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Estimating the variance of a combined forecast: Bootstrap-based approach

JOURNAL OF econometrics 2023年第2期232卷 445-468页

作者： Hounyo, Ulrich Lahiri, Kajal SUNY Albany Dept Econ Albany NY 12222 USA CREATES Aarhus Denmark

This paper considers bootstrap inference in model averaging for predictive regressions. We first show that the standard pairwise bootstrap is not valid in the context of model averaging. This common bootstrap approach induces a bias-related term in the bootstrap variance of averaging estimators. We then propose and justify a fixed-design residual-based bootstrap resampling approach for model averaging. In a local asymptotic framework, we show the validity of the bootstrap in estimating the variance of a combined forecast and the asymptotic covariance matrix of a combined parameter vector with fixed weights. Our proposed method preserves non-parametrically the crosssectional dependence between different models and the time series dependence in the errors simultaneously. The finite sample performance of these methods is assessed via Monte Carlo simulations. We illustrate our approach using an empirical study of the Taylor rule equation with 24 alternative specifications.& COPY;2021 Elsevier B.V. All rights reserved.

关键词： Bootstrap Local asymptotic theory Model average estimators Wild bootstrap Variance of consensus forecast

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Prewhitened long-run variance estimation robust to nonstationarity

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JOURNAL OF econometrics 2024年第1期242卷

作者： Casini, Alessandro Perron, Pierre Univ Roma Tor Vergata Dept Econ & Finance Via Columbia 2 I-00133 Rome Italy Boston Univ Dept Econ 270 Bay State Rd Boston MA 02215 USA

We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite- sample properties under nonstationarity (i.e., fixed-b b methods), or are theoretically valid under the null hypothesis but lead to tests that are not consistent under nonstationary alternative hypothesis (i.e., both fixed-b b and traditional HAC estimators). The proposed estimator accounts explicitly for nonstationarity, unlike previous prewhitened procedures which are known to be unreliable, and leads to tests with accurate null rejection rates and good monotonic power. We also establish MSE bounds for LRV estimation that are sharper than previously established and use them to determine the data-dependent bandwidths.

关键词： asymptotic minimax MSE Data-dependent bandwidths HAC HAR Long-run variance Nonstationarity Prewhitening Spectral density

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asymptotic properties of Bayesian inference in linear regression with a structural break

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JOURNAL OF econometrics 2023年第1期235卷 202-219页

作者： Shimizu, Kenichi Univ Glasgow Adam Smith Business Sch Glasgow Scotland Univ Ave Glasgow G12 8QQ Scotland

This paper studies large sample properties of a Bayesian approach to inference about slope parameters gamma in linear regression models with a structural break. In contrast to the conventional approach to inference about gamma that does not take into account the uncertainty of the unknown break date, the Bayesian approach that we consider incorporates such uncertainty. Our main theoretical contribution is a Bernstein-von Mises type theorem (Bayesian asymptotic normality) for gamma under a wide class of priors, which essentially indicates an asymptotic equivalence between the conventional frequentist and Bayesian inference. Consequently, a frequentist researcher could look at credible intervals of gamma to check robustness with respect to the uncertainty of the break date. Simulation studies show that the conventional confidence intervals of gamma tend to undercover in finite samples whereas the credible intervals offer more reasonable coverages in general. As the sample size increases, the two methods coincide, as predicted from our theoretical conclusion. Using data from Paye and Timmermann (2006) on stock return prediction, we illustrate that the traditional confidence intervals on gamma might underrepresent the true sampling uncertainty.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://***/licenses/by/4.0/).

