Econometrics

33 pages, 415 KB

Open AccessArticle

A Statistical Characterization of Median-Based Inequality Measures

by Charles M. Beach and Russell Davidson

Econometrics 2025, 13(3), 31; https://doi.org/10.3390/econometrics13030031 - 9 Aug 2025

For income distributions divided into middle, lower, and higher regions based on scalar median cut-offs, this paper establishes the asymptotic distribution properties—including explicit empirically applicable variance formulas and hence standard errors—of sample estimates of the proportion of the population within the group, their [...] Read more.

For income distributions divided into middle, lower, and higher regions based on scalar median cut-offs, this paper establishes the asymptotic distribution properties—including explicit empirically applicable variance formulas and hence standard errors—of sample estimates of the proportion of the population within the group, their share of total income, and the groups’ mean incomes. It then applies these results for relative mean income ratios, various polarization measures, and decile-mean income ratios. Since the derived formulas are not distribution-free, the study advises using a density estimation technique proposed by Comte and Genon-Catalot. A shrinking middle-income group with declining relative incomes and marked upper-tail polarization among men’s incomes are all found to be highly statistically significant. Full article

32 pages, 1187 KB

Open AccessArticle

Simple Approximations and Interpretation of Pareto Index and Gini Coefficient Using Mean Absolute Deviations and Quantile Functions

by Eugene Pinsky and Qifu Wen

Econometrics 2025, 13(3), 30; https://doi.org/10.3390/econometrics13030030 - 8 Aug 2025

Abstract

The Pareto distribution has been widely used to model income distribution and inequality. The tail index and the Gini index are typically computed by iteration using Maximum Likelihood and are usually interpreted in terms of the Lorenz curve. We derive an alternative method [...] Read more.

The Pareto distribution has been widely used to model income distribution and inequality. The tail index and the Gini index are typically computed by iteration using Maximum Likelihood and are usually interpreted in terms of the Lorenz curve. We derive an alternative method by considering a truncated Pareto distribution and deriving a simple closed-form approximation for the tail index and the Gini coefficient in terms of the mean absolute deviation and weighted quartile differences. The obtained expressions can be used for any Pareto distribution, even without a finite mean or variance. These expressions are resistant to outliers and have a simple geometric and “economic” interpretation in terms of the quantile function and quartiles. Extensive simulations demonstrate that the proposed approximate values for the tail index and the Gini coefficient are within a few percent relative error of the exact values, even for a moderate number of data points. Our paper offers practical and computationally simple methods to analyze a class of models with Pareto distributions. The proposed methodology can be extended to many other distributions used in econometrics and related fields. Full article

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36 pages, 2033 KB

Open AccessArticle

Beyond GDP: COVID-19’s Effects on Macroeconomic Efficiency and Productivity Dynamics in OECD Countries

by Ümit Sağlam

Econometrics 2025, 13(3), 29; https://doi.org/10.3390/econometrics13030029 - 4 Aug 2025

Abstract

The COVID-19 pandemic triggered unprecedented economic disruptions, raising critical questions about the resilience and adaptability of macroeconomic productivity across countries. This study examines the impact of COVID-19 on macroeconomic efficiency and productivity dynamics in 37 OECD countries using quarterly data from 2018Q1 to [...] Read more.

The COVID-19 pandemic triggered unprecedented economic disruptions, raising critical questions about the resilience and adaptability of macroeconomic productivity across countries. This study examines the impact of COVID-19 on macroeconomic efficiency and productivity dynamics in 37 OECD countries using quarterly data from 2018Q1 to 2024Q4. By employing a Slack-Based Measure Data Envelopment Analysis (SBM-DEA) and the Malmquist Productivity Index (MPI), we decompose total factor productivity (TFP) into efficiency change (EC) and technological change (TC) across three periods: pre-pandemic, during-pandemic, and post-pandemic. Our framework incorporates both desirable (GDP) and undesirable outputs (inflation, unemployment, housing price inflation, and interest rate distortions), offering a multidimensional view of macroeconomic efficiency. Results show broad but uneven productivity gains, with technological progress proving more resilient than efficiency during the pandemic. Post-COVID recovery trajectories diverged, reflecting differences in structural adaptability and innovation capacity. Regression analysis reveals that stringent lockdowns in 2020 were associated with lower productivity in 2023–2024, while more adaptive policies in 2021 supported long-term technological gains. These findings highlight the importance of aligning crisis response with forward-looking economic strategies and demonstrate the value of DEA-based methods for evaluating macroeconomic performance beyond GDP. Full article

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

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18 pages, 1033 KB

Open AccessArticle

Analyzing the Impact of Carbon Mitigation on the Eurozone’s Trade Dynamics with the US and China

by Pathairat Pastpipatkul and Terdthiti Chitkasame

Econometrics 2025, 13(3), 28; https://doi.org/10.3390/econometrics13030028 - 29 Jul 2025

Abstract

This study focusses on the transmission of carbon pricing mechanisms in shaping trade dynamics between the Eurozone and key partners: the USA and China. Using Bayesian variable selection methods and a Time-Varying Structural Vector Autoregressions (TV-SVAR) model, the research identifies the key variables [...] Read more.

