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Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications
An Economic Theory with a Formal-Econometric Test of Its Empirical Relevance

Journal Description

Econometrics

Econometrics is an international, peer-reviewed, open access journal on econometric modeling and forecasting, as well as new advances in econometrics theory, and is published quarterly online by MDPI.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, ESCI (Web of Science), EconLit, EconBiz, RePEc, and other databases.
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 29.6 days after submission; acceptance to publication is undertaken in 7.9 days (median values for papers published in this journal in the second half of 2024).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.

Impact Factor: 1.1 (2023); 5-Year Impact Factor: 1.4 (2023)

Imprint Information Journal Flyer Open Access ISSN: 2225-1146

Latest Articles

14 pages, 388 KiB

Open AccessArticle

Generalized Recentered Influence Function Regressions

by Javier Alejo, Antonio Galvao, Julián Martínez-Iriarte and Gabriel Montes-Rojas

Econometrics 2025, 13(2), 19; https://doi.org/10.3390/econometrics13020019 - 18 Apr 2025

This paper suggests a generalization of covariate shifts to study distributional impacts on inequality and distributional measures. It builds on the recentered influence function (RIF) regression method, originally designed for location shifts in covariates, and extends it to general policy interventions, such as [...] Read more.

This paper suggests a generalization of covariate shifts to study distributional impacts on inequality and distributional measures. It builds on the recentered influence function (RIF) regression method, originally designed for location shifts in covariates, and extends it to general policy interventions, such as location–scale or asymmetric interventions. Numerical simulations for the Gini, Theil, and Atkinson indexes demonstrate strong performance across a myriad of cases and distributional measures. An empirical application examining changes in Mincerian equations is presented to illustrate the method. Full article

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12 pages, 261 KiB

Open AccessArticle

Is VIX a Contrarian Indicator? On the Positivity of the Conditional Sharpe Ratio ^†

by Ehud I. Ronn and Liying Xu

Econometrics 2025, 13(2), 18; https://doi.org/10.3390/econometrics13020018 - 14 Apr 2025

The notion of compensation for systematic risk is well ingrained in finance and constitutes the basis for numerous empirical tests. The concept an increase in systematic risk is accompanied by an increase in the required risk premium has strong intuitive content: The more [...] Read more.

The notion of compensation for systematic risk is well ingrained in finance and constitutes the basis for numerous empirical tests. The concept an increase in systematic risk is accompanied by an increase in the required risk premium has strong intuitive content: The more risk there is to be borne, the greater the compensation therefor. In recognizing previous research on the ex ante and ex post reward to risk, the thrust of this paper is to augment those previous tests of expected and realized returns by providing several distinct empirical tests of the proposition the market rewards the undertaking of systematic equity risk, the latter as measured by the VIX volatility index. Thus, in this paper’s empirical section, we use several empirical approaches to answer the question, Using realized returns, is an increase in systematic risk VIX accompanied by an increase in the equity risk premium? While the empirical results are not always statistically significant, our answer is in the affirmative. Full article

36 pages, 670 KiB

Open AccessArticle

Forecasting Asset Returns Using Nelson–Siegel Factors Estimated from the US Yield Curve

by Massimo Guidolin and Serena Ionta

Econometrics 2025, 13(2), 17; https://doi.org/10.3390/econometrics13020017 - 11 Apr 2025

This paper explores the hypothesis that the returns of asset classes can be predicted using common, systematic risk factors represented by the level, slope, and curvature of the US interest rate term structure. These are extracted using the Nelson–Siegel model, which effectively captures [...] Read more.

