Pub Date : 2022-12-01DOI: 10.1017/S0266466622000524
D. Andrews, Y. Kitamura, G. Kuersteiner
This is the second part of a dual-issue special edition of Econometric Theory in honor of Peter C.B. Phillips. The papers published in these two issues grew out of presentations given at the Cowles Foundation Conference on Econometrics: A Celebration of Peter Phillips’s 40 Years at Yale. Peter C.B. Phillips, the founding editor of this journal, joined Yale University in 1979 where he served as full professor and one of the leading intellects of the Department of Economics for more than 40 years. At the time of his joining the Cowles Foundation and Yale economics faculty, Phillips already had been chair of the Department of Econometrics and Social Statistics at the University of Birmingham and held prior faculty positions at the University of Essex and the University of Auckland. He earned a master’s degree in economics from the University of Auckland under the supervision of A.R. Bergstrom, one of the leading authorities on continuous-time modeling and inference at the time; and his master’s thesis was published in Econometrica in 1972. Phillips studied at the London School of Economics where he obtained his Ph.D. with a dissertation on
这是《计量经济学理论》两期特别版的第二部分，以纪念彼得·c·b·菲利普斯。在这两期杂志上发表的论文都是在考尔斯基金会计量经济学会议上发表的:庆祝彼得·菲利普斯在耶鲁大学40周年。彼得·c·b·菲利普斯，本刊创刊编辑，1979年加入耶鲁大学，担任经济系正教授和领军人物40多年。在他加入考尔斯基金会和耶鲁大学经济学教授时，菲利普斯已经是伯明翰大学计量经济学和社会统计系主任，并在埃塞克斯大学和奥克兰大学担任教职。他在奥克兰大学(University of Auckland)获得经济学硕士学位，师从当时连续时间建模和推理领域的主要权威之一A.R. Bergstrom;1972年在《计量经济学》上发表硕士论文。菲利普斯曾就读于伦敦经济学院，在那里他获得了博士学位
{"title":"GUEST EDITORS’ INTRODUCTION PART TWO: SPECIAL DUAL ISSUE OF ECONOMETRIC THEORY ON YALE 2018 CONFERENCE IN HONOR OF PETER C.B. PHILLIPS","authors":"D. Andrews, Y. Kitamura, G. Kuersteiner","doi":"10.1017/S0266466622000524","DOIUrl":"https://doi.org/10.1017/S0266466622000524","url":null,"abstract":"This is the second part of a dual-issue special edition of Econometric Theory in honor of Peter C.B. Phillips. The papers published in these two issues grew out of presentations given at the Cowles Foundation Conference on Econometrics: A Celebration of Peter Phillips’s 40 Years at Yale. Peter C.B. Phillips, the founding editor of this journal, joined Yale University in 1979 where he served as full professor and one of the leading intellects of the Department of Economics for more than 40 years. At the time of his joining the Cowles Foundation and Yale economics faculty, Phillips already had been chair of the Department of Econometrics and Social Statistics at the University of Birmingham and held prior faculty positions at the University of Essex and the University of Auckland. He earned a master’s degree in economics from the University of Auckland under the supervision of A.R. Bergstrom, one of the leading authorities on continuous-time modeling and inference at the time; and his master’s thesis was published in Econometrica in 1972. Phillips studied at the London School of Economics where he obtained his Ph.D. with a dissertation on","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":"38 1","pages":"1069 - 1072"},"PeriodicalIF":0.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44213637","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 : 2022-11-11DOI: 10.1017/s0266466622000433
Yukitoshi Matsushita, Taisuke Otsu
This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sample size, (ii) arbitrarily weak instruments, and (iii) heteroskedastic errors. In contrast to Crudu, Mellace, and Sándor (2021, Econometric Theory 37, 281–310) and Mikusheva and Sun (2021, Review of Economic Studies 89, 2663–2686), who proposed jackknife Anderson–Rubin tests that are also robust to (i)–(iii), we modify a score statistic by jackknifing and construct its heteroskedasticity robust variance estimator. Compared to the Lagrange multiplier tests by Kleibergen (2002, Econometrica 70, 1781–1803) and Moreira (2001, Tests with Correct Size when Instruments Can Be Arbitrarily Weak, Working paper) and their modification for many instruments by Hansen, Hausman, and Newey (2008, Journal of Business & Economic Statistics 26, 398–422), our JLM test is robust to heteroskedastic errors and may circumvent a possible decrease in the power function. Simulation results illustrate the desirable size and power properties of the proposed method.
