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 language | English |
|---|---|
| Pages (from-to) | 467-482 |
| Number of pages | 16 |
| Journal | Journal of Applied Probability |
| Volume | 41 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1 Jun 2004 |
| Externally published | Yes |
Keywords
- Continuous-time model
- Diffusion process
- Long-range dependence
- Parameter estimation
- Stochastic volatility