This paper explores the hypothesis that the returns of asset classes can be predicted using common, systematic risk factors represented by the level, slope, and curvature of the US interest rate term structure. These are extracted using the Nelson–Siegel model, which effectively captures the three dimensions of the yield curve. To forecast the factors, we applied autoregressive (AR) and vector autoregressive (VAR) models. Using their forecasts, we predict the returns of government and corporate bonds, equities, REITs, and commodity futures. Our predictions were compared against two benchmarks: the historical mean, and an AR(1) model based on past returns. We employed the Diebold–Mariano test and the Model Confidence Set procedure to assess the comparative forecast accuracy. We found that Nelson–Siegel factors had significant predictive power for one-month-ahead returns of bonds, equities, and REITs, but not for commodity futures. However, for 6-month and 12-month-ahead forecasts, neither the AR(1) nor VAR(1) models based on Nelson–Siegel factors outperformed the benchmarks. These results suggest that the Nelson–Siegel factors affect the aggregate stochastic discount factor for pricing all assets traded in the US economy. Full article

(This article belongs to the Special Issue Advancements in Macroeconometric Modeling and Time Series Analysis)

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29 pages, 1630 KiB

Open AccessArticle

A Meta-Analysis of Determinants of Success and Failure of Economic Sanctions

by Binyam Afewerk Demena and Peter A. G. van Bergeijk

Econometrics 2025, 13(2), 16; https://doi.org/10.3390/econometrics13020016 - 9 Apr 2025

Political scientists and economists often assert that they understand how economic sanctions function as a foreign policy tool and claim to have backed their theories with compelling statistical evidence. The research puzzle that this article addresses is the observation that despite almost four [...] Read more.

Political scientists and economists often assert that they understand how economic sanctions function as a foreign policy tool and claim to have backed their theories with compelling statistical evidence. The research puzzle that this article addresses is the observation that despite almost four decades of empirical research on economic sanctions, there is still no consensus on the direction and magnitude of the key variables that theoretically determine the success of economic sanctions. To address part of this research puzzle, we conducted a meta-analysis of 37 studies published between 1985 and 2018, focusing on three key determinants of sanction success: trade linkage, prior relations, and duration. Our analysis examines the factors contributing to the variation in findings reported by these primary studies. By constructing up to 27 moderator variables that capture the contexts in which researchers derive their estimates, we found that the differences across studies are primarily influenced by the data used, the variables controlled for in estimation methods, publication quality, and author characteristics. Our results reveal highly significant effects, indicating that sanctions are more likely to succeed when there is strong pre-sanction trade, when sanctions are implemented swiftly, and when they involve countries with better pre-sanction relationships. In our robustness checks, we consistently confirmed these core findings across different estimation techniques. Full article

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20 pages, 2044 KiB

Open AccessArticle

Inference of Impulse Responses via Bayesian Graphical Structural VAR Models

by Daniel Felix Ahelegbey

Econometrics 2025, 13(2), 15; https://doi.org/10.3390/econometrics13020015 - 2 Apr 2025

Impulse response functions (IRFs) are crucial for analyzing the dynamic interactions of macroeconomic variables in vector autoregressive (VAR) models. However, traditional IRF estimation methods often have limitations with assumptions on variable ordering and restrictive identification constraints. This paper applies the Bayesian graphical structural [...] Read more.

Impulse response functions (IRFs) are crucial for analyzing the dynamic interactions of macroeconomic variables in vector autoregressive (VAR) models. However, traditional IRF estimation methods often have limitations with assumptions on variable ordering and restrictive identification constraints. This paper applies the Bayesian graphical structural vector autoregressive (BGSVAR) model, which integrates structural learning to capture both temporal and contemporaneous dependencies for more accurate impulse response estimation. The BGSVAR framework provides a more efficient and interpretable method for estimating IRFs, which can enhance both forecasting performance and structural inferences in economic modelling. Through extensive simulations across various data-generating processes, we evaluate BGSVAR’s effectiveness in modelling dynamic interactions among US macroeconomic variables. Our results demonstrate that BGSVAR outperforms traditional methods, such as LASSO and Bayesian VAR (BVAR), by delivering more precise impulse response estimates and better capturing the structural dynamics of VAR-based models. Full article

(This article belongs to the Special Issue Innovations in Bayesian Econometrics: Theory, Techniques, and Economic Analysis)

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19 pages, 3796 KiB

Open AccessArticle

Modeling and Forecasting Time-Series Data with Multiple Seasonal Periods Using Periodograms

by Solomon Buke Chudo and Gyorgy Terdik

Econometrics 2025, 13(2), 14; https://doi.org/10.3390/econometrics13020014 - 28 Mar 2025

Applications of high-frequency data, including energy management, economics, and finance, frequently require time-series forecasting characterized by complex seasonality. Recognizing prevailing seasonal trends continues to be difficult, given that the majority of solutions depend on basic decomposition techniques. This study introduces a new approach [...] Read more.