关键词： Structural break Bernstein-von Mises theorem Sensitivity check Model averaging

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Sparse quantile regression

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JOURNAL OF econometrics 2023年第2期235卷 2195-2217页

作者： Chen, Le-Yu Lee, Sokbae Acad Sinica Inst Econ Taipei City Taiwan Columbia Univ Dept Econ New York NY 10027 USA Inst Fiscal Studies Ctr Microdata Methods & Practice London England

We consider both l0-penalized and l0-constrained quantile regression estimators. For the l0-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and apply it to obtain non-asymptotic upper bounds on the mean-square parameter and regression function estimation errors. We also derive analogous results for the l0-constrained estimator. The resulting rates of convergence are nearly minimax-optimal and the same as those for l1-penalized and non-convex penalized estimators. Further, we characterize expected Hamming loss for the l0- penalized estimator. We implement the proposed procedure via mixed integer linear programming and also a more scalable first-order approximation algorithm. We illustrate the finite-sample performance of our approach in Monte Carlo experiments and its usefulness in a real data application concerning conformal prediction of infant birth weights (with n & AP;103 and up to p > 103). In sum, our l0-based method produces a much sparser estimator than the l1-penalized and non-convex penalized approaches without compromising precision. & COPY;2023 Elsevier B.V. All rights reserved.

关键词： Quantile regression Sparse estimation Mixed integer optimization finite sample property Conformal prediction Hamming distance

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asymptotic theory for a stochastic unit root model

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COMMUNICATIONS IN STATISTICS-THEORY AND methods 2022年第5期51卷 1461-1487页

作者： Du, Lingjie Pang, Tianxiao Zhejiang Univ Sch Math Sci Hangzhou 310027 Peoples R China

Lieberman and Phillips (Journal of Time Series Analysis) proposed a stochastic unit root model in which the source of the variation of the autoregressive coefficient is driven by a stationary process. More recently, Lieberman and Phillips (Journal of econometrics) generalized this model to the multivariate case and a hybrid case. Their studies revealed that these stochastic unit root models lead to a generalization of the Black-Scholes formula for derivative pricing. Inspired by their studies, in this paper, we propose a new stochastic unit root model, in which the source of the variation of the autoregressive coefficient is driven by a (nearly) non-stationary process. The asymptotic theory for this model is established. Our study reveals some new findings which are different from those established by Lieberman and Phillips. Results of Monte Carlo simulations are given to illustrate the finite-sample performance of estimators in the model. Moreover, a comparison between the stochastic unit root model proposed by Lieberman and Phillips and that proposed in this paper is conducted via an empirical study.

关键词： asymptotic distribution nonlinear least squares estimator non-stationary stochastic unit root

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Misclassification-robust semiparametric estimation of single-index binary-choice models

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econometrics JOURNAL 2022年第2期25卷 433-454页

作者： Cizek, P. Sadikoglu, S. Tilburg Univ Dept Econometr & OR NL-5000 LE Tilburg Noord Brabant Netherlands

In this paper, a new class of semiparametric estimators for single-index binary-choice models is introduced. The proposed estimators are based on the semiparametric indirect inference that identifies and estimates the parameters of the model via possibly misspecified auxiliary criteria. A large class of considered auxiliary criteria includes the ordinary least squares, nonlinear least squares, and nonlinear least absolute deviations estimators. Besides deriving the consistency and asymptotic normality of the proposed methods, we demonstrate that the proposed indirect inference methodology-at least for selected auxiliary criteria-combines weak distributional assumptions, good estimation precision, and robustness to misclassification of responses. We conduct Monte Carlo experiments and an application study to compare the finite-sample performance of the proposed and existing estimators.

关键词： asymptotic normality binary-choice model breakdown point indirect inference misclassification single-index model

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Correcting Intraday Periodicity Bias in Realized Volatility Measures

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econometrics AND STATISTICS 2022年 23卷 36-52页

作者： Dette, Holger Golosnoy, Vasyl Kellermann, Janosch Ruhr Univ Bochum Fac Math Bochum Germany Ruhr Univ Bochum Fac Management & Econ Univ Str 150 D-44801 Bochum Germany

Diurnal fluctuations in volatility are a well-documented stylized fact of intraday price data. This warrants an investigation how this intraday periodicity (IP) affects both finite sample as well as asymptotic properties of several popular realized estimators of daily integrated volatility which are based on functionals of a finite number of intraday returns. It turns out that most of the estimators considered in this study exhibit a finite-sample bias due to IP, which can however get negligible when the number of intraday returns diverges to infinity. The appropriate correction factors for this bias are derived based on estimates of the IP. The adequacy of the new corrections is evaluated by means of a Monte Carlo simulation study and an empirical example. (c) 2021 EcoSta econometrics and Statistics. Published by Elsevier B.V. All rights reserved.