This study focusses on the transmission of carbon pricing mechanisms in shaping trade dynamics between the Eurozone and key partners: the USA and China. Using Bayesian variable selection methods and a Time-Varying Structural Vector Autoregressions (TV-SVAR) model, the research identifies the key variables impacting EU carbon emissions over time. The results reveal that manufactured products from the US have a diminishing positive impact on EU carbon emissions, suggesting potential exemption from future regulations. In contrast, manufactured goods from the US and petroleum products from China are expected to increase emissions, indicating a need for stricter trade policies. These findings provide strategic insights for policymakers aiming to balance trade and environmental objectives. Full article

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16 pages, 311 KB

Open AccessArticle

Pseudo-Panel Decomposition of the Blinder–Oaxaca Gender Wage Gap

by Jhon James Mora and Diana Yaneth Herrera

Econometrics 2025, 13(3), 27; https://doi.org/10.3390/econometrics13030027 - 19 Jul 2025

Abstract

This article introduces a novel approach to decomposing the Blinder–Oaxaca gender wage gap using pseudo-panel data. In many developing countries, panel data are not available; however, understanding the evolution of the gender wage gap over time requires tracking individuals longitudinally. When individuals change [...] Read more.

This article introduces a novel approach to decomposing the Blinder–Oaxaca gender wage gap using pseudo-panel data. In many developing countries, panel data are not available; however, understanding the evolution of the gender wage gap over time requires tracking individuals longitudinally. When individuals change across time periods, estimators tend to be inconsistent and inefficient. To address this issue, and building upon the traditional Blinder–Oaxaca methodology, we propose an alternative procedure that follows cohorts over time rather than individuals. This approach enables the estimation of both the explained and unexplained components—“endowment effect” and “remuneration effect”—of the wage gap, along with their respective standard errors, even in the absence of true panel data. We apply this methodology to the case of Colombia, finding a gender wage gap of approximately 15% in favor of male cohorts. This gap comprises a −5.6% explained component and a 20% unexplained component without controls. When we control by informality, size of the firm and sector the gap comprises a −3.5% explained component and a 18.7% unexplained component. Full article

11 pages, 346 KB

Open AccessArticle

Daily Emissions of CO₂ in the World: A Fractional Integration Approach

by Luis Alberiko Gil-Alana and Carlos Poza

Econometrics 2025, 13(3), 26; https://doi.org/10.3390/econometrics13030026 - 17 Jul 2025

Abstract

In this article, daily CO₂ emissions for the years 2019–2022 are examined using fractional integration for Brazil, China, EU-27 (and the UK), India, and the USA. According to the findings, all series exhibit long memory mean-reversion tendencies, with orders of integration ranging [...] Read more.

In this article, daily CO₂ emissions for the years 2019–2022 are examined using fractional integration for Brazil, China, EU-27 (and the UK), India, and the USA. According to the findings, all series exhibit long memory mean-reversion tendencies, with orders of integration ranging between 0.22 in the case of India (with white noise errors) and 0.70 for Brazil (under autocorrelated disturbances). Nevertheless, the differencing parameter estimates are all considerably below 1, which supports the theory of mean reversion and transient shocks. These results suggest the need for a greater intensification of green policies complemented with economic structural reforms to achieve the zero-emissions target by 2050. Full article

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31 pages, 2058 KB

Open AccessArticle

The Long-Run Impact of Changes in Prescription Drug Sales on Mortality and Hospital Utilization in Belgium, 1998–2019

by Frank R. Lichtenberg

Econometrics 2025, 13(3), 25; https://doi.org/10.3390/econometrics13030025 - 23 Jun 2025

Abstract

Objectives: We investigate the long-run impact of changes in prescription drug sales on mortality and hospital utilization in Belgium during the first two decades of the 21st century. Methods: We analyze the correlation across diseases between changes in the drugs used to treat [...] Read more.

