. The results of the study represent the strategic policy implications for developing and developed Asian countries with regard to the facilitation of international trade and boosting growth.

In this specific field, the first area of research was concerned with the correlation of exchange rates and inflation or business cycles (De Boer et al. 2020). Forbes et al. (2018) used vector autoregressive modelling to reveal the links between the exchange rate and inflation, and Nguyen and Sato (2020) used the same method to detect asymmetries in the Japanese yen. Using an autoregressive approach, Grabowski and Welfe (2020) identified four main determinants of the currency market: inflation, terms of trade, country-specific risks, and the state of the currency market. The correlation of exchange rates and consumer prices with a vector autoregressive model was then examined by Ha et al. (2020). Thee VAR and the ARDL (autoregressive distributed lag) models were used by Chiappini and Lahet (2020) to find the key factors for 24 emerging economies, thereby demonstrating China's fundamental influence on the exchange rates of other Asian countries. The same method was used by Dogru et al. (2019) to analyze the effect of exchange rates on bilateral trade between the United States, Mexico, Canada, and the United Kingdom. Ponomareva et al. (2019) used time series regression for predicting the exchange rates of the US dollar, Japanese yen, British pound, and euro as well as the Australian and Canadian dollars. When using the baltic dry index to predict the exchange rates, Han et al. (2020) employed the method of time series. The use of other analytical methods is rather an exception. Behavioral equilibrium models used by Kharrat et al. (2020) are also relatively common as part of optimizing monetary investment strategies.

It is mainly these investment strategies and optimal security that represent the second important area of research. Maggiori et al. (2020) focused on global portfolios and pointed out the difference between companies in the United States and other countries where securities were usually subscribed in foreign currency. Opie and Riddiough (2020) presented a new method for dynamically hedging currency exposure in international equity and bond portfolios using time series. The time series prediction test was also the basis of the spot exchange rate model for 16 currencies according to Narayan et al. (2020)Narayan et al.

Bahmani-Oskooee and Hegerty (2007) provided an insight into history and stated that the increase in exchange rate volatility since 1973 has had indeterminate effects on international export and import flows. Although it can be assumed that an increase in risk may lead to a decrease in economic activity, the theoretical literature provides justification for positive or insignificant effects. Similar results were found in empirical tests. While modeling techniques have evolved over time to incorporate new developments into econometric analysis, no single degree of exchange rate volatility has dominated in the literature.

New patterns in intraday currency trading were revealed by Khademalomoom and Narayan (2020); and a currency trading strategy that took into account the predictive power of currency implied volatility was presented by Ornelas and Mauad (2019) and Accominotti et al. (2019).

Bulut (2018) successfully used Google Trends to predict exchange rates. Amo Baffour et al. (2019) dealt with the integration of an asymmetric model into an artificial neural network for the prediction of the exchange rates of five currencies. According to them, this hybrid solution dramatically increased the quality of the model.

The significant risk of generalization in the search for suitable predictive models was pointed out by Cheung et al. (2019). According to their research, the performance of models varied fundamentally, depending on the length of the prediction.

The effect of influencing the exchange rate in relation to the return on equity within the optimization models was revealed by Turkington and Yazdani (2020). An important topic is also investment in so-called safe-haven currencies, where, for example, Cho et al. (2020) are reducing the importance of the euro, which, according to them, is still one of the currencies that moves in opposition to global stock markets. The treasury-EuroDollar (TED) spread, and country-specific volatility and low liquidity factors were revealed by Maurer et al. (2019) as the two key sources of risk in foreign exchange (FX) markets.