Applications of high-frequency data, including energy management, economics, and finance, frequently require time-series forecasting characterized by complex seasonality. Recognizing prevailing seasonal trends continues to be difficult, given that the majority of solutions depend on basic decomposition techniques. This study introduces a new approach employing periodograms from spectral density analysis to identify predominant seasonal periods. When analyzing hourly electricity consumption data from Brazil, we identified three significant seasonal patterns: sub-daily (6 h), half-daily (12 h), and daily (24 h). We assessed the predictive efficacy of the BATS, TBATS, and STL + ETS models using these seasonal periods. We performed data analysis and model fitting in R 4.4.1 and used accuracy metrics like MAE, MAPE, and others to compare the models. The STL + ETS model exhibited an enhanced performance, surpassing both BATS and TBATS in energy forecasting. These findings improve our understanding of multiple seasonal patterns, assist us in selecting dominating periods, provide new practical forecasting approaches for time-series analysis, and inform professionals seeking superior forecasting solutions in various fields. Full article

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25 pages, 513 KiB

Open AccessArticle

Explosive Episodes and Time-Varying Volatility: A New MARMA–GARCH Model Applied to Cryptocurrencies

by Alain Hecq and Daniel Velasquez-Gaviria

Econometrics 2025, 13(2), 13; https://doi.org/10.3390/econometrics13020013 - 24 Mar 2025

Financial assets often exhibit explosive price surges followed by abrupt collapses, alongside persistent volatility clustering. Motivated by these features, we introduce a mixed causal–noncausal invertible–noninvertible autoregressive moving average generalized autoregressive conditional heteroskedasticity (MARMA–GARCH) model. Unlike standard ARMA processes, our model admits roots inside [...] Read more.

Financial assets often exhibit explosive price surges followed by abrupt collapses, alongside persistent volatility clustering. Motivated by these features, we introduce a mixed causal–noncausal invertible–noninvertible autoregressive moving average generalized autoregressive conditional heteroskedasticity (MARMA–GARCH) model. Unlike standard ARMA processes, our model admits roots inside the unit disk, capturing bubble-like episodes and speculative feedback, while the GARCH component explains time-varying volatility. We propose two estimation approaches: (i) Whittle-based frequency-domain methods, which are asymptotically equivalent to Gaussian likelihood under stationarity and finite variance, and (ii) time-domain maximum likelihood, which proves to be more robust to heavy tails and skewness—common in financial returns. To identify causal vs. noncausal structures, we develop a higher-order diagnostics procedure using spectral densities and residual-based tests. Simulation results reveal that overlooking noncausality biases GARCH parameters, downplaying short-run volatility reactions to news (

α

) while overstating volatility persistence (

β

). Our empirical application to Bitcoin and Ethereum enhances these insights: we find significant noncausal dynamics in the mean, paired with pronounced GARCH effects in the variance. Imposing a purely causal ARMA specification leads to systematically misspecified volatility estimates, potentially underestimating market risks. Our results emphasize the importance of relaxing the usual causality and invertibility assumption for assets prone to extreme price movements, ultimately improving risk metrics and expanding our understanding of financial market dynamics. Full article

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20 pages, 345 KiB

Open AccessArticle

Dynamic Interaction Between Microfinance and Household Well-Being: Evidence from the Microcredit Progressive Model for Sustainable Development

by Ahmad Alqatan, Najoua Talbi, Hasan Behbehani, Samira Ben Belgacem, Muhammad Arslan and Wafaa Sbeiti

Econometrics 2025, 13(1), 12; https://doi.org/10.3390/econometrics13010012 - 6 Mar 2025

Microfinance aims to promote financial inclusion among underprivileged individuals, particularly through progressive microcredit, which enables borrowers to access increasing loan amounts over time. This study examines the conditions under which progressive microcredit positively impacts both small business performance and household well-being, considering borrower [...] Read more.

