Finite Sample Properties of Tests Based on Prewhitened Nonparametric\n Covariance Estimators

2014/09/04 by David Preinerstorfer, Preinerstorfer, David
Mathematics · #62F03 #62F35 #62J05 #62M10 #62M15 #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1409.1419

openalex publication_date 2014/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analytically investigate size and power properties of a popular family of\nprocedures for testing linear restrictions on the coefficient vector in a\nlinear regression model with temporally dependent errors. The tests considered\nare autocorrelation-corrected F-type tests based on prewhitened nonparametric\ncovariance estimators that possibly incorporate a data-dependent bandwidth\nparameter, e.g., estimators as considered in Andrews and Monahan (1992), Newey\nand West (1994), or Rho and Shao (2013). For design matrices that are generic\nin a measure theoretic sense we prove that these tests either suffer from\nextreme size distortions or from strong power deficiencies. Despite this\nnegative result we demonstrate that a simple adjustment procedure based on\nartificial regressors can often resolve this problem.\n

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