Fixed-b Asymptotics for t-Statistics in the Presence of Time-Varying Volatility

The fixed-b asymptotic framework provides refinements in the use of heteroskedasticity and autocorrelation consistent variance estimators. We show however that the fixed-b limiting distributions of t-statistics are not pivotal when the variance of the underlying data generating process changes over time. To regain pivotal fixed-b inference under such time heteroskedasticity, we discuss three alternative approaches. We employ (1) the wild bootstrap (Cavaliere and Taylor, 2008, ET), (2) resort to time transformations (Cavaliere and Taylor, 2008, JTSA) and (3) suggest to pick suitable the asymptotics according to the outcome of a heteroskedasticity test, since small-b asymptotics deliver standard limiting distributions irrespective of the so-called variance profile of the series. We quantify the degree of size distortions from using the standard fixed-b approach and compare the effectiveness of the corrections via simulations. We also provide an empirical application to excess returns.