Microfinance aims to promote financial inclusion among underprivileged individuals, particularly through progressive microcredit, which enables borrowers to access increasing loan amounts over time. This study examines the conditions under which progressive microcredit positively impacts both small business performance and household well-being, considering borrower characteristics and business activity conditions. Using a dataset of 278 households across 110 administrative sectors in Tunisia from 2012 to 2020, this study employs two-stage least squares (2SLS) and three-stage least squares (3SLS) econometric techniques to estimate simultaneous equation models. The findings reveal that the cumulative amount of progressive microcredit received is mainly determined by project capital, suggesting that businesses with higher capital requirements tend to secure larger loans over successive cycles. Household well-being is significantly influenced by progressive microcredit, household income, net business benefit, rate of development index, and homeownership. Meanwhile, business profitability is driven by project capital and total fixed assets, highlighting the long-term impact of microcredit. The results highlight the critical role of microfinance in enabling small-scale entrepreneurs to expand their businesses while simultaneously improving household financial security. By promoting sustainable income generation, progressive microcredit serves as a key instrument in poverty alleviation and economic stability. This study underscores the necessity for microfinance institutions (MFIs) to tailor their lending strategies, ensuring optimal loan progression that balances business expansion with financial sustainability. Additionally, policymakers should refine microcredit frameworks to enhance accessibility and long-term economic benefits for low-income borrowers. Overall, these insights contribute to the broader discourse on financial inclusion and sustainable development, emphasizing that progressive microcredit not only facilitates entrepreneurship, but also serves as a driver of socioeconomic mobility. Full article

18 pages, 4617 KiB

Open AccessArticle

Real Option Valuation of an Emerging Renewable Technology Design in Wave Energy Conversion

by James A. DiLellio, John C. Butler, Igor Rizaev, Wanan Sheng and George Aggidis

Econometrics 2025, 13(1), 11; https://doi.org/10.3390/econometrics13010011 - 4 Mar 2025

The untapped potential of wave energy offers another alternative to diversifying renewable energy sources and addressing climate change by reducing CO₂ emissions. However, development costs to mature the technology remain significant hurdles to adoption at scale and the technology often must compete [...] Read more.

The untapped potential of wave energy offers another alternative to diversifying renewable energy sources and addressing climate change by reducing CO₂ emissions. However, development costs to mature the technology remain significant hurdles to adoption at scale and the technology often must compete against other marine energy renewables such as offshore wind. Here, we conduct a real option valuation that includes the uncertain market price of wholesale electricity and managerial flexibility expressed in determining future optimal decisions. We demonstrate the probability that the project’s embedded compound real option value can turn a negative net present value wave energy project to a positive expected value. This change in investment decision uses decision tree analysis, where real options are developed as decision nodes, and models the uncertainty as a risk-neutral stochastic process using chance nodes. We also show how our results are analogous to a financial out-of-the-money call option. Our results highlight the distribution of outcomes and the benefit of a staged long-term investment in wave energy systems to better understand and manage project risk, recognizing that these probabilistic results are subject to the ongoing evolution of wholesale electricity prices and the stochastic process models used here to capture their future dynamics. Lastly, we show that the near-term optimal decision is to continue to fund ongoing development of a reference architecture to a higher technology readiness level to maintain the long-term option to deploy such a renewable energy system through private investment or private–public partnerships. Full article

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17 pages, 1129 KiB

Open AccessArticle

A Study of Economic and Social Preferences in Energy-Saving Behavior Using a Structural Equation Modeling Approach: The Case of Romania

by Cristian Busu, Mihail Busu, Stelian Grasu, Ilona Skačkauskienė and Luis Miguel Fonseca

Econometrics 2025, 13(1), 10; https://doi.org/10.3390/econometrics13010010 - 24 Feb 2025

Examining the energy consumer behavioral model is critical for national governments and academia. This endeavor seeks to uncover effective solutions amid the energy crisis and climate change challenges. This article delves into legislative developments within the energy sector, European Commission recommendations for reducing [...] Read more.