Another area is represented by the use of exchange rates as an indicator of the state of an economy. Augustin et al. (2020) used currency swap spreads for this purpose, and Dahlquist and Hasseltoft (2020) stated the need to include inflation and economic stability in monetary trading strategies. Another important topic is the interconnectedness of exchange rates and commodity prices (Liu et al. 2020). The link between the type of commodities and the exchange rate, or their collapse, was revealed by Bodart and Carpantier (2020), according to whom the impact on agricultural exports was significantly greater compared to the relatively small impact on energy and/or mineral exports. The impact of oil price shocks, especially in the long run, on exchange rates was identified by Huang et al. (2020). Chernov et al. (2018) dealt with the quantification of the risk of currency shocks through an empirical model of bilateral exchange rates. Colacito et al. (2018) also focused on the 10 most traded currencies in the world. They stated their heterogeneity of exposure to trade and currency shocks. A separate chapter of the research concerns the assessment of the effectiveness of monetary unions (Groll and Monacelli 2020), very often with an overlap to crises such as that in Greece (Kriwoluzky et al. 2019). Chari et al. (2020) addressed the performance of economies and the benefits of a single currency. Bonadio et al. (2020) focused on the speed of the impact of an exchange rate shock in Switzerland. Furthermore, the topic of interventions in exchange rates in order to support export potential due to events in global markets is also current. However, as Rajkovi´c et al. (2020) showed in the example of the currencies of the Balkans and Central and Eastern Europe, currency depreciation did not have a significant effect on the trade deficit. Interestingly, Xing (2018) found the complete opposite to be true, with rising wages and the cumulative appreciation of the RMB undermining China's comparative advantage. This was also confirmed by Choi and Choi (2018), who found that the devaluation of the RMB had a direct effect on reducing unemployment. Min and Yang (2019) looked at the problem of debt risks in a currency other than the domestic currency in South Korean companies.

With regard to the RMB, attention must also be paid to the impact of exchange rate changes on economic growth and income distribution. Ribeiro et al. (2020) stated that although low exchange rates lead to increased exports, they have a negative impact on the income of selected groups of the population. In a sample of 2500 pairs, Gopinath et al. (2020) primarily assessed the effect of exchange rates on business elasticity and determined the monetary paradigm. Research on the RMB is extensive, partly as a result of a series of analyses of the impact of the reform of the People's Bank of China, which, according to Wen and Wang (2020), has led to reduced exchange rate volatility. This significant change was also addressed by Smallwood (2019), according to whom, exchange rate uncertainty has no effect on trade with the United

States, or Cheung et al. (2018), who dealt with the impact of these changes on central parity. Liu and Woo (2018) also extensively analyzed the effects of the so-called trade war between these great powers, drawing attention to the rather vague term "equilibrium exchange rate" used by many politicians and economists.

Ho (2020) pointed out the strong effects of virtual currencies and their exchange rates, even in terms of inflation and economic growth for Taiwan and China.

#### **3. Materials and Methods**

The data for the analysis are accessible on the World Bank (2020) website. The information on the mutual exchange rates of the Czech crown (hereinafter referred to as "CZK") and the Chinese yuan (hereinafter referred to as "RMB") were used for the purpose of the analysis (i.e., the daily exchange rate records of these currencies). The time period began on 6 October 2009 and closed on 21 October 2018, which was the equivalent of 3303 data inputs. The unit was several CZK to one RMB.

The descriptive characteristics of the dataset are presented in Table 1.


**Table 1.** Characteristics of the dataset.

Source: Own research.

Statistica software, version 12, by Dell Inc. was used for the data processing. Data mining, neural networks (i.e., automated neural networks (ANS)) were utilized for the computation of the neural structures. A regression was performed using neural structures. Multi-layer perceptron networks (MLP) and radial basis function (RBF) NNs were then generated. The MLP network has one or more hidden layers between the input and output layers, with the neurons arranged in layers, the connections always routed from the lower to higher layers, and with no interconnection between neurons in the same layer (see Figure 1) (Ramchoun et al. 2017).

The RBF network in its simplest form is a three-layer forward neural network. The first layer corresponds to the inputs to the network, the second layer is a hidden layer consisting of a series of non-linear activation RBF units, and the last layer corresponds to the final output of the network. Activation functions in RBF are conventionally implemented as Gaussian functions (see Figure 2).

Two sets of new neural networks were generated:

1. The self-sufficient variable was time and the dependent variable was defined as the CZK/RMB exchange rate.

2. Time was an independent variable. The seasonal variable was characterized by a categorical variable represented by year, month, day of month, and day of week, in which the value was measured for each variable independently. The purpose was to work with the potential daily, monthly, and annual seasonal fluctuations in time series. The dependent variable was the CZK/RMB exchange rate.

