Frank J. Fabozzi, Hasan Fallahgoul, Vincentius Franstianto, Grégoire Loeper
Recently, machine learning algorithms have increasing become popular tools for economic and financial forecasting. While there are several machine learning algorithms for doing so, a powerful and efficient algorithm for forecasting purposes is the multi-layer, multi-node neural network with rectified linear unit (ReLU) activation function – deep neural network (DNN). Studies have demonstrated the empirical applications of DNN but have devoted less research to investigate its statistical properties which is mainly due to its severe nonlinearity and heavy parametrization. By borrowing tools from a non-parametric regression framework, sieve estimator, we first show that there exists such a sieve estimator for a DNN. We next establish three asymptotic properties of the ReLU network: consistency, sieve-based convergence rate, and asymptotic normality, and then validate our theoretical results using Monte Carlo analysis.
{"title":"Asymptotic Properties of ReLU FFN Sieve Estimators","authors":"Frank J. Fabozzi, Hasan Fallahgoul, Vincentius Franstianto, Grégoire Loeper","doi":"10.1515/snde-2023-0072","DOIUrl":"https://doi.org/10.1515/snde-2023-0072","url":null,"abstract":"Recently, machine learning algorithms have increasing become popular tools for economic and financial forecasting. While there are several machine learning algorithms for doing so, a powerful and efficient algorithm for forecasting purposes is the multi-layer, multi-node neural network with rectified linear unit (ReLU) activation function – deep neural network (DNN). Studies have demonstrated the empirical applications of DNN but have devoted less research to investigate its statistical properties which is mainly due to its severe nonlinearity and heavy parametrization. By borrowing tools from a non-parametric regression framework, sieve estimator, we first show that there exists such a sieve estimator for a DNN. We next establish three asymptotic properties of the ReLU network: consistency, sieve-based convergence rate, and asymptotic normality, and then validate our theoretical results using Monte Carlo analysis.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"65 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183141","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joshua Chan, Arnaud Doucet, Roberto León-González, Rodney W. Strachan
A new methodology that decomposes shocks into homoscedastic and heteroscedastic components is developed. This specification implies there exist linear combinations of heteroscedastic variables that eliminate heteroscedasticity; a property known as co-heteroscedasticity. The heteroscedastic part of the model uses a multivariate stochastic volatility inverse Wishart process. The resulting model is invariant to the ordering of the variables, which is shown to be important for volatility estimation. By incorporating testable co-heteroscedasticity restrictions, the specification allows estimation in moderately high-dimensions. The computational strategy uses a novel particle filter algorithm, a reparameterization that substantially improves algorithmic convergence and an alternating-order particle Gibbs that reduces the amount of particles needed for accurate estimation. An empirical application to a large Vector Autoregression (VAR) is provided, finding strong evidence for co-heteroscedasticity and that the new method outperforms some previously proposed methods in terms of forecasting at all horizons. It is also found that the structural monetary shock is 98.8 % homoscedastic, and that investment and the SP 500 index are nearly 100 % determined by fat tail heteroscedastic shocks. A Monte Carlo experiment illustrates that the new method estimates well the characteristics of approximate factor models with heteroscedastic errors.
{"title":"Multivariate Stochastic Volatility with Co-Heteroscedasticity","authors":"Joshua Chan, Arnaud Doucet, Roberto León-González, Rodney W. Strachan","doi":"10.1515/snde-2023-0056","DOIUrl":"https://doi.org/10.1515/snde-2023-0056","url":null,"abstract":"A new methodology that decomposes shocks into homoscedastic and heteroscedastic components is developed. This specification implies there exist linear combinations of heteroscedastic variables that eliminate heteroscedasticity; a property known as co-heteroscedasticity. The heteroscedastic part of the model uses a multivariate stochastic volatility inverse Wishart process. The resulting model is invariant to the ordering of the variables, which is shown to be important for volatility estimation. By incorporating testable co-heteroscedasticity restrictions, the specification allows estimation in moderately high-dimensions. The computational strategy uses a novel particle filter algorithm, a reparameterization that substantially improves algorithmic convergence and an alternating-order particle Gibbs that reduces the amount of particles needed for accurate estimation. An empirical application to a large Vector Autoregression (VAR) is provided, finding strong evidence for co-heteroscedasticity and that the new method outperforms some previously proposed methods in terms of forecasting at all horizons. It is also found that the structural monetary shock is 98.8 % homoscedastic, and that investment and the SP 500 index are nearly 100 % determined by fat tail heteroscedastic shocks. A Monte Carlo experiment illustrates that the new method estimates well the characteristics of approximate factor models with heteroscedastic errors.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Konstantinos Gkillas, Maria Tantoula, Manolis Tzagarakis
We analyze properties identified in the price volatility of Bitcoin and some of the leading cryptocurrencies namely Litecoin, Ripple, and Ethereum. We employ Heterogeneous Autoregressive models (HAR) in both a univariate and multivariate level of analysis. First, the significance of heterogeneity and jumps is examined, considering the ability of several univariate HAR models, to predict realized volatility of cryptocurrencies. Second, we examine the relevance of realized volatility jumps and covariances in the transmission of volatility spillovers among cryptocurrencies. We perform a comparative spillover analysis of the multivariate HAR models in two versions, considering variances only and covariances as well. Our results indicate that covariances and jumps inclusion lead to an increase in spillovers. The time-varying spillover analysis indicates higher dependency between Bitcoin and the other cryptocurrencies mostly at short frequencies.