本文提出了一种用于工具变量回归模型的jackknife拉格朗日乘子（JLM）检验，该检验对（i）许多工具具有鲁棒性，其中工具的数量可能随着样本量成比例增加，（ii）任意弱工具，以及（iii）异基误差。与Crudu、Mellace和Sándor（2021，计量经济学理论37281-310）以及Mikusheva和Sun（2021，经济研究综述892663-2686）相比，他们提出了对（i）-（iii）也具有鲁棒性的jackknife-Anderson–Rubin检验，我们通过Jackknifeng修改了分数统计，并构建了其异方差稳健方差估计器。与Kleibergen（2002，Econometrica 701781-1803）和Moreira（2001，仪器可以任意弱时的正确大小测试，工作论文）的拉格朗日乘数测试及其对Hansen、Hausman和Newey（2008，Journal of Business&Economic Statistics 26398–422）的许多仪器的修改相比，我们的JLM测试对异方差是鲁棒的，并且可以避免幂函数的可能降低。仿真结果说明了所提出方法的理想尺寸和功率特性。
{"title":"A JACKKNIFE LAGRANGE MULTIPLIER TEST WITH MANY WEAK INSTRUMENTS","authors":"Yukitoshi Matsushita, Taisuke Otsu","doi":"10.1017/s0266466622000433","DOIUrl":"https://doi.org/10.1017/s0266466622000433","url":null,"abstract":"This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sample size, (ii) arbitrarily weak instruments, and (iii) heteroskedastic errors. In contrast to Crudu, Mellace, and Sándor (2021, Econometric Theory 37, 281–310) and Mikusheva and Sun (2021, Review of Economic Studies 89, 2663–2686), who proposed jackknife Anderson–Rubin tests that are also robust to (i)–(iii), we modify a score statistic by jackknifing and construct its heteroskedasticity robust variance estimator. Compared to the Lagrange multiplier tests by Kleibergen (2002, Econometrica 70, 1781–1803) and Moreira (2001, Tests with Correct Size when Instruments Can Be Arbitrarily Weak, Working paper) and their modification for many instruments by Hansen, Hausman, and Newey (2008, Journal of Business & Economic Statistics 26, 398–422), our JLM test is robust to heteroskedastic errors and may circumvent a possible decrease in the power function. Simulation results illustrate the desirable size and power properties of the proposed method.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44104873","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 : 2022-11-10DOI: 10.1017/s0266466622000536
Federico Carlini, P. Gagliardini
We study semiparametric inference in a small-dimensional vector autoregressive (VAR) model of order p augmented by unobservable common factors with a dynamic described by a VAR process of order q. This state-space specification is useful to measure separately the direct causality effects and the responses to dynamic common factors. We show that the state-space parameters are identifiable from the autocovariance function of the observed process. We estimate the model by means of a multistep procedure in closed-form, which combines an eigenvalue–eigenvector matrix decomposition and a linear instrumental variable estimation allowing for Hansen–Sargan specification tests. We study the asymptotic and finite-sample properties of the parameter estimators and of rank tests for selecting the number of unobservable factors and VAR orders. In an empirical illustration, we investigate the dynamic common factors and the spillover effects that explain the co-movements among the log daily realized volatilities of four European stock market indices.
