Fixed-b Inference in the Presence of Time-Varying Volatility

TLDR: In this paper, the authors employ the wild bootstrap (Cavaliere and Taylor, 2008, ET), resort to time transformations and select test statistics and asymptotics according to the outcome of a heteroscedasticity test.

Abstract: The fixed-b asymptotic framework provides refinements in the use of heteroskedasticity and autocorrelation consistent variance estimators. The resulting limiting distributions of t-statistics are, however, not pivotal when the unconditional variance changes over time. Such time-varying volatility is an important issue for many financial and macroeconomic time series. To regain pivotal fixed-b inference under time-varying volatility, we discuss three alternative approaches. We (i) employ the wild bootstrap (Cavaliere and Taylor, 2008, ET), (ii) resort to time transformations (Cavaliere and Taylor, 2008, JTSA) and (iii) consider to select test statistics and asymptotics according to the outcome of a heteroscedasticity test, since small-b asymptotics deliver standard limiting distributions irrespective of the socalled variance profile of the series. We quantify the degree of size distortions from using the standard fixed-b approach assuming homoskedasticity and compare the effectiveness of the corrections via simulations. It turns out that the wild bootstrap approach is highly recommendable in terms of size and power. An application to testing for equal predictive ability using the Survey of Professional Forecasters illustrates the usefulness of the proposed corrections.