Estimation of the long memory parameter in stochastic volatility models by quadratic variations

2011 ◽  
Vol 19 (2) ◽  
Author(s):  
Ionuţ Florescu ◽  
Ciprian A. Tudor
Keyword(s):  
Stochastic Volatility ◽  
Long Memory ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Quadratic Variations ◽  
Memory Parameter

scholarly journals ON THE LOG PERIODOGRAM REGRESSION ESTIMATOR OF THE MEMORY PARAMETER IN LONG MEMORY STOCHASTIC VOLATILITY MODELS

2001 ◽  
Vol 17 (4) ◽  
pp. 686-710 ◽  
Author(s):  
Rohit S. Deo ◽  
Clifford M. Hurvich
Keyword(s):  
Stochastic Volatility ◽  
Long Memory ◽  
Recent Literature ◽  
Stochastic Volatility Model ◽  
Asymptotic Bias ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Memory Parameter ◽  
Memory Series

We consider semiparametric estimation of the memory parameter in a long memory stochastic volatility model. We study the estimator based on a log periodogram regression as originally proposed by Geweke and Porter-Hudak (1983, Journal of Time Series Analysis 4, 221–238). Expressions for the asymptotic bias and variance of the estimator are obtained, and the asymptotic distribution is shown to be the same as that obtained in recent literature for a Gaussian long memory series. The theoretical result does not require omission of a block of frequencies near the origin. We show that this ability to use the lowest frequencies is particularly desirable in the context of the long memory stochastic volatility model.

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