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

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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.

Original languageEnglish
Pages (from-to)467-482
Number of pages16
JournalJournal of Applied Probability
Volume41
Issue number2
DOIs
Publication statusPublished - 1 Jun 2004
Externally publishedYes

Keywords

  • Continuous-time model
  • Diffusion process
  • Long-range dependence
  • Parameter estimation
  • Stochastic volatility

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