我们分析了比特币和一些主要加密货币（即莱特币、瑞波币和以太坊）的价格波动特性。我们采用异质自回归模型（HAR）进行单变量和多变量分析。首先，考虑到几个单变量 HAR 模型预测加密货币已实现波动率的能力，我们研究了异质性和跳跃的重要性。其次，我们研究了已实现波动率跳跃和协方差在加密货币间波动溢出效应传播中的相关性。我们对两个版本的多变量 HAR 模型进行了溢出比较分析，分别只考虑了方差和协方差。我们的结果表明，包含协方差和跳跃会导致溢出效应增加。时变溢出效应分析表明，比特币与其他加密货币之间的依赖性较高，主要表现在短频率上。
{"title":"Heterogeneity, Jumps and Co-Movements in Transmission of Volatility Spillovers Among Cryptocurrencies","authors":"Konstantinos Gkillas, Maria Tantoula, Manolis Tzagarakis","doi":"10.1515/snde-2023-0088","DOIUrl":"https://doi.org/10.1515/snde-2023-0088","url":null,"abstract":"We analyze properties identified in the price volatility of Bitcoin and some of the leading cryptocurrencies namely Litecoin, Ripple, and Ethereum. We employ Heterogeneous Autoregressive models (HAR) in both a univariate and multivariate level of analysis. First, the significance of heterogeneity and jumps is examined, considering the ability of several univariate HAR models, to predict realized volatility of cryptocurrencies. Second, we examine the relevance of realized volatility jumps and covariances in the transmission of volatility spillovers among cryptocurrencies. We perform a comparative spillover analysis of the multivariate HAR models in two versions, considering variances only and covariances as well. Our results indicate that covariances and jumps inclusion lead to an increase in spillovers. The time-varying spillover analysis indicates higher dependency between Bitcoin and the other cryptocurrencies mostly at short frequencies.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"157 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As the demand for accuracy in volatility modeling and forecasting increases, the literature tends to incorporate different volatility measures with heterogeneous information content to construct the hybrid volatility model. This study focuses on one of the popular hybrid volatility models: the Realized Generalized Autoregressive Heteroskedasticity (Realized GARCH) and embeds various volatility measures, including the CBOE VIX, VIX1D, Realized Volatility, and Daily Range to examine their heterogeneous impact on the conditional volatility estimation and forecasting. To evaluate the impact of the volatility measures, we first construct a volatility response function. This involves calculating the difference in one-step-ahead conditional volatility forecasts that incorporate information from both return and volatility measures against the forecasts based on return innovations only. Subsequently, the variance share is calculated to evaluate its role in explaining future variations in the Realized GARCH. Our results show that among these four volatility measures, VIX is the most informative volatility. Although VIX1D is overemphasized by the literature, its significance in volatility forecasting remains substantial, confirming that risk-neutral volatility measures are generally more informative than physical measures. Finally, we also find that incorporating multiple risk-neutral volatility measures does not improve forecasting performance compared to using a single measure due to overlapping information.
{"title":"Heterogeneous Volatility Information Content for the Realized GARCH Modeling and Forecasting Volatility","authors":"Wen Xu, Pakorn Aschakulporn, Jin E. Zhang","doi":"10.1515/snde-2024-0013","DOIUrl":"https://doi.org/10.1515/snde-2024-0013","url":null,"abstract":"As the demand for accuracy in volatility modeling and forecasting increases, the literature tends to incorporate different volatility measures with heterogeneous information content to construct the hybrid volatility model. This study focuses on one of the popular hybrid volatility models: the Realized Generalized Autoregressive Heteroskedasticity (Realized GARCH) and embeds various volatility measures, including the CBOE VIX, VIX1D, Realized Volatility, and Daily Range to examine their heterogeneous impact on the conditional volatility estimation and forecasting. To evaluate the impact of the volatility measures, we first construct a volatility response function. This involves calculating the difference in one-step-ahead conditional volatility forecasts that incorporate information from both return and volatility measures against the forecasts based on return innovations only. Subsequently, the variance share is calculated to evaluate its role in explaining future variations in the Realized GARCH. Our results show that among these four volatility measures, VIX is the most informative volatility. Although VIX1D is overemphasized by the literature, its significance in volatility forecasting remains substantial, confirming that risk-neutral volatility measures are generally more informative than physical measures. Finally, we also find that incorporating multiple risk-neutral volatility measures does not improve forecasting performance compared to using a single measure due to overlapping information.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142183144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers a heterogeneous panel data model with an unknown number of breaks. We propose a so-called two-stage procedure to determine the number of breaks and detect the location of break points. The consistency of the estimated number of breaks and the estimated break points are established under fairly general conditions. Monte Carlo simulations and two empirical applications are provided to demonstrate the finite sample performance of the proposed method.