Examining the energy consumer behavioral model is critical for national governments and academia. This endeavor seeks to uncover effective solutions amid the energy crisis and climate change challenges. This article delves into legislative developments within the energy sector, European Commission recommendations for reducing energy consumption, and existing constraints impacting individual consumers. By scrutinizing the relevant literature, we aimed to identify and analyze factors that can enhance individual benefits derived from energy savings. Then, a comprehensive set of variables was formulated to model the final consumers’ behavior. Data collection involved administering questionnaires to individual consumers, consumer associations, and energy micro-enterprises in Romania. The gathered data were meticulously analyzed using the Smart-Pls 4 statistical software. Building upon insights from specialized literature, this paper pinpoints the behavioral determinants influencing the reduction in energy consumption. These determinants serve as independent variables shaping the voluntary adoption of measures in lifestyle and behavior among various types of energy users. This study’s findings validate the assumptions presented in this article, highlighting that a reduction in energy consumption is a direct and intrinsic outcome achieved by cumulatively addressing several factors. These factors encompass investments in the energy sector, budget allocation for energy consumption expenditure, adherence to social behavior norms, access to pertinent information about the consequences of the energy crisis, and individual responsibility. Notably, the perception of energy-saving opportunities emerges as a mediator between the independent variables and energy savings with a significant effect. This aspect, developed for the first time in this article, draws inspiration from the prospect theory introduced by Kahneman and Tversky. Full article

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13 pages, 314 KiB

Open AccessArticle

Investigating Some Issues Relating to Regime Matching

by Anthony D. Hall and Adrian R. Pagan

Econometrics 2025, 13(1), 9; https://doi.org/10.3390/econometrics13010009 - 21 Feb 2025

Markov switching models are a common tool used in many disciplines as well as in Economics, and estimation methods are available in many software packages. Estimated models are commonly used for allocating observations to regimes. This allocation is usually done using a rule [...] Read more.

Markov switching models are a common tool used in many disciplines as well as in Economics, and estimation methods are available in many software packages. Estimated models are commonly used for allocating observations to regimes. This allocation is usually done using a rule based on the estimated smoothed probabilities, such as, in the two regime case, when it exceeds the threshold of 0.5. The accuracy of the regime matching is often measured by the concordance index. Can regime matching be improved by using other rules? By replicating a number of published two-and three- regime studies and the use of simulation methods, it demonstrates that other rules can improve on the performance of the rule based on the threshold of 0.5. Using simulated models we extend the analysis of a single series to investigate, and demonstrate the efficacy of Markov switching models identifying a common factor in multiple time series. Full article

(This article belongs to the Special Issue Advancements in Macroeconometric Modeling and Time Series Analysis)

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36 pages, 2332 KiB

Open AccessArticle

Comparative Analysis of VAR and SVAR Models in Assessing Oil Price Shocks and Exchange Rate Transmission to Consumer Prices in South Africa

by Luyanda Majenge, Sakhile Mpungose and Simiso Msomi

Econometrics 2025, 13(1), 8; https://doi.org/10.3390/econometrics13010008 - 20 Feb 2025

This study compared standard VAR, SVAR with short-run restrictions, and SVAR with long-run restrictions to investigate the effects of oil price shocks and the foreign exchange rate (ZAR/USD) on consumer prices in South Africa after the 2008 financial crisis. The standard VAR model [...] Read more.

This study compared standard VAR, SVAR with short-run restrictions, and SVAR with long-run restrictions to investigate the effects of oil price shocks and the foreign exchange rate (ZAR/USD) on consumer prices in South Africa after the 2008 financial crisis. The standard VAR model revealed that consumer prices responded positively to oil price shocks in the short term, whereas the foreign exchange rate (ZAR/USD) revealed a fluctuating currency over time. That is, the South African rand (ZAR) initially appreciated against the US dollar (USD) in response to oil price shocks (periods 1:7), followed by a depreciation in periods 8:12. Imposing short-run restrictions on the SVAR model revealed that the foreign exchange rate (ZAR/USD) reacted to oil price shocks in a manner similar to the VAR model, with ZAR appreciating during the initial periods (1:7) and subsequently depreciating in the later periods (8:12). Consumer prices responded positively to oil price shocks, causing consumer prices to increase in the short run, which is consistent with the VAR findings. However, imposing long-run restrictions on our SVAR model yielded results that contrasted with those obtained under short-run restrictions and the standard VAR model. That is, oil price shocks had long-lasting effects on the foreign exchange rate, resulting in the depreciation of ZAR relative to USD over time. Additionally, oil price shocks reduced consumer prices, resulting in a deflationary effect in the long run. This study concluded that South Africa’s position as a net oil importer with a floating exchange rate renders the country vulnerable to short-term external shocks. Nonetheless, in the long term, the results indicated that the economy tends to adapt to oil price shocks over time. Full article