{"title":"INSTRUMENTAL VARIABLES INFERENCE IN A SMALL-DIMENSIONAL VAR MODEL WITH DYNAMIC LATENT FACTORS","authors":"Federico Carlini, P. Gagliardini","doi":"10.1017/s0266466622000536","DOIUrl":"https://doi.org/10.1017/s0266466622000536","url":null,"abstract":"We study semiparametric inference in a small-dimensional vector autoregressive (VAR) model of order p augmented by unobservable common factors with a dynamic described by a VAR process of order q. This state-space specification is useful to measure separately the direct causality effects and the responses to dynamic common factors. We show that the state-space parameters are identifiable from the autocovariance function of the observed process. We estimate the model by means of a multistep procedure in closed-form, which combines an eigenvalue–eigenvector matrix decomposition and a linear instrumental variable estimation allowing for Hansen–Sargan specification tests. We study the asymptotic and finite-sample properties of the parameter estimators and of rank tests for selecting the number of unobservable factors and VAR orders. In an empirical illustration, we investigate the dynamic common factors and the spillover effects that explain the co-movements among the log daily realized volatilities of four European stock market indices.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44427873","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 : 2022-11-10DOI: 10.1017/s0266466622000585
Donggyu Kim
This paper introduces a novel Itô diffusion process to model high-frequency financial data that can accommodate low-frequency volatility dynamics by embedding the discrete-time nonlinear exponential generalized autoregressive conditional heteroskedasticity (GARCH) structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Itô models, the instantaneous volatility process has a nonlinear structure, which ensures that the log-integrated volatilities have the realized GARCH structure. We call this the exponential realized GARCH-Itô model. Given the autoregressive structure of the log-integrated volatility, we propose a quasi-likelihood estimation procedure for parameter estimation and establish its asymptotic properties. We conduct a simulation study to check the finite-sample performance of the proposed model and an empirical study with 50 assets among the S&P 500 compositions. Numerical studies show the advantages of the proposed model.
{"title":"EXPONENTIAL REALIZED GARCH-ITÔ VOLATILITY MODELS","authors":"Donggyu Kim","doi":"10.1017/s0266466622000585","DOIUrl":"https://doi.org/10.1017/s0266466622000585","url":null,"abstract":"This paper introduces a novel Itô diffusion process to model high-frequency financial data that can accommodate low-frequency volatility dynamics by embedding the discrete-time nonlinear exponential generalized autoregressive conditional heteroskedasticity (GARCH) structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Itô models, the instantaneous volatility process has a nonlinear structure, which ensures that the log-integrated volatilities have the realized GARCH structure. We call this the exponential realized GARCH-Itô model. Given the autoregressive structure of the log-integrated volatility, we propose a quasi-likelihood estimation procedure for parameter estimation and establish its asymptotic properties. We conduct a simulation study to check the finite-sample performance of the proposed model and an empirical study with 50 assets among the S&P 500 compositions. Numerical studies show the advantages of the proposed model.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44453626","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 : 2022-11-07DOI: 10.1017/s026646662200055x
C. Baumeister, James D. Hamilton
This paper surveys recent advances in drawing structural conclusions from vector autoregressions (VARs), providing a unified perspective on the role of prior knowledge. We describe the traditional approach to identification as a claim to have exact prior information about the structural model and propose Bayesian inference as a way to acknowledge that prior information is imperfect or subject to error. We raise concerns from both a frequentist and a Bayesian perspective about the way that results are typically reported for VARs that are set-identified using sign and other restrictions. We call attention to a common but previously unrecognized error in estimating structural elasticities and show how to correctly estimate elasticities even in the case when one only knows the effects of a single structural shock.
{"title":"ADVANCES IN USING VECTOR AUTOREGRESSIONS TO ESTIMATE STRUCTURAL MAGNITUDES","authors":"C. Baumeister, James D. Hamilton","doi":"10.1017/s026646662200055x","DOIUrl":"https://doi.org/10.1017/s026646662200055x","url":null,"abstract":"This paper surveys recent advances in drawing structural conclusions from vector autoregressions (VARs), providing a unified perspective on the role of prior knowledge. We describe the traditional approach to identification as a claim to have exact prior information about the structural model and propose Bayesian inference as a way to acknowledge that prior information is imperfect or subject to error. We raise concerns from both a frequentist and a Bayesian perspective about the way that results are typically reported for VARs that are set-identified using sign and other restrictions. We call attention to a common but previously unrecognized error in estimating structural elasticities and show how to correctly estimate elasticities even in the case when one only knows the effects of a single structural shock.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46652095","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 : 2022-11-07DOI: 10.1017/s0266466622000548
Ruoyao Shi
In a two-step extremum estimation (M-estimation) framework with a finite-dimensional parameter of interest and a potentially infinite-dimensional first-step nuisance parameter, this paper proposes an averaging estimator that combines a semiparametric estimator based on a nonparametric first step and a parametric estimator which imposes parametric restrictions on the first step. The averaging weight is an easy-to-compute sample analog of an infeasible optimal weight that minimizes the asymptotic quadratic risk. Under Stein-type conditions, the asymptotic lower bound of the truncated quadratic risk difference between the averaging estimator and the semiparametric estimator is strictly less than zero for a class of data generating processes that includes both correct specification and varied degrees of misspecification of the parametric restrictions, and the asymptotic upper bound is weakly less than zero. The averaging estimator, along with an easy-to-implement inference method, is demonstrated in an example.
