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The Local Whittle Estimator of Long-Memory Stochastic Volatility

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Author Info
Clifford M. Hurvich
Bonnie K. Ray

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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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Publisher Info
Article provided by Oxford University Press in its journal Journal of Financial Econometrics.

Volume (Year): 1 (2003)
Issue (Month): 3 ()
Pages: 445-470
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Handle: RePEc:oup:jfinec:v:1:y:2003:i:3:p:445-470

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  1. Per Frederiksen & Morten Ørregaard Nielsen, 2008. "Bias-reduced estimation of long memory stochastic volatility," CREATES Research Papers 2008-35, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  2. Clifford Hurvich & Eric Moulines & Philippe Soulier, 2004. "Estimating Long Memory in Volatility," Econometrics 0412006, EconWPA. [Downloadable!]
    Other versions:
  3. Josu Arteche, 2005. "Semiparametric estimation in perturbed long memory series," BILTOKI 200502, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística). [Downloadable!]
    Other versions:
  4. Afonso Gonçalves da Silva & Peter M Robinson, 2006. "Finite Sample Performance in CointegrationAnalysis of Nonlinear Time Series with LongMemory," STICERD - Econometrics Paper Series /2006/501, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE. [Downloadable!]
    Other versions:
  5. Per Frederiksen & Frank S. Nielsen & Morten Ørregaard Nielsen, 2008. "Local polynomial Whittle estimation of perturbed fractional processes," CREATES Research Papers 2008-29, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  6. Rohit Deo & Meng-Chen Hsieh & Clifford M. Hurvich & Philippe Soulier, 2007. "Long Memory in Nonlinear Processes," Quantitative Finance Papers 0706.1836, arXiv.org. [Downloadable!]
  7. Per Frederiksen & Frank S. Nielsen, 2008. "Estimation of Dynamic Models with Nonparametric Simulated Maximum Likelihood," CREATES Research Papers 2008-59, School of Economics and Management, University of Aarhus. [Downloadable!]
  8. Frank S. Nielsen, 2008. "Local polynomial Whittle estimation covering non-stationary fractional processes," CREATES Research Papers 2008-28, School of Economics and Management, University of Aarhus. [Downloadable!]
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