{"title":"Determination of the Number of Breaks in Heterogeneous Panel Data Models","authors":"Lu Wang, Shuke Hu","doi":"10.1515/snde-2024-0018","DOIUrl":"https://doi.org/10.1515/snde-2024-0018","url":null,"abstract":"This paper considers a heterogeneous panel data model with an unknown number of breaks. We propose a so-called two-stage procedure to determine the number of breaks and detect the location of break points. The consistency of the estimated number of breaks and the estimated break points are established under fairly general conditions. Monte Carlo simulations and two empirical applications are provided to demonstrate the finite sample performance of the proposed method.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Instead of assuming a certain factor structure, we statistically test for the factor structure driving common global dynamics in macroeconomic and financial data by employing a stochastic factor selection approach. Using a sample of 16 developed countries from 1996Q1 to 2019Q4, we present strong empirical evidence of a global macro-financial cycle and an independent global financial cycle. Moreover, the global macro-financial cycle we estimate is essentially the global business cycle identified in the literature. It captures the common global macroeconomic dynamics and drives a significant share of the comovement in the financial sector. The remaining commonality in financial variables is driven by separate global financial cycles: the global credit cycle and the global capital flow cycle.
{"title":"Which Global Cycle? A Stochastic Factor Selection Approach for Global Macro-Financial Cycles","authors":"Tino Berger, Sebastian Hienzsch","doi":"10.1515/snde-2023-0093","DOIUrl":"https://doi.org/10.1515/snde-2023-0093","url":null,"abstract":"Instead of assuming a certain factor structure, we statistically test for the factor structure driving common global dynamics in macroeconomic and financial data by employing a stochastic factor selection approach. Using a sample of 16 developed countries from 1996Q1 to 2019Q4, we present strong empirical evidence of a global macro-financial cycle and an independent global financial cycle. Moreover, the global macro-financial cycle we estimate is essentially the global business cycle identified in the literature. It captures the common global macroeconomic dynamics and drives a significant share of the comovement in the financial sector. The remaining commonality in financial variables is driven by separate global financial cycles: the global credit cycle and the global capital flow cycle.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes the inversion of likelihood ratio tests for the construction of confidence intervals for multiple threshold parameters. Using Monte Carlo simulations, conservative likelihood-ratio-based confidence intervals are shown to exhibit empirical coverage rates at least as high as nominal levels for all threshold parameters, while still being informative in the sense of only including relatively few observations in each confidence interval. These findings are robust to the magnitude of the threshold effect, the sample size and the presence of serial correlation. Applications to existing models with multiple thresholds for U.S. real GDP growth and for the wage Phillips curve demonstrate how the proposed approach is empirically relevant to make inferences about the uncertainty of threshold estimates.
本文提出用似然比检验反演来构建多个临界参数的置信区间。通过蒙特卡罗模拟，基于似然比的保守置信区间显示出所有临界值参数的经验覆盖率至少与名义水平一样高，同时在每个置信区间只包含相对较少的观测值的意义上仍然具有信息量。这些发现对临界值效应的大小、样本大小和序列相关性的存在都是稳健的。对美国实际 GDP 增长和工资菲利普斯曲线具有多个临界值的现有模型的应用表明，所提出的方法在推断临界值估计值的不确定性方面具有经验相关性。
{"title":"Likelihood-Ratio-Based Confidence Intervals for Multiple Threshold Parameters","authors":"Luiggi Donayre","doi":"10.1515/snde-2023-0029","DOIUrl":"https://doi.org/10.1515/snde-2023-0029","url":null,"abstract":"This paper proposes the inversion of likelihood ratio tests for the construction of confidence intervals for multiple threshold parameters. Using Monte Carlo simulations, conservative likelihood-ratio-based confidence intervals are shown to exhibit empirical coverage rates at least as high as nominal levels for all threshold parameters, while still being informative in the sense of only including relatively few observations in each confidence interval. These findings are robust to the magnitude of the threshold effect, the sample size and the presence of serial correlation. Applications to existing models with multiple thresholds for U.S. real GDP growth and for the wage Phillips curve demonstrate how the proposed approach is empirically relevant to make inferences about the uncertainty of threshold estimates.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Homogeneity identification of panel data models has been popular in the literature in recent years. Most of the existing works only focus on the complete data case. This paper considers a functional-coefficient quantile regression model for panel data with homogeneity when its response variables are subject to censoring. In particular, we consider a more general censoring framework, i.e. different types of censoring are allowed to occur in the model simultaneously. For this, a “three-stage” method is proposed, which includes the preliminary estimation of subject-specific function coefficients based on data augmentation, the identification of group structure over subjects by clustering, and post-grouping estimation of function coefficients. Simulation studies considering the left-, right-, and double-censored data, are carried out to verify the finite-sample properties of the proposed method. Simulation results show that our method gives comparable performance to the complete data case. The application to the bank stock data further illustrates the practical advantages of this method.