What follows next is the analogical work with the datasets. The time series was divided into three datasets (i.e., training, testing, and validation). The first dataset included 70% of the input data. The neural structures were created on the basis of the training set. Each of the two remaining datasets included 15% of the input data, respectively. Both of these datasets served to verify the reliability of the discovered neural structure (i.e., the discovered model). The time series delay was 1. In total, 100,000 neural networks were created, of which the five with the best traits were retained. The hidden layer contained at least two neurons and at most 50 neurons. For the radial basis function, the hidden layer contained at least 21 neurons and at most 30 neurons. The following distribution functions were considered for a multiple perceptron network in the hidden and output layers: Atanh, exponential, linear, logistic, and sinus. The performance of the individual datasets was defined in the form of a correlation coefficient. There were, of course, other performance measures such as root mean square error (RMSE), the mean absolute percentage error (MAPE), mean absolute bias error (MABE), and coefficient of determination (R2). The root mean square error (RMSE) is the square root of the mean square error (MSE). RMSE measures the differences between the values predicted by the hypothetical model and the observed values. In other words, it measures the quality of the fit between the actual data and the predicted model. Similarly, MAPE is a simple average of absolute percentage errors, a formula used to calculate an error in a statistical forecast that measures the magnitude of a predicted error. The coefficient of determination, R2, is a useful measure of the total value of the predictor variable(s) when predicting the resulting variable in a linear regression setting (Salkind 2010).

**Figure 1.** MLP network structure (Source: Khalafi and Mirvakili 2011).

**Figure 2.** RBF network structure (Source: Faris et al. 2017).

The other settings remained in the default (as for ANS—automated neural networks). Finally, the results of both retained sets of neural networks were compared.

#### **4. Results**

#### *4.1. Neural Structure A*

A total of 100,000 NNs were generated in the course of the above-defined procedure. The five that displayed the best parameters were retained and are presented in Table 2.


**Table 2.** Retained neural networks.

Source: Own research; according to Machova and Marecek (2019).

All were radial basis function NNs with only one variable in the input layer (i.e., time). The NNs contained from 25 to 30 neurons in the hidden layer. There was a solo neuron and a solo output variable (i.e., the CZK/RMB exchange rate) in the output layer. The RBFT (redundant byzantine fault tolerance) training algorithm was applied to all the networks. The hidden layer of neurons of all the neural networks was activated by the same function (i.e., the Gaussian curve). Likewise, the external layers of neurons used the same function for the purpose of activation (see Table 2). The search was for a network that performed equally well across all the datasets (note: the data distribution across the datasets took place randomly), while the error should be the smallest possible. The performance of the individual datasets was represented by a correlation coefficient. The values for the individual datasets for the retained NNs are presented in Table 2.

The figures revealed that the performance of all the retained neural networks reached approximately the same results. The unimportant differences had no impact on the performance of the respective networks. The values of the correlation coefficients for all the training datasets was below 0.983. The values of the correlation coefficients for the testing datasets were very similar to the training datasets (i.e., always above 0.983) and was above 0.984 for the validation datasets. Note that the error for all the datasets was slightly above 0.002. The error differences for the equalized time series were almost insignificant for the datasets. A more detailed analysis is required to determine the most appropriate neural network. Table 3 provides an overview of the basic statistical characteristics of the individual datasets for the five retained neural networks.

Under ideal circumstances, the statistical characteristics of the neural networks should comply, in an interspace manner, in all the sets of a certain neural structure (i.e., minima, maxima, residuals, etc.). In the case of the retained neural networks, the differences between the equalized time series were minimal, both in terms of absolute values and residuals. It is therefore not clear which of the retained NNs generated the most suitable results. Therefore, all the neural networks seem to be applicable in practice.


**Table 3.** Statistical characteristics of the individual datasets according to the retained neural network.

Source: Machova and Marecek (2019).

Figure 3 is a line graph that shows the actual development of the CZK/RMB exchange rate at the individual intervals in a slightly different manner. The x-axis (case number) shows information about the input data (i.e., about the time series (marked by numbers due to the software settings)), whilst the y-axis shows the value of the CZK/RMB exchange rate. The blue line indicates the actual development of the exchange rate, and the other colors show the predictions according to the individually generated and retained networks (as presented in Table 2). The close similarity of the predictions of the individual networks is not important, but rather the extent of compliance to the actual development of the exchange rate. Within this context, it can be concluded that all the undistributed neural networks are seemingly very interesting. On the face of it, the basic directions of the lines, which assess the course of the CZK/RMB exchange rate, display the extremes in the development of the actual exchange rate.

**Figure 3.** Actual and predicted (according to retained neural networks) development of CZK/RMB exchange rate during the monitored period (Source: Own research; according to Machova and Marecek 2019).

Given that the network structure (as depicted in Figure 1) contains 3303 items of data on the CZK/RMB exchange rate, this may seem unclear. It is therefore appropriate to present the situation for a selected data interval. Therefore, the line graph in Figure 4 compares the actual development of the CZK/RMB exchange rate for the final 100 days of the monitored period (i.e., from 14 July to 21 October 2018.)

