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The Local Whittle Estimator of Long-Memory Stochastic Volatility

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  • Clifford M. Hurvich
  • Bonnie K. Ray

Abstract

We propose a new semiparametric estimator of the degree of persistence in volatility for long memory stochastic volatility (LMSV) models. The estimator uses the periodogram of the log squared returns in a local Whittle criterion which explicitly accounts for the noise term in the LMSV model. Finite-sample and asymptotic standard errors for the estimator are provided. An extensive simulation study reveals that the local Whittle estimator is much less biased and that the finite-sample standard errors yield more accurate confidence intervals than the widely-used GPH estimator. The estimator is also found to be robust against possible leverage effects. In an empirical analysis of the daily Deutsche Mark/US Dollar exchange rate, the new estimator indicates stronger persistence in volatility than the GPH estimator, provided that a large number of frequencies is used. , .

Suggested Citation

  • Clifford M. Hurvich & Bonnie K. Ray, 2003. "The Local Whittle Estimator of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 445-470.
  • Handle: RePEc:oup:jfinec:v:1:y:2003:i:3:p:445-470
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