{"title":"Homogeneity Pursuit in the Functional-Coefficient Quantile Regression Model for Panel Data with Censored Data","authors":"Lu Li, Yue Xia, Shuyi Ren, Xiaorong Yang","doi":"10.1515/snde-2023-0024","DOIUrl":"https://doi.org/10.1515/snde-2023-0024","url":null,"abstract":"Homogeneity identification of panel data models has been popular in the literature in recent years. Most of the existing works only focus on the complete data case. This paper considers a functional-coefficient quantile regression model for panel data with homogeneity when its response variables are subject to censoring. In particular, we consider a more general censoring framework, i.e. different types of censoring are allowed to occur in the model simultaneously. For this, a “three-stage” method is proposed, which includes the preliminary estimation of subject-specific function coefficients based on data augmentation, the identification of group structure over subjects by clustering, and post-grouping estimation of function coefficients. Simulation studies considering the left-, right-, and double-censored data, are carried out to verify the finite-sample properties of the proposed method. Simulation results show that our method gives comparable performance to the complete data case. The application to the bank stock data further illustrates the practical advantages of this method.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141739791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we examine the relationship between income inequality and mental health using a sample of low and middle-income countries over the period 1990–2019. Using a dynamic panel threshold model that allows for endogeneity in both the regressors and threshold variable, we find a non-linear relationship between income inequality and the prevalence of mental health disorders. Specifically, income inequality is associated with reduced prevalence of mental health disorders at low levels of income inequality but after it surpasses a threshold Gini coefficient (estimated between 39 and 49), it has an adverse effect on mental health. The impact is more pronounced in low income and lower middle-income countries. We also find evidence of heterogenous effects by age and gender. Our findings indicate the importance of modelling non-linearity in the income inequality-health relationship and highlight the importance of keeping income inequality within reasonable bounds.
{"title":"Non-Linear Impact of Income Inequality on Mental Health: Evidence from Low and Middle-Income Countries","authors":"Ankita Mishra, Abebe Hailemariam, Preety Srivastava, Greeni Maheshwari","doi":"10.1515/snde-2023-0113","DOIUrl":"https://doi.org/10.1515/snde-2023-0113","url":null,"abstract":"In this study, we examine the relationship between income inequality and mental health using a sample of low and middle-income countries over the period 1990–2019. Using a dynamic panel threshold model that allows for endogeneity in both the regressors and threshold variable, we find a non-linear relationship between income inequality and the prevalence of mental health disorders. Specifically, income inequality is associated with reduced prevalence of mental health disorders at low levels of income inequality but after it surpasses a threshold Gini coefficient (estimated between 39 and 49), it has an adverse effect on mental health. The impact is more pronounced in low income and lower middle-income countries. We also find evidence of heterogenous effects by age and gender. Our findings indicate the importance of modelling non-linearity in the income inequality-health relationship and highlight the importance of keeping income inequality within reasonable bounds.","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141739790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we show that a regression-based approach can be used to estimate generalised entropy and Atkinson inequality indices and their associated standard errors. The applicability of this approach is demonstrated using the health expenditure data from the United States (US) medical expenditure panel survey (MEPS).
{"title":"A Regression-based Method for Estimating Generalised Entropy and Atkinson Inequality Indices and their Standard Errors","authors":"Sriram Shankar","doi":"10.1515/snde-2024-0021","DOIUrl":"https://doi.org/10.1515/snde-2024-0021","url":null,"abstract":"In this paper we show that a regression-based approach can be used to estimate generalised entropy and Atkinson inequality indices and their associated standard errors. The applicability of this approach is demonstrated using the health expenditure data from the United States (US) medical expenditure panel survey (MEPS).","PeriodicalId":501448,"journal":{"name":"Studies in Nonlinear Dynamics & Econometrics","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141613541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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