Publication Date: January 2006
There is an emerging consensus in empirical ﬁnance that realized volatility series typically display long range dependence with a memory parameter (d) around 0.4 (Andersen et. al. (2001), Martens et. al. (2004)). The present paper provides some analytical explanations for this evidence and shows how recent results in Lieberman and Phillips (2004a, 2004b) can be used to reﬁne statistical inference about d with little computational eﬀort. In contrast to standard asymptotic normal theory now used in the literature which has an O(n-1/2) error rate on error rejection probabilities, the asymptotic approximation used here has an error rate of o(n-1/2). The new formula is independent of unknown parameters, is simple to calculate and highly user-friendly. The method is applied to test whether the reported long memory parameter estimates of Andersen et. al. (2001) and Martens et. al. (2004) diﬀer signiﬁcantly from the lower boundary (d = 0.5) of nonstationary long memory.
ARFIMA; Edgeworth expansion; Fourier integral expansion; Fractional diﬀerencing; Improved inference; Long memory; Pivotal statistic; Realized volatility; Singularity
JEL Classification Codes: C13, C22