Pub Date : 2023-05-17DOI: 10.1017/s0266466623000154
Jean-Yves Pitarakis
We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample mean squared error loss differentials between the two competing models, leads to nuisance parameter-free Gaussian asymptotics, and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g., stationary and local to unit root). A local power analysis also establishes their ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes.
{"title":"A NOVEL APPROACH TO PREDICTIVE ACCURACY TESTING IN NESTED ENVIRONMENTS","authors":"Jean-Yves Pitarakis","doi":"10.1017/s0266466623000154","DOIUrl":"https://doi.org/10.1017/s0266466623000154","url":null,"abstract":"We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample mean squared error loss differentials between the two competing models, leads to nuisance parameter-free Gaussian asymptotics, and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g., stationary and local to unit root). A local power analysis also establishes their ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135813115","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}
Pub Date : 2023-05-12DOI: 10.1017/s0266466623000142
C. Francq, Baye Matar Kandji, J. Zakoian
In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real financial data.
{"title":"INFERENCE ON GARCH-MIDAS MODELS WITHOUT ANY SMALL-ORDER MOMENT","authors":"C. Francq, Baye Matar Kandji, J. Zakoian","doi":"10.1017/s0266466623000142","DOIUrl":"https://doi.org/10.1017/s0266466623000142","url":null,"abstract":"In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real financial data.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48099360","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}
Pub Date : 2023-05-03DOI: 10.1017/s0266466623000117
Rustam Ibragimov, Jihyun Kim, Anton Skrobotov
We propose a robust inference method for predictive regression models under heterogeneously persistent volatility as well as endogeneity, persistence, or heavy-tailedness of regressors. This approach relies on two methodologies, nonlinear instrumental variable estimation and volatility correction, which are used to deal with the aforementioned characteristics of regressors and volatility, respectively. Our method is simple to implement and is applicable both in the case of continuous and discrete time models. According to our simulation study, the proposed method performs well compared with widely used alternative inference procedures in terms of its finite sample properties in various dependence and persistence settings observed in real-world financial and economic markets.
{"title":"NEW ROBUST INFERENCE FOR PREDICTIVE REGRESSIONS","authors":"Rustam Ibragimov, Jihyun Kim, Anton Skrobotov","doi":"10.1017/s0266466623000117","DOIUrl":"https://doi.org/10.1017/s0266466623000117","url":null,"abstract":"We propose a robust inference method for predictive regression models under heterogeneously persistent volatility as well as endogeneity, persistence, or heavy-tailedness of regressors. This approach relies on two methodologies, nonlinear instrumental variable estimation and volatility correction, which are used to deal with the aforementioned characteristics of regressors and volatility, respectively. Our method is simple to implement and is applicable both in the case of continuous and discrete time models. According to our simulation study, the proposed method performs well compared with widely used alternative inference procedures in terms of its finite sample properties in various dependence and persistence settings observed in real-world financial and economic markets.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134922892","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}
Pub Date : 2023-05-02DOI: 10.1017/s0266466623000130
Deborah Kim
This article analyzes the theoretical properties of the hybrid test for superior predictive ability. A simple example reveals that the test may not be size-controlled at common significance levels with rejection rates exceeding $11%$ at a $5%$ nominal level. Generalizing this observation, the main results show the pointwise asymptotic invalidity of the hybrid test under reasonable conditions. Monte Carlo simulations support these theoretical findings.