关键词： Integrated volatility Realized measures Intraday periodicity Simulation -based methods

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Data driven robust estimation methods for fixed effects panel data models

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2022年第7期92卷 1401-1425页

作者： Beyaztas, Beste Hamiye Bandyopadhyay, Soutir Istanbul Medeniyet Univ Dept Stat Istanbul Turkey Colorado Sch Mines Dept Appl Math & Stat Golden CO USA

The panel data regression models have gained increasing attention in different areas of research including econometrics, environmental sciences, epidemiology, behavioural and social sciences. However, the presence of outlying observations in panel data may often lead to biased and inefficient estimates of the model parameters resulting in unreliable inferences when the least squares method is applied. We propose extensions of the M-estimation and Exponential squared loss function-based approaches with a data-driven selection of tuning parameters to achieve desirable level of robustness against outliers without loss of estimation efficiency. The consistency and asymptotic normality of the proposed estimators have also been proved under some mild regularity conditions. The finite-sample performance of our proposed methods have been examined via several Monte Carlo experiments and their results are compared with the ones from existing methods. In addition, a macroeconomic dataset is analysed using the proposed methods to demonstrate their superiorities.

关键词： Panel data fixed effects robust estimation M-estimation least squares

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Nonparametric inference for quantile cointegrations with stationary covariates

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JOURNAL OF econometrics 2022年第2期230卷 453-482页

作者： Tu, Yundong Liang, Han-Ying Wang, Qiying Peking Univ Guanghua Sch Management Beijing 100871 Peoples R China Peking Univ Ctr Stat Sci Beijing 100871 Peoples R China Tongji Univ Sch Math Sci Shanghai 200092 Peoples R China Univ Sydney Sch Math & Stat Sydney NSW 2006 Australia

This paper considers the inference problems in nonlinear quantile regressions with both stationary and nonstationary covariates. The nonparametric local constant quantile estimator is proposed to estimate the unknown quantile regression function, whose asymptotic properties are established under quite general conditions. Specification testing of the quantile regression function is further considered through a statistic constructed based on the integrated squared distance between the parametric and the nonparametric estimators for the regression function. The test statistic is shown to converge to a random variable related to the local time of an Ornstein-Uhlenbeck process under the parametric null. The power of the test against local alternatives is also investigated. Additional asymptotic results on the null parametric quantile estimators and a bootstrap test are developed as well. Numerical results demonstrate that the proposed nonparametric estimator and the specification test enjoy attractive finite sample performance. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Model specification testing Nonparametric methods Nonstationarity Predictive regression Quantile cointegration

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Time-varying instrumental variable estimation

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JOURNAL OF econometrics 2021年第2期224卷 394-415页

作者： Giraitis, Liudas Kapetanios, George Marcellino, Massimiliano Queen Mary Univ London London England Kings Coll London London England Bocconi Univ IGIER Milan Italy CEPR Rome Italy

We develop non-parametric instrumental variable estimation and inferential theory for econometric models with possibly endogenous regressors whose coefficients can vary over time either deterministically or stochastically, and the time-varying and uniform versions of the standard Hausman exogeneity test. After deriving the asymptotic properties of the proposed procedures, we assess their finite sample performance by means of a set of Monte Carlo experiments, and illustrate their application by means of an empirical example on the Phillips curve. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Instrumental variables Time-varying parameters Endogeneity Hausman test Non-parametric methods Phillips curve

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