Objectives: We investigate the long-run impact of changes in prescription drug sales on mortality and hospital utilization in Belgium during the first two decades of the 21st century. Methods: We analyze the correlation across diseases between changes in the drugs used to treat the disease and changes in mortality or hospital utilization from that disease. The measure of the change in prescription drug sales we use is the long-run (1998–2018 or 2000–2019) change in the fraction of post-1999 drugs sold. A post-1999 drug is a drug that was not sold during 1989–1999. Results: The 1998–2018 increase in the fraction of post-1999 drugs sold is estimated to have reduced the number of years of life lost before ages 85, 75, and 65 in 2018 by about 438 thousand (31%), 225 thousand (31%), and 114 thousand (32%), respectively. The 1995–2014 increase in in the fraction of post-1999 drugs sold is estimated to have reduced the number of hospital days in 2019 by 2.66 million (20%). Conclusions: Even if we ignore the reduction in hospital utilization attributable to changes in pharmaceutical consumption, a conservative estimate of the 2018 cost per life-year before age 85 gained is EUR 6824. We estimate that previous changes in pharmaceutical consumption reduced 2019 expenditure on inpatient curative and rehabilitative care by EUR 3.55 billion, which is higher than the 2018 expenditure on drugs that were authorized during the period 1998–2018: EUR 2.99 billion. Full article

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31 pages, 1988 KB

Open AccessArticle

The Effect of Macroeconomic Announcements on U.S. Treasury Markets: An Autometric General-to-Specific Analysis of the Greenspan Era

by James J. Forest

Econometrics 2025, 13(3), 24; https://doi.org/10.3390/econometrics13030024 - 21 Jun 2025

Abstract

This research studies the impact of macroeconomic announcement surprises on daily U.S. Treasury excess returns during the heart of Alan Greenspan’s tenure as Federal Reserve Chair, addressing the possible limitations of standard static regression (SSR) models, which may suffer from omitted variable bias, [...] Read more.

This research studies the impact of macroeconomic announcement surprises on daily U.S. Treasury excess returns during the heart of Alan Greenspan’s tenure as Federal Reserve Chair, addressing the possible limitations of standard static regression (SSR) models, which may suffer from omitted variable bias, parameter instability, and poor mis-specification diagnostics. To complement the SSR framework, an automated general-to-specific (Gets) modeling approach, enhanced with modern indicator saturation methods for robustness, is applied to improve empirical model discovery and mitigate potential biases. By progressively reducing an initially broad set of candidate variables, the Gets methodology steers the model toward congruence, dispenses unstable parameters, and seeks to limit information loss while seeking model congruence and precision. The findings, herein, suggest that U.S. Treasury market responses to macroeconomic news shocks exhibited stability for a core set of announcements that reliably influenced excess returns. In contrast to computationally costless standard static models, the automated Gets-based approach enhances parameter precision and provides a more adaptive structure for identifying relevant predictors. These results demonstrate the potential value of incorporating interpretable automated model selection techniques alongside traditional SSR and Markov switching approaches to improve empirical insights into macroeconomic announcement effects on financial markets. Full article

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

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22 pages, 956 KB

Open AccessArticle

Leveraging Success: The Hidden Peak in Debt and Firm Performance

by Suzan Dsouza, Krishnamoorthy Kathavarayan, Franklin Mathias, Dharmesh Bhatia and Abdallah AlKhawaja

Econometrics 2025, 13(2), 23; https://doi.org/10.3390/econometrics13020023 - 10 Jun 2025

Abstract

This study investigates the relationship between capital structure and financial performance in South African firms, focusing on the potential non-linear, inverse U-shaped effect of leverage on profitability. Drawing on data from 1548 firm-year observations covering 183 publicly listed South African companies between 2013 [...] Read more.

This study investigates the relationship between capital structure and financial performance in South African firms, focusing on the potential non-linear, inverse U-shaped effect of leverage on profitability. Drawing on data from 1548 firm-year observations covering 183 publicly listed South African companies between 2013 and 2022, the analysis employs both Fixed Effects (FE) and System Generalized Method of Moments (System-GMM) models to address endogeneity and capture dynamic adjustments. The findings indicate that moderate levels of debt enhance profitability, but excessive leverage leads to diminishing returns, confirming an inverse U-shaped relationship. System-GMM results further reveal the persistence of past profitability and validate the dynamic nature of capital structure decisions. Larger firms appear more capable of sustaining higher leverage without adverse effects, while smaller firms benefit from maintaining lower debt levels. The study concludes that strategic debt management, tailored to firm size and economic context, is critical for optimizing financial performance in emerging markets like South Africa. The study identifies the optimal leverage ratio for South African firms and shows how firm size moderates the relationship between debt and profitability, offering tailored insights for firms of different sizes. These insights offer valuable guidance for managers, investors, and policymakers aiming to strengthen financial stability and efficiency through informed capital structure choices. Full article

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26 pages, 743 KB

Open AccessArticle

Dependent and Independent Time Series Errors Under Elliptically Countered Models

by Fredy O. Pérez-Ramirez, Francisco J. Caro-Lopera, José A. Díaz-García and Graciela González Farías

Econometrics 2025, 13(2), 22; https://doi.org/10.3390/econometrics13020022 - 21 May 2025

Abstract

We explore the impact of time series behavior on model errors when working under an elliptically contoured distribution. By adopting a time series approach aligned with the realistic dependence between errors under such distributions, this perspective shifts the focus from increasingly complex and [...] Read more.