The graph shows that none of the retained neural networks were completely and accurately able to trace the actual course of the CZK/RMB exchange rate during the monitored period. However, it was clear that the 3.RBF 1-25-1 and 5.RBF 1-30-1 networks came the closest to reality. Their predicted values were almost identical to the actual exchange rate at the beginning of the monitored period, with more significant differences showing at the end of the monitored period. The difference in both cases was about CZK 0.08 to one RMB. Even the least accurate network, namely 2.RBF 1-26-1, differed from the actual figures for the exchange rate by less than CZK 0.011. An examination of the residuals therefore seems appropriate. The development of the residuals during the period from 14 July to 21 October 2018 is presented in Figure 5.

**Figure 5.** Development of residuals for the equalized time series during the period from 14 July to 21 October (Source: Own research; according to Machova and Marecek 2019).

The graph shows that, with exception of the 5.RBF 1-30-1 network, the aggregate of the residuals for all the neural networks during the monitored period was almost zero. The residuals achieved quite high positive values in this period. To illustrate this, Table 4 shows the aggregate of the residuals for the equalized time series.



Under ideal circumstances, if we ignore the residual fluctuations for the individual cases during the monitored period, the absolute value of the aggregates of the residuals will total zero. The absolute value of the aggregate of the residuals of the second neural network (2.RBF 1-29-1), which was nearly −1.026, was the closest to zero. In contrast, the 3.RBF 1-30-1 and 5.RBF 1-26-1 networks produced the highest aggregate of residuals in absolute terms, with values above 3. However, it is necessary to point out that this value is minimal in relation to the 3303 measurements. It is therefore possible to state that the most accomplished neural networks were 3.RBF 1-25-1 and 5.RBF 1-30-1.

#### *4.2. Neural Structure B*

A total of 100,000 NNs were generated on the basis of the defined procedure. The five that displayed the best parameters were retained and are presented in Table 5.


**Table 5.** Retained neural networks.

Source: Own research.

All were multi-layer perceptron neural networks. There were four variables (i.e., time, year, day of month, day of week, in the input layer). Time was represented by one neuron in the input layer, a year by 10 neurons, a month by 12 neurons, a weekday by 7 neurons, and a day of the month by 31 neurons, respectively. The total (i.e., 61 neurons) formed the input layer of the generated and retained neural networks. The neural networks contained either 10 or 11 neurons in the hidden layer. Consequently, there was a single neuron and a single output variable, which was the CZK/RMB exchange rate, in the output layer. The Quasi-Newton training algorithm was applied to all the networks. All the neural networks used either the hyperbolic tangent or logistic functions for the purpose of the activation of the neural hidden layer. For the activation of the neural output layer, the retained neural networks used the hyperbolic tangent, exponential, and identity functions (see Table 5).

The search was for a network that performed equally well across all the datasets (note: the data distribution across the datasets took place randomly), while the error should be the smallest possible.

The performance of the individual sets was represented by a correlation coefficient. The values for the individual datasets for the retained NNs are presented in Table 5.

The table shows that the performance of all the retained neural networks was approximately the same. The insignificant differences bear no influence on the performance of the individual networks. The values of the correlation coefficients for all the training datasets significantly exceeded 0.998. The values of the correlation coefficients for the testing datasets exceeded 0.997, and for the validation datasets, they significantly exceeded 0.997. Note that the error for all the datasets fell within the interval >0.0001 to <0.0005. The error differences for the equalized time series were completely insignificant for the individual datasets.

A more detailed analysis is required to determine the most appropriate neural network. Table 6 provides an overview of the basic statistical characteristics of the individual datasets for the five retained neural networks.


**Table 6.** Statistical characteristics of individual datasets according to the retained neural network.

Source: Own research.

In the case of the retained neural structures, the differences over the equalized time series were minimal, both in terms of absolute values and residuals. It is therefore not clear which of the retained NNs generated the most suitable results. All the neural networks therefore seem to be applicable in practice.

Figure 6 is a line graph, which shows the actual development of the CZK/RMB exchange rate and the development of predictions with the help of the individually generated and retained networks (i.e., the equalized time series). The graph clearly shows that all the neural structures predicted the development of the CZK/RMB exchange rate almost identically. Furthermore, the course of the equalized time series was very similar to the actual course of the CZK/RMB exchange rate.

