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Modelling long-range-dependent Gaussian processes with application in continuous-time financial models

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Jiti Gao
Jiti Gao*
Affiliation:
University of Western Australia
*
∗ Postal address: School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia. Email address: jiti@maths.uwa.edu.au
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Abstract

This paper considers a class of continuous-time long-range-dependent Gaussian processes. The corresponding spectral density is assumed to have a general and flexible form, which covers some important and special cases. For example, the spectral density of a continuous-time fractional stochastic differential equation is included. A modelling procedure is then established through estimating the parameters involved in the spectral density by using an extended continuous-time version of the Gauss–Whittle objective function. The resulting estimates are shown to be strongly consistent and asymptotically normal. An application of the modelling procedure to the identification and modelling of a fractional stochastic volatility is discussed in some detail.

Keywords

Continuous-time modeldiffusion processlong-range dependenceparameter estimationstochastic volatility

MSC classification

Primary: 60G17: Sample path properties
Secondary: 60G10: Stationary processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 467 - 482
Copyright
Copyright © Applied Probability Trust 2004 

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