Seminars 2007 — Abstracts

Friday, September 14

Speaker: Hsien Kew, Melbourne

Title: Fractional Dickey-Fuller tests under heteroskedasticity

Abstract: In a recent paper, Dolado, Gonzalo and Mayoral (2002) introduce a fractional Dickey-Fuller (FD-F) t-statistic for testing a unit root against the alternative of a mean reverting fractional unit root process. This t-statistic is based on the assumption that the errors are unconditionally homoskedastic. However, Busetti and Taylor (2003), McConnell and Perez-Quiros (2000), and van Dijk et al. (2002) have found compelling evidence that such an assumption is unlikely to hold in many macroeconomic and financial time series, especially those obtained at a longer time span. In this paper, we investigate the finite-sample properties of the FD-F statistic when the errors are unconditionally heteroskedastic. We find that, depending on the form of heteroskedasticity, the FD-F statistic suffers from substantial size distortions. In order to correct for such distortions, we propose the use of White standard errors (White (1980)) when computing the FD-F statistic. This yields a test that is robust to heteroskedasticity of unknown form. We demonstrate that the FD-F statistic that employs White standard error has a standard normal limiting distribution under the unit root null hypothesis as in the FD-F statistic with homoskedastic errors. Monte Carlo results suggest that: (i) White's correction is effective in reducing the size distortions; and (ii) the power loss of using White standard error in the case of homoskedasticity is very small. These results suggest that it is prudent to use the White robust standard errors regardless of whether the errors are heteroskedastic or not.