Taking into consideration that the graph illustrated in Figure 6 contains 3303 items of data on the CZK/RMB exchange rate, it may seem confusing. For this reason, it is suitable to present the situation for a selected data interval. The line graph in Figure 7 therefore compares the actual development of the CZK/RMB exchange rate for the final 100 days of the monitored period (i.e., from 14 July to 21 October 2018).

**Figure 6.** Actual and predicted (according to retained neural networks) development of the CZK/RMB exchange rate during the monitored period (Source: Own research).

**Figure 7.** Actual and predicted (according to retained neural networks) development of the CZK/RMB exchange rate for the period from 14 July to 21 October 2018 (Source: Own research).

The graph clearly shows that all the neural structures were able to copy the CZK/RMB exchange rate quite well. The maximum difference across the interval was CZK 0.05. The biggest difference could be found within the period from 9/26/2018 to 10/1/2018, when the difference was still less than CZK 0.1. It is therefore possible to state on the mere basis of the graphic comparison that all the retained neural structures are usable for predictive purposes. An examination of the residuals therefore seems appropriate and interesting. The development of the residuals during the period from 14 July to 21 October is presented in Figure 8.

**Figure 8.** Development of residuals for the equalized time series during the period from 14 July to 21 October (Source: Own research).

The graph clearly shows that the aggregate of the residuals for all neural networks during the monitored period verged on zero. To illustrate this, Table 7 shows the aggregate of the residuals for the equalized time series.


**Table 7.** Aggregate of the residuals for the individual equalized time series.

The aggregate of the residuals for the fifth neural structure, namely 2.MLP 61-11-1, was closest to the value zero (i.e., 0.12). In contrast, the neural network with the highest value for the aggregate of the residuals (0.738) was 4.MLP 61-11-1 where the differences were absolutely minimal. It is therefore possible to conclude that all the retained neural structures are able to equalize the time series for the CZK/RMB exchange rate in a very reliable manner and are usable for the prediction of the development of the exchange rate.

#### **5. Discussion**

All the generated and retained ANNs were able to balance the examined time series (i.e., the CZK/RMB exchange rate). A comparison of the correlation coefficients clearly showed (see tables 2 and 5) that alternative B (i.e., the retained MLP neural networks, which include the use of additional categorical variables) was more efficient. This is reflected in tables 3 and 6 with regard to the evaluation of the basic statistical characteristics for predictions or equalized time series. The retained MLP neural networks (i.e., their equalized time series) generated smaller mutual differences in the training, testing, and validation datasets than the retained RBF neural networks (i.e., without an additional variable). This was confirmed in Figures 3–8. It is very clear that only the retained MLP neural networks under neural structure B were able to describe the time series according to their actual course (for more details see Figure 9).

**Figure 9.** Comparison of selected neural networks for equalized time series for thee CZK/RMB exchange rate during the period from 14 July to 21 October 2018 (Source: Own research).

A number of other authors have also dealt with the prediction of exchange rates using ANN. Although their findings are interesting, they deal with a partially different application than the one addressed in this contribution.

For example, the goal of Ismail et al. (2018) was to predict the exchange rate of the US dollar expressed in Malaysian ringgit. The exchange rate prediction was performed using two methods, namely artificial neural networks and the autoregressive integrated moving average (ARIMA). To predict the exchange rate, a feed-forward neural network was chosen as the artificial neural structure because this proved to be inherently stable. On the other hand, ARIMA (0,1,1) was chosen as the best model for time series based on the Box–Jenkins method. When comparing the two methods, the authors concluded that, compared to ARIMA, the feed-forward neural network showed better results because it had a smaller mean square error and a root mean square error. The research therefore shows that for predicting the US dollar exchange rate expressed in Malaysian ringgit, the use of a feed-forward neural structure seems to be a more suitable prediction method than the ARIMA time series model (0,1,1). The neural structures highlighted in this contribution also generated very good results. The neural networks faithfully copied the development of the time series and predicted the development of the exchange rate.

Through their research, Jiang and Song (2010) demonstrated the chaotic nature of time series for exchange rates. The authors also calculated the embedding dimension and time series delay, and determined the exchange rate prediction model using the NARX network (non-linear autoregressive model). The authors used the time series for exchange rates to empirically evaluate the proposed approach for mid-period forecasting tasks. The results showed that the proposed approach consistently outperformed standard predictors based on neural networks such as BP (back propagation) or SVM (support vector machine).

