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Journal of Financial Econometrics Advance Access originally published online on July 17, 2008
Journal of Financial Econometrics 2008 6(4):496-512; doi:10.1093/jjfinec/nbn009
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Bias-Reduced Estimation of Long-Memory Stochastic Volatility

Per Frederiksen
     Equity Trading & Derivatives, Nordea Markets

Morten Ørregaard Nielsen
     Cornell University and CREATES

Address correspondence to Per Frederiksen, Equity Trading & Derivatives, Nordea Markets, 1401 Copenhagen C, Denmark, e-mail: per.frederiksen{at}nordea.com.

JEL Classification: C14, C22


  Abstract

We propose to use a variant of the local polynomial Whittle estimator to estimate the memory parameter in volatility for long-memory stochastic volatility models with potential nonstationarity in the volatility process. We show that the estimator is asymptotically normal and capable of obtaining bias reduction as well as a rate of convergence arbitrarily close to the parametric rate, n1/2. A Monte Carlo study is conducted to support the theoretical results, and an analysis of daily exchange rates demonstrates the empirical usefulness of the estimators.

KEYWORDS: bias reduction, local Whittle estimation, long memory stochastic volatility model

We are grateful to Torben G. Andersen, Niels Haldrup, Esben Høg, Asger Lunde, Frank S. Nielsen, two anonymous referees, an anonymous associate editor, and the co-editor Eric Ghysels for comments. This work was partly done while Frederiksen was visiting Northwestern University and Nielsen was visiting Queen's University and the University of Aarhus; their hospitality is gratefully acknowledged. We are grateful for financial support from the Danish Social Sciences Research Council (grant no. FSE 275-05-0220) and the Center for Econometric Analysis of Time Series (CREATES, funded by the Danish National Research Foundation).

Received April 25, 2006; revised December 17, 2007; accepted June 20, 2008


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