A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests

Abstract

A new …rst order asymptotic theory for heteroskedasticity-autocorrelation (HAC) robust tests based on nonparametric covariance matrix estimators is developed. The bandwidth of the covariance matrix estimator is modeled as a …xed proportion of the sample size. This leads to a distribution theory for HAC robust tests that explicitly captures the choice of bandwidth and kernel. This contrasts with the traditional asymptotics (where the bandwidth increases slower than the sample size) where the asymptotic distributions of HAC robust tests do not depend on the bandwidth or kernel. Finite sample simulations show that the new approach is more accurate than the traditional asymptotics. The impact of bandwidth and kernel choice on size and power of t-tests is analyzed. Smaller bandwidths lead to tests with higher power but greater size distortions and large bandwidths lead to tests with lower power but less size distortions. Size distortions across bandwidths increase as the serial correlation in the data becomes stronger. A new data dependent bandwidth is proposed in light of these results. Within a group of popular kernels, it shown that the Bartlett kernel has approximately the highest power and the quadratic spectral (QS) kernel has the lowest power regardless of the bandwidth. However, the Bartlett kernel gives the most size distorted tests whereas the QS kernels give the least size distorted tests. Overall, the results clearly indicate that for bandwidth and kernel choice there is a trade-o¤ between size distortions and power.

Fixed-B Asymptotics for the Studentized Mean From Time Series With Short, Long, or Negative Memory

“…As in Kiefer and Vogelsang (2005), let the bandwidth M be proportional to sample size n, i.e., M = bn with b ∈ (0, 1]. We first introduce the following notation: the sample autocovariance is A derivative of Λ from the left (with respect to x) is denotedΛ − , whereas from the right isΛ + ; the second derivative isΛ.…”

“…The SM case was covered in Kiefer and Vogelsang (2005) who used the Bartlett kernel for smoothing; our results provide extensions to LM and NM DGPs with a variety of kernels. The chief problem of interest is to properly normalize the partial sums S n = n t=1 Y t , which have finite-sample variance V n .…”

Nonparametric Cointegrating Regression With Endogeneity and Long Memory

“…Further, φ can be estimated by standard HAC methods. Alternative HAR sieve methods (Phillips, 2005;Sun, 2011;Chen, Liao, and Sun, 2014) or fixed-b kernel methods (Kiefer and Vogelsang, 2005;Sun, 2014) may be used after some changes to the limit theory to address the random limit theory involved in the estimation of φ but these methods are not explored here. These facts imply that, in the short terms of use, available at https://www.cambridge.org/core/terms.…”

The Impact of OECD Countries’ Macroeconomic Factors on Turkey’s Foreign Trade

“…Vogelsang (2012) Driscoll-Kraay created fixed b asymptotic approaches; Kiefer and Vogelsang (2005) created resistive standard errors in the context of cross-sectional correlation, compared to the standard normal asymptotic approaches.…”