The Local Whittle Estimator of Long-Memory Stochastic Volatility

Ray, Bonnie K. and Hurvich, Clifford M., "The Local Whittle Estimator of Long-Memory Stochastic Volatility" . Journal of Financial Econometrics, Vol. 1, No. 3, pp. 445-470, 2003

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.

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