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14 pages, 312 KiB

Open AccessArticle

Conditional β-Convergence in APEC Economies, 1960–2020: Empirical Evidence from the Pooled Mean Group Estimator

by César Lenin Navarro-Chávez, Julio César Morán-Figueroa and Francisco Javier Ayvar-Campos

Econometrics 2025, 13(1), 7; https://doi.org/10.3390/econometrics13010007 - 18 Feb 2025

The aim of this research is to analyze the impact of conditional variables—physical capital, population, and Total Factor Productivity (TFP)—on the economic convergence of the member economies of the Asia-Pacific Economic Cooperation (APEC) Forum over the period 1960–2020. This study employs a causal [...] Read more.

The aim of this research is to analyze the impact of conditional variables—physical capital, population, and Total Factor Productivity (TFP)—on the economic convergence of the member economies of the Asia-Pacific Economic Cooperation (APEC) Forum over the period 1960–2020. This study employs a causal and correlational methodological approach, utilizing the pooled mean group (PMG) estimator within a non-experimental design framework for quantitative analysis. This methodology facilitates the estimation of conditional β-convergence, ensuring the statistical significance of estimates even in heterogeneous data panels with variables of integration order I(0) and I(1). The results indicate that physical capital, population growth, and TFP have significantly influenced the growth rates of APEC economies, contributing to economic convergence within the region during the 1960–2020 period. This study offers significant contributions by analyzing the 21 APEC economies over a 60-year period, utilizing a PMG model to estimate conditional β-convergence, and conducting comprehensive evaluations of short- and long-term trends. Consequently, the research recommends implementing policies that prioritize innovation, strengthen capital, create employment opportunities, and enhance productivity to reduce inequalities and foster sustainable growth across APEC economies. Full article

17 pages, 1028 KiB

Open AccessArticle

Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications

by Marcos Escobar-Anel, Sebastian Ferrando, Fuyu Li and Ke Xu

Econometrics 2025, 13(1), 6; https://doi.org/10.3390/econometrics13010006 - 12 Feb 2025

This paper revisits the topic of time-scale parameterizations of the Heston–Nandi GARCH (1,1) model to create a new, theoretically valid setting compatible with real financial data. We first estimate parameters using three US market indices and six frequencies to let data reveal the [...] Read more.

This paper revisits the topic of time-scale parameterizations of the Heston–Nandi GARCH (1,1) model to create a new, theoretically valid setting compatible with real financial data. We first estimate parameters using three US market indices and six frequencies to let data reveal the correct, data-implied, time-scale parameterizations. We compared the data-implied parametrization to two popular candidates in the literature, demonstrating structurally different continuous-time limits, i.e., the data favor fractional Brownian motion (fBM)—instead of the standard Brownian motion (BM)-based parametrization. We then propose a theoretically flexible time-scale parameterization compatible with this fBM behavior. In this context, a fractional derivative analysis of our empirically based parametrization is performed, confirming an anomalous diffusion in the continuous-time limit. Such a finding is yet another endorsement of the recent and popular stylized fact known as rough volatility. Full article

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12 pages, 611 KiB

Open AccessArticle

Application of Fuzzy Discount Factors in Behavioural Decision-Making for Financial Market Modelling

by Joanna Siwek and Patryk Żywica

Econometrics 2025, 13(1), 5; https://doi.org/10.3390/econometrics13010005 - 26 Jan 2025

This paper presents an innovative approach to financial market modelling by integrating fuzzy discount factors into the decision-making process, thereby reflecting the complexities of human behaviour. Traditional financial models often fail to account for market dynamics’ psychological factors. The proposed method utilizes fuzzy [...] Read more.

