**3. Data**

#### *3.1. Data Source*

The foreign exchange market (Forex) is a global network of brokers and computers that serves as a place of currency exchange. The market is active from Monday morning in Asia to Friday afternoon in New York and is active 24 h per day.

The most important feature of the Forex market (and very natural) is that the exchange is quoted in pairs in difference to stock markets, where each stokes has its value. It is important to mention that the arbitrage on Forex is possible in a short time scale [52–54]. This induces some bias on the analysis, because the choice of the base currency may influence the results, particularly on the very short time scale. On the other hand, one can distinguish a group of leading currencies, which are the most frequently traded: US dollar, euro, and Japanese yen, which are dominating in the market. The bias resulting from the arbitrage is reduced by PLCS feature—due to the averaging procedure. Moreover, in the present study, the euro, as the leading currency, has been chosen as a central currency and exchange rate time series investigated in this paper.

Within this study, the daily exchange rates registered on the Forex market were analysed. The data set consists of 34 time series with the euro as the base currency. The following exchange rates have been investigated: AR, CZK, AUD, DKK, BGN, EGP, BRL, HKD, CAD, HRK, CHF, HUF, IDR, CNY, ISK, JPY, KRW, MXN, MYR, NAD, NOK, NZD, PHP, PLN, RON, RUB, SEK, SGD, THB, TRY, TWD, UAH, USD, and ZAR. Standard abbreviations are used. The period is from 03.09.1996 until 05.02.2020, i.e., 1000 data points.

Within the considered period, one can distinguish several crises (on a regional and global scale). The crises are playing a special role in the presented analysis, because we can expect highlighting the globalisation processes. To mention the most serious crises within the considered interval: 1997—Asian financial crisis [55], 1998—Russian crisis [56], 1999—Argentine crisis [57], early 2000s recession [58], dot-com bubble [59], 2008 financial crisis [60], 2010 European sovereign debt crisis [61], national governmen<sup>t</sup> debt-crises (Spanish, Greek, Russian, and Turkish), and others. Those crises are discussed in view of the performed analysis results.

#### *3.2. Descriptive Statistics of the Series*

The exchange rate time series were converted into return time series by Equation (2).

$$r\_i(t) = \frac{a\_i(t) - a\_i(t-1)}{a\_i(t-1)}\tag{2}$$

where *ai* denotes the analysed time series.

Table 1 presents the statistical properties of the investigated time series. The mean value of the exchange rate returns of the considered time series was in the interval (−0.629 × <sup>10</sup>−4, 9.087 × <sup>10</sup>−<sup>4</sup>), so the average daily fluctuations are rather small, and they are close to zero. However, the range of observed returns is significant—the lowest noticed return was −0.282, while the greatest was 0.585. The next considered parameter— standard deviation—is particularly important, because it is broadly used as a measure of volatility. When comparing the values of standard deviation and the mean, one can notice that the dispersion is huge. The standard deviation is two orders of magnitude greater than the mean. Another important piece of information is given by skewness analysis. Many of the time series have skewness that is much different from zero, which means that the return distribution is asymmetric. The lowest skewness is observed for CHF exchange rate return, while the highest value is achieved for EGP. The last discussed statistical feature is the result of kurtosis, which is much bigger than one and are leptokurtic for all considered time series. The highest values are observed for EGP, CHF, AR, UAH, IDR, and RUB.


**Table 1.** Statistical properties of the exchange rate returns.

Additionally, the time evolution of the mean return exchange rate is presented in Figure 1. This graph allows for obtaining a general idea of Forex market evolution, particularly to distinguish the periods of instability of the market.

**Figure 1.** The mean value of the exchange rates return of the considered time series.
