Refined inference on long memory in realized volatility

Offer Lieberman, Peter C.B. Phillips

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


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 article provides some illustrative analysis of how long memory may arise from the accumulative process underlying realized volatility. The article also uses results in Lieberman and Phillips (2004, 2005) to refine statistical inference about d by higher order theory. Standard asymptotic theory has an O(n-1/2) error rate for error rejection probabilities, and the theory used here refines the approximation to an error rate of o(n-1/2). The new formula is independent of unknown parameters, is simple to calculate and 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, and generally confirms earlier findings.

Original languageEnglish
Pages (from-to)254-267
Number of pages14
JournalEconometric Reviews
Issue number1-3
StatePublished - Jan 2008
Externally publishedYes


  • Edgeworth expansion
  • Long memory
  • Realized volatility


Dive into the research topics of 'Refined inference on long memory in realized volatility'. Together they form a unique fingerprint.

Cite this