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Refined Inference on Long Memory in Realized Volatility

  • Offer Lieberman
  • Peter Phillips

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.

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Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 27 (2008)
Issue (Month): 1-3 ()
Pages: 254-267

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Handle: RePEc:taf:emetrv:v:27:y:2008:i:1-3:p:254-267
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  11. Federico Bandi & Benoit Perron, 2003. "Long memory and the relation between implied and realized volatility," Econometrics 0305004, EconWPA.
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  14. Lieberman, Offer & Phillips, Peter C.B., 2004. "Expansions For The Distribution Of The Maximum Likelihood Estimator Of The Fractional Difference Parameter," Econometric Theory, Cambridge University Press, vol. 20(03), pages 464-484, June.
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