The moving blocks bootstrap and robust inference for linear least squares and quantile regressions

Abstract

Abstract This paper presents the moving blocks bootstrap (MBB) as a new inference procedure for linear regression estimation which is robust to heteroskedasticity and autocorrelation of unknown forms. The MBB covariance estimator is shown to provide heteroskedasticity and autocorrelation consistent (HAC) standard errors for least squares (LS) and quantile regression (QR) coefficient estimators. The MBB covariance estimator is shown to be asymptotically equivalent to the Bartlett kernel estimator suggested by Newey and West (1987) and the asymptotically optimal choice of the blocksize is discussed. A Monte Carlo study is included showing that the MBB fares well in comparison to standard HAC inference procedures. Considering strong mixing data generating processes, the paper extends existing asymptotic results for the QR estimator. The analogy to the LS case is stressed. The paper analyzes both the cases of stochastic and of nonstochastic regressors and suggests two new Grenander-like conditions for the latter case. The use of the MBB approach is illustrated for a practical example using a standard econometric package.