We explore the impact of time series behavior on model errors when working under an elliptically contoured distribution. By adopting a time series approach aligned with the realistic dependence between errors under such distributions, this perspective shifts the focus from increasingly complex and challenging correlation analyses to volatility modeling that utilizes a novel likelihood framework based on dependent probabilistic samples. With the introduction of a modified Bayesian Information Criterion, which incorporates a ranking of degrees of evidence of significant differences between the compared models, the critical issue of model selection is reinforced, clarifying the relationships among the most common information criteria and revealing limited relevance among the models based on independent probabilistic samples, when tested on a well-established database. Our approach challenges the traditional hierarchical models commonly used in time series analysis, which assume independent errors. The application of rigorous differentiation criteria under this novel perspective on likelihood, based on dependent probabilistic samples, provides a new viewpoint on likelihood that arises naturally in the context of finance, adding a novel result. We provide new results for criterion selection, evidence invariance, and transitions between volatility models and heuristic methods to calibrate nested or non-nested models via convergence properties in a distribution. Full article

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24 pages, 6005 KB

Open AccessArticle

Decomposing the Household Herding Behavior in Stock Investment: The Case of China

by Yung-Ching Tseng, I.-Fan Hsiao and Guo-Chen Wang

Econometrics 2025, 13(2), 21; https://doi.org/10.3390/econometrics13020021 - 12 May 2025

Abstract

Financial studies on the herding effect have been very popular for decades, as detecting herding behavior helps to explain price deviations and market inefficiencies. However, studying the herding effect as a single influencing factor is believed to be insufficient to explain the changes [...] Read more.

Financial studies on the herding effect have been very popular for decades, as detecting herding behavior helps to explain price deviations and market inefficiencies. However, studying the herding effect as a single influencing factor is believed to be insufficient to explain the changes in investment behavior, as the herding effect itself may be caused by other influencing factors. In other words, the issue must be studied alongside other factors. In this study, we adopt the quantile regression model to comprehensively understand the herding effect’s influence on household investment in China, and the empirical results indicate that herding behavior leads to different investment outcomes for households in different scenarios. In this analysis, we consider a variety of household characteristics, such as income level and risk tolerance, to provide a nuanced understanding of investment behavior. Additionally, in this study, we explore the interaction between herding behavior and macroeconomic variables. Nevertheless, the results suggest that, if herding behavior can be reduced by the head of the household, profitability can be increased, or at the very least, losses can be reduced. Full article

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26 pages, 3420 KB

Open AccessArticle

Government Subsidies and Industrial Productivity in South Africa: A Focus on the Channels

by Brian Tavonga Mazorodze

Econometrics 2025, 13(2), 20; https://doi.org/10.3390/econometrics13020020 - 1 May 2025

Cited by 1

Abstract

This article estimates the impact of government subsidies on productivity growth in South Africa, joining the ongoing debate among economists regarding the effectiveness of subsidies as a driver of industrial productivity. While some argue that subsidies address market failures, facilitate R&D, and improve [...] Read more.

This article estimates the impact of government subsidies on productivity growth in South Africa, joining the ongoing debate among economists regarding the effectiveness of subsidies as a driver of industrial productivity. While some argue that subsidies address market failures, facilitate R&D, and improve efficiency, others criticise the attendant dependence, which reduces the incentive for industries to operate efficiently. This article contributes by examining the specific channels—efficiency and technical changes—through which subsidies affect productivity in South Africa. The analysis is based on a panel dataset comprising 64 three-digit industries observed between 1993 and 2023. Estimation is performed through an endogeneity robust panel stochastic frontier model, which treats subsidies as both an inefficiency driver and a technology variable. An additional estimation approach is proposed integrating the true fixed effects with a control function in a bid to account for both unobserved heterogeneity and idiosyncratic endogeneity. The results show that subsidies are detrimental to productivity, particularly through stifling technological progress. This result supports the view that subsidies reduce the incentive for beneficiaries to innovate. This evidence calls for a reevaluation and a possible restructuring of subsidy programmes in South Africa in a bid to mitigate their adverse effects on industrial productivity. Full article

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14 pages, 388 KB

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

Abstract

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 KB

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

Abstract

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 KB

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

Abstract

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 KB

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

Abstract

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 KB

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

Abstract

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 KB

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

Cited by 2

Abstract

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 KB

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

Cited by 1

Abstract

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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