Abstract Estimation of agent-based models in economics and finance confronts researchers with a number of challenges. Typically, the complex structures of such models do not allow to derive closed-form likelihood functions so that either numerical approximations to the likelihood or moment-based estimators have to be used for parameter inference. However, all these approaches suffer from extremely high computational demands as they typically work with simulations (of the agent-based model) embedded in (Monte Carlo) simulations conducted for the purpose of parameter identification. One approach that is very generally applicable and that has the potential of alleviating the computational burden is Approximate Bayesian Computation (ABC). While popular in other areas of agent-based modelling, it seems not to have been used so far in economics and finance. This paper provides an introduction to this methodology and demonstrates its potential with the example of a well-studied model of speculative dynamics. As it turns out, ABC appears to make more efficient use of moment-based information than frequentist SMM (Simulated Method of Moments), and it can be used for sample sizes of an order far beyond the reach of numerical likelihood methods.
{"title":"Approximate Bayesian inference for agent-based models in economics: a case study","authors":"T. Lux","doi":"10.1515/snde-2021-0052","DOIUrl":"https://doi.org/10.1515/snde-2021-0052","url":null,"abstract":"Abstract Estimation of agent-based models in economics and finance confronts researchers with a number of challenges. Typically, the complex structures of such models do not allow to derive closed-form likelihood functions so that either numerical approximations to the likelihood or moment-based estimators have to be used for parameter inference. However, all these approaches suffer from extremely high computational demands as they typically work with simulations (of the agent-based model) embedded in (Monte Carlo) simulations conducted for the purpose of parameter identification. One approach that is very generally applicable and that has the potential of alleviating the computational burden is Approximate Bayesian Computation (ABC). While popular in other areas of agent-based modelling, it seems not to have been used so far in economics and finance. This paper provides an introduction to this methodology and demonstrates its potential with the example of a well-studied model of speculative dynamics. As it turns out, ABC appears to make more efficient use of moment-based information than frequentist SMM (Simulated Method of Moments), and it can be used for sample sizes of an order far beyond the reach of numerical likelihood methods.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46345501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper studies the tail behaviours of the stationary distribution of multiple-regime threshold AR models with multiple heavy-tailed innovations. It is shown that the marginal tail probability has the same order as that of the innovation with the heaviest tail. Other new results in this paper include the geometric ergodicity and the tail dependence of TAR models with multiple heavy-tailed innovations.
{"title":"Tail behaviours of multiple-regime threshold AR models with heavy-tailed innovations","authors":"Jiazhu Pan, Yali He","doi":"10.1515/snde-2020-0071","DOIUrl":"https://doi.org/10.1515/snde-2020-0071","url":null,"abstract":"Abstract This paper studies the tail behaviours of the stationary distribution of multiple-regime threshold AR models with multiple heavy-tailed innovations. It is shown that the marginal tail probability has the same order as that of the innovation with the heaviest tail. Other new results in this paper include the geometric ergodicity and the tail dependence of TAR models with multiple heavy-tailed innovations.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":"27 1","pages":"377 - 395"},"PeriodicalIF":0.8,"publicationDate":"2022-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43887354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper provides a theoretical investigation of possible sources of long-run economic growth in the future. Historically, in the industrial era and during the ongoing digital revolution (which began approximately in the 1980s) the main engine of global economic growth has been research and development (R&D), translating into systematic labor-augmenting technological progress and trend growth in labor productivity. If in the future all essential production or R&D tasks will eventually be subject to automation, though, the engine of growth will be shifted to the accumulation of programmable hardware (capital), and R&D will lose its prominence. Economic growth will then accelerate, no longer constrained by the scarce human input. By contrast, if some essential production and R&D tasks will never be fully automatable, then R&D may forever remain the main growth engine, and the human input may forever remain the scarce, limiting factor of global growth. Additional studied mechanisms include the accumulation of R&D capital and hardware-augmenting technical change.