{"title":"AN AVERAGING ESTIMATOR FOR TWO-STEP M-ESTIMATION IN SEMIPARAMETRIC MODELS","authors":"Ruoyao Shi","doi":"10.1017/s0266466622000548","DOIUrl":"https://doi.org/10.1017/s0266466622000548","url":null,"abstract":"In a two-step extremum estimation (M-estimation) framework with a finite-dimensional parameter of interest and a potentially infinite-dimensional first-step nuisance parameter, this paper proposes an averaging estimator that combines a semiparametric estimator based on a nonparametric first step and a parametric estimator which imposes parametric restrictions on the first step. The averaging weight is an easy-to-compute sample analog of an infeasible optimal weight that minimizes the asymptotic quadratic risk. Under Stein-type conditions, the asymptotic lower bound of the truncated quadratic risk difference between the averaging estimator and the semiparametric estimator is strictly less than zero for a class of data generating processes that includes both correct specification and varied degrees of misspecification of the parametric restrictions, and the asymptotic upper bound is weakly less than zero. The averaging estimator, along with an easy-to-implement inference method, is demonstrated in an example.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46740439","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 : 2022-10-28DOI: 10.1017/s0266466622000512
Yoonseok Lee, Yulong Wang
This paper develops a test for homogeneity of the threshold parameter in threshold regression models. The test has a natural interpretation from time series perspectives and can also be applied to test for additional change points in the structural break models. The limiting distribution of the test statistic is derived, and the finite sample properties are studied in Monte Carlo simulations. We apply the new test to the tipping point problem studied by Card, Mas, and Rothstein (2008, Quarterly Journal of Economics 123, 177–218) and statistically justify that the location of the tipping point varies across tracts.
本文提出了阈值回归模型中阈值参数均匀性的检验方法。该测试具有从时间序列角度的自然解释，并且也可以应用于测试结构断裂模型中的附加变化点。推导了检验统计量的极限分布，并在蒙特卡罗模拟中研究了有限样本特性。我们将新的检验应用于Card、Mas和Rothstein (2008, Quarterly Journal of Economics, 123, 177-218)研究的临界点问题，并从统计上证明了临界点的位置在不同地区是不同的。
{"title":"TESTING FOR HOMOGENEOUS THRESHOLDS IN THRESHOLD REGRESSION MODELS","authors":"Yoonseok Lee, Yulong Wang","doi":"10.1017/s0266466622000512","DOIUrl":"https://doi.org/10.1017/s0266466622000512","url":null,"abstract":"This paper develops a test for homogeneity of the threshold parameter in threshold regression models. The test has a natural interpretation from time series perspectives and can also be applied to test for additional change points in the structural break models. The limiting distribution of the test statistic is derived, and the finite sample properties are studied in Monte Carlo simulations. We apply the new test to the tipping point problem studied by Card, Mas, and Rothstein (2008, Quarterly Journal of Economics 123, 177–218) and statistically justify that the location of the tipping point varies across tracts.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44588083","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 : 2022-10-28DOI: 10.1017/s0266466622000469
M. Carrasco, Ada Nayihouba
In a dynamic panel data model, the number of moment conditions increases rapidly with the time dimension, resulting in a large dimensional covariance matrix of the instruments. As a consequence, the generalized method of moments (GMM) estimator exhibits a large bias in small samples, especially when the autoregressive parameter is close to unity. To address this issue, we propose a regularized version of the one-step GMM estimator using three regularization schemes based on three different ways of inverting the covariance matrix of the instruments. Under double asymptotics, we show that our regularized estimators are consistent and asymptotically normal. These regularization schemes involve a tuning or regularization parameter which needs to be chosen. We derive a data-driven selection of this regularization parameter based on an approximation of the higher-order mean square error and show its optimality. As an empirical application, we estimate a model of income dynamics.