It is also worth mentioning Abdullah (2013), who, on the basis of the aforementioned, predicted the MYR/USD (MYR = Malaysian Ringgit) exchange rate. In his study, the author also tested the exchange rate performance using a distance-based fuzzy time series model. MYR/USD exchange rate data were tested according to a prediction model from 11 August 2009 to 15 September 2009. A performance comparison sample was performed between MYR/USD and TWD/USD (TWD = Taiwan New Dollar) datasets. The research results showed that the predictions for MYR/USD were smaller than TWD/USD.

The application of the research presented in this contribution is also interesting. It is clear that the RMB is perceived, mainly due to the strict monetary control of the People's Bank of China (Cheong et al. 2017), as a relatively controversial currency. On the other hand, in the current situation of relatively massive budget deficits and quantitative easing, where Aizenman et al. (2020) already point out the correlation, it is clear that for users of less important currencies (CZK, PLN, HUF, and others), it provides monetary security. Security is therefore not only to be considered through currency pairs with the USD or the EUR, respectively, but also within the framework of risk diversification and partly against the RMB. On one hand, this approach presents risks due to the potential for trade wars between China and the United States (Liu and Woo 2018), but it also presents extraordinary opportunities. As Ding et al. (2020), who analyzed the link between RMB and the price of oil, and Kunze (2019) stated, the controlled exchange rate can act as a stabilizing element, or even as a refining factor for predictions. However, high-quality analytical-predictive tools are absolutely necessary for this approach. This is exactly what has been provided by this study.

#### **6. Conclusions**

The aim of this contribution was to put forward a methodology for how to account for seasonal variations in the process of equalizing time series for the CZK/RMB exchange rate through the use of ANNs. In general, the fulfilment of every forecast is, to a certain degree, determined by the probability

this will occur on its own. When predicting the future development of any variable, there is an attempt to estimate the evolution of this variable on the basis of past data. Even though we are able to integrate the majority of factors that influence the target quantity into a model, there is always an element of simplification involved. It is for this reason that a certain degree of probability that a predicted scenario will take place is always taken into account. This can be considered as a limitation of the research, as can the use of basic types of NNs and the comparison of this method with the results of other suitable alternatives.

This contribution refers to the application of an identical instrument to various initial tasks. Prior to the experiment, the assumption was made that there was no reason to apply categorical variables in order to describe the seasonal fluctuations in the CZK/RMB exchange rate. However, the opposite turned out to be true. Extra variables-in the form of a year, a month, day of month, and day of week–the values of which were determined—brought better order and accuracy into the time series. The development of the CZK/RMB exchange rate can be defined on the basis of any statistical, causal, or easy-to-use methods. In this case, statistical methods were used. However, these only provided us with a potential framework for future development. Within this context, it is also important to consider possible future developments in economic policy and/or the legal environment. At the same time, the personality of the evaluator is of equal importance. Generally speaking, they are economists who correct the price defined by the framework methods and modify them on the basis of casual relations and/or on the basis of their experience and knowledge. Nevertheless, in this case, it seems appropriate to try to make a prediction using neural structure B, which is quite accurate.

The results of the MPL networks were very interesting. The objective of this contribution was therefore fulfilled. Interestingly, in the case of neural structure A, only radial basis function neural networks were retained as the most successful, whereas multi-layer perceptron neural networks were the most successful for neural structure B. What would have been interesting would have been to generate only one type of neural network for a specific situation (i.e., every time in a different manner from the acquired results (for alternative A, an MPL network, and for alternative B, an RBF network)).

In further research, it would also be interesting to compare the performance of neural structures with the performance of other models used for time series predictions such as ARIMA models, assuming the use of identical data. However, this would still require the use of statistical methods, which, once again, only provide a possible framework for exchange rate developments. As a result, it would be desirable to include information on the development of the economic, political, and/or legal environments in the model. Where it is possible to do so and to predict such developments, it will then be possible to project this into the monitored variable accordingly.

**Author Contributions:** Conceptualization, Z.R. and G.L.; Methodology, Z.R.; Software, Z.R.; Validation, G.L.; Formal analysis, I.P.; Investigation, G.L.; Resources, I.P.; Data curation, Z.R. and G.L.; Writing—original draft preparation, Z.R. and G.L.; Writing—review and editing, I.P.; Visualization, Z.R. and I.P.; Supervision, Z.R.; Project administration, Z.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**







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