{"title":"What will drive global economic growth in the digital age?","authors":"J. Growiec","doi":"10.1515/snde-2021-0079","DOIUrl":"https://doi.org/10.1515/snde-2021-0079","url":null,"abstract":"Abstract This paper provides a theoretical investigation of possible sources of long-run economic growth in the future. Historically, in the industrial era and during the ongoing digital revolution (which began approximately in the 1980s) the main engine of global economic growth has been research and development (R&D), translating into systematic labor-augmenting technological progress and trend growth in labor productivity. If in the future all essential production or R&D tasks will eventually be subject to automation, though, the engine of growth will be shifted to the accumulation of programmable hardware (capital), and R&D will lose its prominence. Economic growth will then accelerate, no longer constrained by the scarce human input. By contrast, if some essential production and R&D tasks will never be fully automatable, then R&D may forever remain the main growth engine, and the human input may forever remain the scarce, limiting factor of global growth. Additional studied mechanisms include the accumulation of R&D capital and hardware-augmenting technical change.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":"27 1","pages":"335 - 354"},"PeriodicalIF":0.8,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44281571","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Using annual data from two panels, one of 11 Eurozone countries and another of 31 OECD countries, we estimate a two-regime log-linear as well as a nonlinear model for the spread as a function of macroeconomic and quality-of-institutions variables. The two regimes, a high-spread and a low-spread regime, are distinguished by using a threshold, in accordance with the perceived “fair” value of the spread as a reference point. Our results suggest that government-bond spreads are regime-dependent, as most of the regression coefficients of the determinants of the spread are larger (in absolute value) in the high-spread regime than in the low-spread regime. That is, an improvement in the macroeconomic environment (e.g., lower unemployment, lower inflation, lower growth of the debt-to-GDP ratio, less macroeconomic uncertainty, higher growth of real GDP), and/or an improvement in the quality of institutions (e.g., less corruption) reduce the spread facing a country (by enhancing its creditworthiness) to a greater extent in high-spread situations than in low-spread situations. A possible explanation is that the demand for and the supply of loans are inelastic at higher than “fair” interest rates and elastic at lower rates.
{"title":"A threshold model for the spread","authors":"Dimitris Hatzinikolaou, Georgios Sarigiannidis","doi":"10.1515/snde-2020-0007","DOIUrl":"https://doi.org/10.1515/snde-2020-0007","url":null,"abstract":"Abstract Using annual data from two panels, one of 11 Eurozone countries and another of 31 OECD countries, we estimate a two-regime log-linear as well as a nonlinear model for the spread as a function of macroeconomic and quality-of-institutions variables. The two regimes, a high-spread and a low-spread regime, are distinguished by using a threshold, in accordance with the perceived “fair” value of the spread as a reference point. Our results suggest that government-bond spreads are regime-dependent, as most of the regression coefficients of the determinants of the spread are larger (in absolute value) in the high-spread regime than in the low-spread regime. That is, an improvement in the macroeconomic environment (e.g., lower unemployment, lower inflation, lower growth of the debt-to-GDP ratio, less macroeconomic uncertainty, higher growth of real GDP), and/or an improvement in the quality of institutions (e.g., less corruption) reduce the spread facing a country (by enhancing its creditworthiness) to a greater extent in high-spread situations than in low-spread situations. A possible explanation is that the demand for and the supply of loans are inelastic at higher than “fair” interest rates and elastic at lower rates.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":"27 1","pages":"67 - 82"},"PeriodicalIF":0.8,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41449947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jujie Wang, Zhenzhen Zhuang, Dongming Gao, Yang Li, Liu Feng
Abstract Stock price prediction has become a focal topic for relevant investors and scholars in these years. However, owning to the non-stationarity and complexity of stock price data, it is challenging to predict stock price accurately. This research develops a novel multi-scale nonlinear ensemble learning framework for stock price prediction, which consists of variational mode decomposition (VMD), evolutionary weighted support vector regression (EWSVR) and long short-term memory network (LSTM). The VMD is utilized to extract the basic features from an original stock price signal and eliminate the disturbance of illusive components. The EWSVR is utilized to predict each sub-signal with corresponding features, whose penalty weights are determined according to the time order and whose parameters are optimized by tree-structured Parzen estimator (TPE). The LSTM-based nonlinear ensemble learning paradigm is employed to integrate the predicted value of each sub-signal into the final prediction result of stock price. Four real prediction cases are utilized to test the proposed model. The proposed model’s prediction results of multiple evaluation metrics are significantly improved compared to other benchmark models both in stock market closing price forecasting.