This paper presents an innovative approach to financial market modelling by integrating fuzzy discount factors into the decision-making process, thereby reflecting the complexities of human behaviour. Traditional financial models often fail to account for market dynamics’ psychological factors. The proposed method utilizes fuzzy logic to encapsulate the uncertainty and subjective judgment inherent in financial decisions. By representing financial variables as fuzzy numbers, the model better simulates the way humans assess information and make decisions under uncertainty. The incorporation of fuzzy discount factors marks a significant shift from deterministic to a more realistic representation of financial markets, suitable for practical application. This methodology offers a nuanced investment strategy that balances theoretical rigour with real-world applicability, appealing to a broad spectrum of investors. The aim of the following paper is to introduce an alternative to price modelling with the use of fuzzy return rates, which results in some errors in the mathematical model. The solution has the form of introducing fuzzy discount factors (FDFs) that retain the advantages of the fuzzy approach (e.g., encompassing subjectivity and imprecision) while preserving the shape of the fuzzy number modelling a price. Full article

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24 pages, 337 KiB

Open AccessArticle

An Economic Theory with a Formal-Econometric Test of Its Empirical Relevance

by Bernt Petter Stigum

Econometrics 2025, 13(1), 4; https://doi.org/10.3390/econometrics13010004 - 16 Jan 2025

The paper contains five parts—a theory about entrepreneurial choice under uncertainty, a formal econometric structure for a test, the test, an appraisal of the test, and a description of the data generating process. Here, an entrepreneur is an individual who manages a firm [...] Read more.

The paper contains five parts—a theory about entrepreneurial choice under uncertainty, a formal econometric structure for a test, the test, an appraisal of the test, and a description of the data generating process. Here, an entrepreneur is an individual who manages a firm that produces one commodity with labor, an intermediate good, and capital. He pays dividends to shareholders, invests in bonds and capital, and has an n-period planning horizon. Conditioned on the values of current-period prices, the entrepreneur aims to maximize the expected value of a utility function that varies with the dividends he pays each period and with his firm’s balance sheet variables at the end of the planning horizon. The test comprises a family of trials of theorems that I derive from the axioms of the theory part of the formal econometric structure. In the test, the theorems are appraised for their empirical relevance in an empirical context, where each one of a random sample of four hundred entrepreneurs has chosen the first-period part of his optimal n-period expenditure plan. My formal econometric arguments demonstrate that the theorems pass all the trials. At the end, I show that my formal econometric results imply that the theory is empirically relevant. Full article

23 pages, 827 KiB

Open AccessArticle

Optimal Time Series Forecasting Through the GARMA Model

by Adel Hassan A. Gadhi, Shelton Peiris, David E. Allen and Richard Hunt

Econometrics 2025, 13(1), 3; https://doi.org/10.3390/econometrics13010003 - 8 Jan 2025

This paper examines the use of machine learning methods in modeling and forecasting time series with long memory through GARMA. By employing rigorous model selection criteria through simulation study, we find that the hybrid GARMA-LSTM model outperforms traditional approaches in forecasting long-memory time [...] Read more.

This paper examines the use of machine learning methods in modeling and forecasting time series with long memory through GARMA. By employing rigorous model selection criteria through simulation study, we find that the hybrid GARMA-LSTM model outperforms traditional approaches in forecasting long-memory time series. This characteristic is confirmed using popular datasets such as sunspot data and Australian beer production data. This approach provides a robust framework for accurate and reliable forecasting in long-memory time series. Additionally, we compare the GARMA-LSTM model with other implemented models, such as GARMA, TBATS, ARIMA, and ANN, highlighting its ability to address both long-memory and non-linear dynamics. Finally, we discuss the representativeness of the datasets selected and the adaptability of the proposed hybrid model to various time series scenarios. Full article

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26 pages, 850 KiB

Open AccessArticle

Forecasting Half-Hourly Electricity Prices Using a Mixed-Frequency Structural VAR Framework

by Gaurav Kapoor, Nuttanan Wichitaksorn, Mengheng Li and Wenjun Zhang

Econometrics 2025, 13(1), 2; https://doi.org/10.3390/econometrics13010002 - 8 Jan 2025

Electricity price forecasting has been a topic of significant interest since the deregulation of electricity markets worldwide. The New Zealand electricity market is run primarily on renewable fuels, and so weather metrics have a significant impact on electricity price and volatility. In this [...] Read more.

