提出两种适用于离散和连续时间预测回归模型的稳健检验方法，利用 Cauchy 估计器处理内生性、持久性和厚尾性，分别采用组估计量 t 统计推断与波动性非参数校正控制异质波动性，在有限样本下表现优于常用替代方法。
摘要：
我们提出了两种稳健方法，用于在异质与持久波动性，以及内生、持久和/或厚尾回归变量和误差下，检验预测回归模型未知参数的假设。所提出的稳健检验方法适用于离散和连续时间模型。两种方法均使用 Cauchy 估计器有效处理回归变量和误差中的内生性、持久性和/或厚尾性问题。两种方法的区别在于如何控制异质波动性。第一种方法依赖使用 Ibragimov 和 Muller（2010）提出的感兴趣的回归参数的组估计量进行稳健 t 统计量推断。该方法易于实现，但需要外生波动性假设。为放宽外生波动性假设，我们提出另一种依赖波动性非参数校正的方法。所提方法在有限样本性质方面表现良好，优于广泛使用的替代推断方法。
英文摘要：
We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed robust testing approaches are applicable both in the case of discrete and continuous time models. Both of the methods use the Cauchy estimator to effectively handle the problems of endogeneity, persistence and/or fat-tailedness in regressors and errors. The difference between our two methods is how the heterogeneous volatility is controlled. The first method relies on robust t-statistic inference using group estimators of a regression parameter of interest proposed in Ibragimov and Muller, 2010. It is simple to implement, but requires the exogenous volatility assumption. To relax the exogenous volatility assumption, we propose another method which relies on the nonparametric correction of volatility. The proposed methods perform well compared with widely used alternative inference procedures in terms of their finite sample properties.
Explanatory variables in a predictive regression typically exhibit low signal strength and various degrees of persistence. Variable selection in such a context is of great importance. In this paper, we explore the pitfalls and possibilities of the LASSO methods in this predictive regression framework. In the presence of stationary, local unit root, and cointegrated predictors, we show that the adaptive LASSO cannot asymptotically eliminate all cointegrating variables with zero regression coefficients. This new finding motivates a novel post-selection adaptive LASSO, which we call the twin adap…
We propose an econometric environment for structural break detection in nonstationary quantile predictive regressions. We establish the limit distributions for a class of Wald and fluctuation type statistics based on both the ordinary least squares estimator and the endogenous instrumental regression estimator proposed by Phillips and Magdalinos (2009a, Econometric Inference in the Vicinity of Unity. Working paper, Singapore Management University). Although the asymptotic distribution of these test statistics appears to depend on the chosen estimator, the IVX based tests are shown to be asympt…
We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a Hölder class and is assumed to be monotone with respect to some or all of the arguments. We derive the minimax rate of convergence for confidence intervals (CIs) that adapt to the underlying smoothness, and provide an adaptive inference procedure that obtains this minimax rate. The procedure differs from that of Cai and Low (2004), intended to yield shorter CIs under practically relevant specifications. The proposed method…
The paper focuses on econometrically justified robust analysis of the effects of the COVID-19 pandemic on financial markets in different countries across the World. It provides the results of robust estimation and inference on predictive regressions for returns on major stock indexes in 23 countries in North and South America, Europe, and Asia incorporating the time series of reported infections and deaths from COVID-19. We also present a detailed study of persistence, heavy-tailedness and tail risk properties of the time series of the COVID-19 infections and death rates that motivate the nece…
We develop a novel "decouple-recouple" dynamic predictive strategy and contribute to the literature on forecasting and economic decision making in a data-rich environment. Under this framework, clusters of predictors generate different latent states in the form of predictive densities that are later synthesized within an implied time-varying latent factor model. As a result, the latent inter-dependencies across predictive densities and biases are sequentially learned and corrected. Unlike sparse modeling and variable selection procedures, we do not assume a priori that there is a given subset …
We propose pair copula constructed point-optimal sign tests in the context of linear and nonlinear predictive regressions with endogenous, persistent regressors, and disturbances exhibiting serial (nonlinear) dependence. The proposed approach entails considering the entire dependence structure of the signs to capture the serial dependence, and building feasible test statistics based on pair copula constructions of the sign process. The tests are exact and valid in the presence of heavy tailed and nonstandard errors, as well as heterogeneous and persistent volatility. Furthermore, they may be i…
We develop uniformly valid confidence regions for regression coefficients in a high-dimensional sparse median regression model with homoscedastic errors. Our methods are based on a moment equation that is immunized against non-regular estimation of the nuisance part of the median regression function by using Neyman's orthogonalization. We establish that the resulting instrumental median regression estimator of a target regression coefficient is asymptotically normally distributed uniformly with respect to the underlying sparse model and is semi-parametrically efficient. We also generalize our …
This Appendix (dated: July 2021) includes supplementary derivations related to the main limit results of the econometric framework for structural break testing in predictive regression models based on the OLS-Wald and IVX-Wald test statistics, developed by Katsouris C (2021). In particular, we derive the asymptotic distributions of the test statistics when the predictive regression model includes either mildly integrated or persistent regressors. Moreover, we consider the case in which a model intercept is included in the model vis-a-vis the case that the predictive regression model has no mod…
In this paper we aim to improve existing empirical exchange rate models by accounting for uncertainty with respect to the underlying structural representation. Within a flexible Bayesian non-linear time series framework, our modeling approach assumes that different regimes are characterized by commonly used structural exchange rate models, with their evolution being driven by a Markov process. We assume a time-varying transition probability matrix with transition probabilities depending on a measure of the monetary policy stance of the central bank at the home and foreign country. We apply thi…
High dimensional predictive regressions are useful in wide range of applications. However, the theory is mainly developed assuming that the model is stationary with time invariant parameters. This is at odds with the prevalent evidence for parameter instability in economic time series, but theories for parameter instability are mainly developed for models with a small number of covariates. In this paper, we present two $L_2$ boosting algorithms for estimating high dimensional models in which the coefficients are modeled as functions evolving smoothly over time and the predictors are locally st…
This paper develops bootstrap methods for practical statistical inference in panel data quantile regression models with fixed effects. We consider random-weighted bootstrap resampling and formally establish its validity for asymptotic inference. The bootstrap algorithm is simple to implement in practice by using a weighted quantile regression estimation for fixed effects panel data. We provide results under conditions that allow for temporal dependence of observations within individuals, thus encompassing a large class of possible empirical applications. Monte Carlo simulations provide numeric…
Improved inference for nonparametric regression and regression-discontinuity designs
University of Bologna（博洛尼亚大学）；Exeter Business School（埃克塞特商学院）；McGill University（麦吉尔大学）；CIREQ（魁北克经济学研究中心）；Aarhus Center for Econometrics（奥胡斯计量经济学中心）；Aarhus University（奥胡斯大学）
LASSO Inference for High Dimensional Predictive Regressions
Southern Methodist University（南方卫理公会大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；University of Macau（澳门大学）；The Chinese University of Hong Kong（香港中文大学）
This paper proposes a new method of inference in high-dimensional regression models and high-dimensional IV regression models. Estimation is based on a combined use of the orthogonal greedy algorithm, high-dimensional Akaike information criterion, and double/debiased machine learning. The method of inference for any low-dimensional subvector of high-dimensional parameters is based on a root-$N$ asymptotic normality, which is shown to hold without requiring the exact sparsity condition or the $L^p$ sparsity condition. Simulation studies demonstrate superior finite-sample performance of this pro…