{"title":"Stock price prediction using multi-scale nonlinear ensemble of deep learning and evolutionary weighted support vector regression","authors":"Jujie Wang, Zhenzhen Zhuang, Dongming Gao, Yang Li, Liu Feng","doi":"10.1515/snde-2021-0096","DOIUrl":"https://doi.org/10.1515/snde-2021-0096","url":null,"abstract":"Abstract Stock price prediction has become a focal topic for relevant investors and scholars in these years. However, owning to the non-stationarity and complexity of stock price data, it is challenging to predict stock price accurately. This research develops a novel multi-scale nonlinear ensemble learning framework for stock price prediction, which consists of variational mode decomposition (VMD), evolutionary weighted support vector regression (EWSVR) and long short-term memory network (LSTM). The VMD is utilized to extract the basic features from an original stock price signal and eliminate the disturbance of illusive components. The EWSVR is utilized to predict each sub-signal with corresponding features, whose penalty weights are determined according to the time order and whose parameters are optimized by tree-structured Parzen estimator (TPE). The LSTM-based nonlinear ensemble learning paradigm is employed to integrate the predicted value of each sub-signal into the final prediction result of stock price. Four real prediction cases are utilized to test the proposed model. The proposed model’s prediction results of multiple evaluation metrics are significantly improved compared to other benchmark models both in stock market closing price forecasting.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":"27 1","pages":"397 - 421"},"PeriodicalIF":0.8,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43184725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper studies high-dimensional threshold models with a time-varying threshold approximated using a Fourier function. We develop a weighted LASSO estimator of regression coefficients as well as the threshold parameters. Our LASSO estimator can not only select covariates but also distinguish between linear and threshold models. We derive non-asymptotic oracle inequalities for the prediction risk, the l 1 and l ∞ bounds for regression coefficients, and provide an upper bound on the l 1 estimation error of the time-varying threshold estimator. The bounds can be translated easily into asymptotic consistency for prediction and estimation. We also establish the variable selection consistency and threshold detection consistency based on the l ∞ bounds. Through Monte Carlo simulations, we show that the thresholded LASSO works reasonably well in finite samples in terms of variable selection, and there is little harmness by the allowance for Fourier approximation in the estimation procedure even when there is no time-varying feature in the threshold. On the contrary, the estimation and variable selection are inconsistent when the threshold is time-varying but being misspecified as a constant. The model is illustrated with an empirical application to the famous debt-growth nexus.
{"title":"High dimensional threshold model with a time-varying threshold based on Fourier approximation","authors":"Lixiong Yang","doi":"10.1515/snde-2021-0047","DOIUrl":"https://doi.org/10.1515/snde-2021-0047","url":null,"abstract":"Abstract This paper studies high-dimensional threshold models with a time-varying threshold approximated using a Fourier function. We develop a weighted LASSO estimator of regression coefficients as well as the threshold parameters. Our LASSO estimator can not only select covariates but also distinguish between linear and threshold models. We derive non-asymptotic oracle inequalities for the prediction risk, the l 1 and l ∞ bounds for regression coefficients, and provide an upper bound on the l 1 estimation error of the time-varying threshold estimator. The bounds can be translated easily into asymptotic consistency for prediction and estimation. We also establish the variable selection consistency and threshold detection consistency based on the l ∞ bounds. Through Monte Carlo simulations, we show that the thresholded LASSO works reasonably well in finite samples in terms of variable selection, and there is little harmness by the allowance for Fourier approximation in the estimation procedure even when there is no time-varying feature in the threshold. On the contrary, the estimation and variable selection are inconsistent when the threshold is time-varying but being misspecified as a constant. The model is illustrated with an empirical application to the famous debt-growth nexus.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42276293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
W. Barnett, G. Bella, T. Ghosh, P. Mattana, Beatrice Venturi
Abstract In a New Keynesian model, it is believed that combining active monetary policy using a Taylor rule with a passive fiscal rule can achieve local equilibrium determinacy. However, even with such policies, indeterminacy can occur from the emergence of a Shilnikov chaotic attractor in the region of the feasible parameter space. That result, shown by Barnett et al. (2022a), “Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics,” Journal of Economic Dynamics and Control 134, and again by Barnett et al. (2022b), “Is Policy Causing Chaos in the United Kingdom,” Economic Modeling 108, implies that the presence of the Shilnikov chaotic attractor can cause the economy to drift towards and finally become stuck in the vicinity of lower-than-targeted inflation and nominal interest rates. The result can become the source of a liquidity trap phenomenon. We propose policy options for eliminating or controlling Shilnikov chaotic dynamics to help the economy escape from the liquidity trap or avoid drifting into it in the first place. We consider ways to eliminate or control the chaos by replacing the usual Taylor rule by an alternative policy design without interest rate feedback, such as a Taylor rule with monetary quantity feedback, an active fiscal policy rule with passive monetary rule, or an open loop policy without feedback. We also consider approaches that retain the Taylor rule with interest rate feedback and the associated Shilnikov chaos, while controlling the chaos through a well-known engineering algorithm using a second policy instrument. We find that a second instrument is needed to incorporate a long-run terminal condition missing from the usual myopic Taylor rule.
