Abstract
By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations.
| Original language | English |
|---|---|
| Pages (from-to) | 2331-2362 |
| Number of pages | 32 |
| Journal | Stochastic Processes and their Applications |
| Volume | 120 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 1 Dec 2010 |
| Externally published | Yes |
Keywords
- Fractional Brownian motion
- Multiple Wiener-It integral
- Noncentral limit theorem
- Parameter estimation
- Rosenblatt process
- Self-similarity
- Wavelet analysis