ESTIMATION OF MIXED FRACTIONAL STABLE PROCESSES USING HIGH-FREQUENCY DATA

The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable Levy processes, and fractional Brownian motion. For this reason, it may be regarded as a basic building block for con-tinuous time models. We study a stylized model consisting of a superposition of independent linear fractional stable motions and our focus is on parame-ter estimation of the model. Applying an estimating equations approach, we construct estimators for the whole set of parameters and derive their asymp-totic normality in a high-frequency regime. The conditions for consistency turn out to be sharp for two prominent special cases: (i) for Levy processes, that is, for the estimation of the successive Blumenthal-Getoor indices and (ii) for the mixed fractional Brownian motion introduced by Cheridito. In the remaining cases, our results reveal a delicate interplay between the Hurst pa-rameters and the indices of stability. Our asymptotic theory is based on new limit theorems for multiscale moving average processes.