Further Results on Size and Power of Heteroskedasticity and Autocorrelation Robust Tests, with an Application to Trend Testing

TL;DR

This paper provides additional finite sample insights into the size and power of heteroskedasticity and autocorrelation robust tests, highlighting the necessity of certain conditions and revealing size distortions in trend testing.

Contribution

It extends previous theory with finite sample results and demonstrates the necessity of conditions for size control, also applying findings to trend tests in time series.

Findings

Many existing trend tests are strongly size-distorted.

Necessary conditions for size control are often also sufficient.

Finite sample results improve understanding of test performance.

Abstract

We complement the theory developed in Preinerstorfer and P\"otscher (2016) with further finite sample results on size and power of heteroskedasticity and autocorrelation robust tests. These allows us, in particular, to show that the sufficient conditions for the existence of size-controlling critical values recently obtained in P\"otscher and Preinerstorfer (2018) are often also necessary. We furthermore apply the results obtained to tests for hypotheses on deterministic trends in stationary time series regressions, and find that many tests currently used are strongly size-distorted.