Electricity price forecasting has been a topic of significant interest since the deregulation of electricity markets worldwide. The New Zealand electricity market is run primarily on renewable fuels, and so weather metrics have a significant impact on electricity price and volatility. In this paper, we employ a mixed-frequency vector autoregression (MF-VAR) framework where we propose a VAR specification to the reverse unrestricted mixed-data sampling (RU-MIDAS) model, called RU-MIDAS-VAR, to provide point forecasts of half-hourly electricity prices using several weather variables and electricity demand. A key focus of this study is the use of variational Bayes as an estimation technique and its comparison with other well-known Bayesian estimation methods. We separate forecasts for peak and off-peak periods in a day since we are primarily concerned with forecasts for peak periods. Our forecasts, which include peak and off-peak data, show that weather variables and demand as regressors can replicate some key characteristics of electricity prices. We also find the MF-VAR and RU-MIDAS-VAR models achieve similar forecast results. Using the LASSO, adaptive LASSO, and random subspace regression as dimension-reduction and variable selection methods helps to improve forecasts where random subspace methods perform well for large parameter sets while the LASSO significantly improves our forecasting results in all scenarios. Full article

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16 pages, 1296 KiB

Open AccessArticle

Relationship Between Coefficients in Parametric Survival Models for Exponentially Distributed Survival Time—Registered Unemployment in Poland

by Beata Bieszk-Stolorz

Econometrics 2025, 13(1), 1; https://doi.org/10.3390/econometrics13010001 - 2 Jan 2025

Survival analysis is a popular research tool in medicine and demography. It has been used for many years to study the duration of socio-economic phenomena. The aim of this article is to evaluate the relationship between the coefficients of the proportional hazards model [...] Read more.

Survival analysis is a popular research tool in medicine and demography. It has been used for many years to study the duration of socio-economic phenomena. The aim of this article is to evaluate the relationship between the coefficients of the proportional hazards model (PH) and the accelerated failure time model (AFT), assuming an exponential distribution of survival time. The coefficients of the PH and AFT exponential models have the same magnitude but have opposite signs. It follows that there is a symmetric relation between the coefficients. In the case of exponential PH and AFT models, there is a relation of equality between the parameters describing the quality and fit of the model, as well as between the standard errors of the parameters of both models. In this case also, we can talk about a symmetric relation. The exponential PH model is valid if the exponential AFT model is valid. The study showed that the intensity of starting work was higher in the case of men, people with work experience, people with higher education and young people. The job search time was longer for women, people with no work experience, and people aged 60+, but shorter for people with higher education. Full article

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14 pages, 1100 KiB

Open AccessArticle

Dynamic Factor Models and Fractional Integration—With an Application to US Real Economic Activity

by Guglielmo Maria Caporale, Luis Alberiko Gil-Alana and Pedro Jose Piqueras Martinez

Econometrics 2024, 12(4), 39; https://doi.org/10.3390/econometrics12040039 - 19 Dec 2024

This paper makes a twofold contribution. First, it develops the dynamic factor model of by allowing for fractional integration instead of imposing the classical dichotomy between I(0) stationary and I(1) non-stationary series. This more general setup provides valuable information on the [...] Read more.

This paper makes a twofold contribution. First, it develops the dynamic factor model of by allowing for fractional integration instead of imposing the classical dichotomy between I(0) stationary and I(1) non-stationary series. This more general setup provides valuable information on the degree of persistence and mean-reverting properties of the series. Second, the proposed framework is used to analyse five annual US Real Economic Activity series (Employees, Energy, Industrial Production, Manufacturing, Personal Income) over the period from 1967 to 2019 in order to shed light on their degree of persistence and cyclical behaviour. The results indicate that economic activity in the US is highly persistent and is also characterised by cycles with a periodicity of 6 years and 8 months. Full article

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