{"title":"ON THE SIZE CONTROL OF THE HYBRID TEST FOR SUPERIOR PREDICTIVE ABILITY","authors":"Deborah Kim","doi":"10.1017/s0266466623000130","DOIUrl":"https://doi.org/10.1017/s0266466623000130","url":null,"abstract":"This article analyzes the theoretical properties of the hybrid test for superior predictive ability. A simple example reveals that the test may not be size-controlled at common significance levels with rejection rates exceeding \u0000\u0000 \u0000 \u0000 \u0000$11%$\u0000\u0000 \u0000 at a \u0000\u0000 \u0000 \u0000 \u0000$5%$\u0000\u0000 \u0000 nominal level. Generalizing this observation, the main results show the pointwise asymptotic invalidity of the hybrid test under reasonable conditions. Monte Carlo simulations support these theoretical findings.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42194809","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}
Pub Date : 2023-04-24DOI: 10.1017/s0266466623000105
Wiji Arulampalam, Valentina Corradi, Daniel Gutknecht
We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then consider the case in which the monotonic index restriction does not hold and/or the set of observations with a propensity score close to one is thin so that convergence occurs at a rate that is arbitrarily close to the cubic rate. We explore the finite sample behavior in a Monte Carlo study and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity.
{"title":"INTERCEPT ESTIMATION IN NONLINEAR SELECTION MODELS","authors":"Wiji Arulampalam, Valentina Corradi, Daniel Gutknecht","doi":"10.1017/s0266466623000105","DOIUrl":"https://doi.org/10.1017/s0266466623000105","url":null,"abstract":"We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then consider the case in which the monotonic index restriction does not hold and/or the set of observations with a propensity score close to one is thin so that convergence occurs at a rate that is arbitrarily close to the cubic rate. We explore the finite sample behavior in a Monte Carlo study and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135223075","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}
Pub Date : 2023-04-24DOI: 10.1017/s0266466623000129
Junlong Feng
This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in the quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of interactive fixed effects at any quantile level. We demonstrate the performance of the estimator via Monte Carlo simulations.
{"title":"NUCLEAR NORM REGULARIZED QUANTILE REGRESSION WITH INTERACTIVE FIXED EFFECTS","authors":"Junlong Feng","doi":"10.1017/s0266466623000129","DOIUrl":"https://doi.org/10.1017/s0266466623000129","url":null,"abstract":"This paper studies large N and large T conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the interactive fixed effects. The estimator solves a convex minimization problem, not requiring pre-estimation of the (number of) interactive fixed effects. It also allows the number of covariates to grow slowly with N and T. We derive an error bound on the estimator that holds uniformly in the quantile level. The order of the bound implies uniform consistency of the estimator and is nearly optimal for the low-rank component. Given the error bound, we also propose a consistent estimator of the number of interactive fixed effects at any quantile level. We demonstrate the performance of the estimator via Monte Carlo simulations.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47009294","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}
Pub Date : 2023-04-20DOI: 10.1017/s0266466623000233
Y. Hoga
Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for systemic risk as measured by the marginal expected shortfall (MES). It is based on first de-volatilizing the observations and, then, calculating systemic risk for the residuals using an estimator based on extreme value theory. We show the validity of the method by establishing the asymptotic normality of the MES forecasts. The good finite-sample coverage of the implied MES forecast intervals is confirmed in simulations. An empirical application to major U.S. banks illustrates the significant time variation in the precision of MES forecasts, and explores the implications of this fact from a regulatory perspective.
{"title":"THE ESTIMATION RISK IN EXTREME SYSTEMIC RISK FORECASTS","authors":"Y. Hoga","doi":"10.1017/s0266466623000233","DOIUrl":"https://doi.org/10.1017/s0266466623000233","url":null,"abstract":"Systemic risk measures have been shown to be predictive of financial crises and declines in real activity. Thus, forecasting them is of major importance in finance and economics. In this paper, we propose a new forecasting method for systemic risk as measured by the marginal expected shortfall (MES). It is based on first de-volatilizing the observations and, then, calculating systemic risk for the residuals using an estimator based on extreme value theory. We show the validity of the method by establishing the asymptotic normality of the MES forecasts. The good finite-sample coverage of the implied MES forecast intervals is confirmed in simulations. An empirical application to major U.S. banks illustrates the significant time variation in the precision of MES forecasts, and explores the implications of this fact from a regulatory perspective.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44672832","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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