{"title":"REGULARIZED ESTIMATION OF DYNAMIC PANEL MODELS","authors":"M. Carrasco, Ada Nayihouba","doi":"10.1017/s0266466622000469","DOIUrl":"https://doi.org/10.1017/s0266466622000469","url":null,"abstract":"\u0000 In a dynamic panel data model, the number of moment conditions increases rapidly with the time dimension, resulting in a large dimensional covariance matrix of the instruments. As a consequence, the generalized method of moments (GMM) estimator exhibits a large bias in small samples, especially when the autoregressive parameter is close to unity. To address this issue, we propose a regularized version of the one-step GMM estimator using three regularization schemes based on three different ways of inverting the covariance matrix of the instruments. Under double asymptotics, we show that our regularized estimators are consistent and asymptotically normal. These regularization schemes involve a tuning or regularization parameter which needs to be chosen. We derive a data-driven selection of this regularization parameter based on an approximation of the higher-order mean square error and show its optimality. As an empirical application, we estimate a model of income dynamics.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45075103","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 : 2022-10-28DOI: 10.1017/s0266466622000494
Zhonghao Fu, Shang Gao, Liangjun Su, Xia Wang
This paper proposes a model-free test for the strict stationarity of a potentially vector-valued time series using the discrete Fourier transform (DFT) approach. We show that the DFT of a residual process based on the empirical characteristic function weakly converges to a zero spectrum in the frequency domain for a strictly stationary time series and a nonzero spectrum otherwise. The proposed test is powerful against various types of nonstationarity including deterministic trends and smooth or abrupt structural changes. It does not require smoothed nonparametric estimation and, thus, can detect the Pitman sequence of local alternatives at the parametric rate $T^{-1/2}$ , faster than all existing nonparametric tests. We also design a class of derivative tests based on the characteristic function to test the stationarity in various moments. Monte Carlo studies demonstrate that our test has reasonarble size and excellent power. Our empirical application of exchange rates strongly suggests that both nominal and real exchange rate returns are nonstationary, which the augmented Dickey–Fuller and Kwiatkowski–Phillips–Schmidt–Shin tests may overlook.
{"title":"TESTING FOR STRICT STATIONARITY VIA THE DISCRETE FOURIER TRANSFORM","authors":"Zhonghao Fu, Shang Gao, Liangjun Su, Xia Wang","doi":"10.1017/s0266466622000494","DOIUrl":"https://doi.org/10.1017/s0266466622000494","url":null,"abstract":"This paper proposes a model-free test for the strict stationarity of a potentially vector-valued time series using the discrete Fourier transform (DFT) approach. We show that the DFT of a residual process based on the empirical characteristic function weakly converges to a zero spectrum in the frequency domain for a strictly stationary time series and a nonzero spectrum otherwise. The proposed test is powerful against various types of nonstationarity including deterministic trends and smooth or abrupt structural changes. It does not require smoothed nonparametric estimation and, thus, can detect the Pitman sequence of local alternatives at the parametric rate $T^{-1/2}$ , faster than all existing nonparametric tests. We also design a class of derivative tests based on the characteristic function to test the stationarity in various moments. Monte Carlo studies demonstrate that our test has reasonarble size and excellent power. Our empirical application of exchange rates strongly suggests that both nominal and real exchange rate returns are nonstationary, which the augmented Dickey–Fuller and Kwiatkowski–Phillips–Schmidt–Shin tests may overlook.","PeriodicalId":49275,"journal":{"name":"Econometric Theory","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45740363","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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