在新凯恩斯主义模型中，采用泰勒规则的积极货币政策与被动财政规则相结合，可以实现局部均衡的确定性。然而，即使采用了这样的策略，在可行参数空间区域中出现希尔尼科夫混沌吸引子也会产生不确定性。Barnett et al. (2022a)《希尔尼科夫混沌、低利率和新凯恩斯主义宏观经济学》(《经济动力学与控制杂志》134)和Barnett et al. (2022b)《英国的政策导致混乱吗》(《经济建模》108)表明，这一结果表明，希尔尼科夫混沌吸引子的存在会导致经济向低于目标的通胀和名义利率附近流动，并最终陷入困境。其结果可能成为流动性陷阱现象的根源。我们提出了消除或控制希尔尼科夫混沌动力学的政策选择，以帮助经济摆脱流动性陷阱或避免在一开始就陷入流动性陷阱。我们考虑用一种没有利率反馈的替代政策设计来取代通常的泰勒规则来消除或控制混乱，例如带有货币数量反馈的泰勒规则，带有被动货币规则的积极财政政策规则，或者没有反馈的开环政策。我们还考虑了保留带有利率反馈的泰勒规则和相关的希尔尼科夫混沌的方法，同时通过使用第二种政策工具的著名工程算法来控制混沌。我们发现需要第二种工具来纳入通常短视的泰勒规则中缺失的长期终末条件。
{"title":"Controlling chaos in New Keynesian macroeconomics","authors":"W. Barnett, G. Bella, T. Ghosh, P. Mattana, Beatrice Venturi","doi":"10.1515/snde-2021-0106","DOIUrl":"https://doi.org/10.1515/snde-2021-0106","url":null,"abstract":"Abstract In a New Keynesian model, it is believed that combining active monetary policy using a Taylor rule with a passive fiscal rule can achieve local equilibrium determinacy. However, even with such policies, indeterminacy can occur from the emergence of a Shilnikov chaotic attractor in the region of the feasible parameter space. That result, shown by Barnett et al. (2022a), “Shilnikov Chaos, Low Interest Rates, and New Keynesian Macroeconomics,” Journal of Economic Dynamics and Control 134, and again by Barnett et al. (2022b), “Is Policy Causing Chaos in the United Kingdom,” Economic Modeling 108, implies that the presence of the Shilnikov chaotic attractor can cause the economy to drift towards and finally become stuck in the vicinity of lower-than-targeted inflation and nominal interest rates. The result can become the source of a liquidity trap phenomenon. We propose policy options for eliminating or controlling Shilnikov chaotic dynamics to help the economy escape from the liquidity trap or avoid drifting into it in the first place. We consider ways to eliminate or control the chaos by replacing the usual Taylor rule by an alternative policy design without interest rate feedback, such as a Taylor rule with monetary quantity feedback, an active fiscal policy rule with passive monetary rule, or an open loop policy without feedback. We also consider approaches that retain the Taylor rule with interest rate feedback and the associated Shilnikov chaos, while controlling the chaos through a well-known engineering algorithm using a second policy instrument. We find that a second instrument is needed to incorporate a long-run terminal condition missing from the usual myopic Taylor rule.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":"27 1","pages":"219 - 236"},"PeriodicalIF":0.8,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43057424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The unemployment is the main channel through which the economic and financial crises influence the social development. In this paper, we propose a mathematical model to study the interactions between financial crisis spread, economic growth and unemployment. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the adverse effects of the financial crisis. The analysis of the model leads us to two equilibria: (1) a stress free equilibrium, where the economy and the employment are optimal, and (2) a stressed equilibrium. We obtain a theoretical confirmation of Okun’s law and a formula to compute the minimum reservation wage in terms of model parameters. Numerical simulations are performed to illustrate the theoretical results obtained.
{"title":"Financial crisis spread, economic growth and unemployment: a mathematical model","authors":"C. Tadmon, Eric Rostand Njike Tchaptchet","doi":"10.1515/snde-2021-0081","DOIUrl":"https://doi.org/10.1515/snde-2021-0081","url":null,"abstract":"Abstract The unemployment is the main channel through which the economic and financial crises influence the social development. In this paper, we propose a mathematical model to study the interactions between financial crisis spread, economic growth and unemployment. We also solve an optimal control problem focusing on the minimization, at the lowest cost, of the adverse effects of the financial crisis. The analysis of the model leads us to two equilibria: (1) a stress free equilibrium, where the economy and the employment are optimal, and (2) a stressed equilibrium. We obtain a theoretical confirmation of Okun’s law and a formula to compute the minimum reservation wage in terms of model parameters. Numerical simulations are performed to illustrate the theoretical results obtained.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":"27 1","pages":"147 - 170"},"PeriodicalIF":0.8,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44374923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We perform an extensive investigation of different specifications of the BEKK-type multivariate volatility models for a moderate number of assets, focusing on how the degree of parametrization affects forecasting performance. Because the unrestricted specification may be too generously parameterized, often one imposes restrictions on coefficient matrices constraining them to have a diagonal or even scalar structure. We frame all three model variations (full, diagonal, scalar) as special cases of a ridge-type regularized estimator, where the off-diagonal elements are shrunk towards zero and the diagonal elements are shrunk towards homogeneity. Our forecasting experiments with BEKK-type Conditional Autoregressive Wishart model for realized volatility confirm the superiority of the more parsimonious scalar and diagonal model variations. Even though sometimes a moderate degree of regularization of the diagonal and off-diagonal parameters may be beneficial for forecasting performance, it does not regularly lead to tangible performance improvements irrespective of how precise is tuning of regularization intensity. Additionally, our results highlight the crucial importance of frequent model re-estimation in improving the forecast precision, and, perhaps paradoxically, a slight advantage of shorter estimation windows compared to longer windows.
{"title":"Unrestricted, restricted, and regularized models for forecasting multivariate volatility","authors":"Stanislav Anatolyev, Filip Staněk","doi":"10.1515/snde-2021-0064","DOIUrl":"https://doi.org/10.1515/snde-2021-0064","url":null,"abstract":"Abstract We perform an extensive investigation of different specifications of the BEKK-type multivariate volatility models for a moderate number of assets, focusing on how the degree of parametrization affects forecasting performance. Because the unrestricted specification may be too generously parameterized, often one imposes restrictions on coefficient matrices constraining them to have a diagonal or even scalar structure. We frame all three model variations (full, diagonal, scalar) as special cases of a ridge-type regularized estimator, where the off-diagonal elements are shrunk towards zero and the diagonal elements are shrunk towards homogeneity. Our forecasting experiments with BEKK-type Conditional Autoregressive Wishart model for realized volatility confirm the superiority of the more parsimonious scalar and diagonal model variations. Even though sometimes a moderate degree of regularization of the diagonal and off-diagonal parameters may be beneficial for forecasting performance, it does not regularly lead to tangible performance improvements irrespective of how precise is tuning of regularization intensity. Additionally, our results highlight the crucial importance of frequent model re-estimation in improving the forecast precision, and, perhaps paradoxically, a slight advantage of shorter estimation windows compared to longer windows.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":"27 1","pages":"199 - 218"},"PeriodicalIF":0.8,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48805424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this work we study the effects by including threshold, constant and time-dependent correlation in stochastic volatility (SV) models to capture the asymmetry relationship between stock returns and volatility. We develop SV models which include only time-dependent correlated innovations and both threshold and time-dependent correlation, respectively. It has been shown in literature that the SV model with only constant correlation does a better job of capturing asymmetry than threshold stochastic volatility (TSV) model. We show here that the SV model with time-dependent correlation performs better than the model with constant correlation on capturing asymmetry, and the comprehensive model with both threshold and time-dependently correlated innovations dominates models with pure threshold, constant and time-dependent correlation, and both threshold and constant correlation as well. In our comprehensive model, volatility and returns are time-dependently correlated, where the time-varying correlation is negative, and the volatility is more persistent, less volatile and higher following negative returns as expected. An empirical study is provided to illustrate our findings.
{"title":"Asymmetry in stochastic volatility models with threshold and time-dependent correlation","authors":"Torben Schäfers, Long Teng","doi":"10.1515/snde-2021-0020","DOIUrl":"https://doi.org/10.1515/snde-2021-0020","url":null,"abstract":"Abstract In this work we study the effects by including threshold, constant and time-dependent correlation in stochastic volatility (SV) models to capture the asymmetry relationship between stock returns and volatility. We develop SV models which include only time-dependent correlated innovations and both threshold and time-dependent correlation, respectively. It has been shown in literature that the SV model with only constant correlation does a better job of capturing asymmetry than threshold stochastic volatility (TSV) model. We show here that the SV model with time-dependent correlation performs better than the model with constant correlation on capturing asymmetry, and the comprehensive model with both threshold and time-dependently correlated innovations dominates models with pure threshold, constant and time-dependent correlation, and both threshold and constant correlation as well. In our comprehensive model, volatility and returns are time-dependently correlated, where the time-varying correlation is negative, and the volatility is more persistent, less volatile and higher following negative returns as expected. An empirical study is provided to illustrate our findings.","PeriodicalId":46709,"journal":{"name":"Studies in Nonlinear Dynamics and Econometrics","volume":"27 1","pages":"131 - 146"},"PeriodicalIF":0.8,"publicationDate":"2022-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41864136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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