LIMIT-THEOREMS FOR STABLE PROCESSES WITH APPLICATION TO SPECTRAL DENSITY-ESTIMATION

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:57

Article

关键词: KERNEL ESTIMATOR;    LIMIT THEOREM;    STABLE PROCESS;   

DOI  :  10.1016/0304-4149(94)00068-5

来源: Elsevier

【 摘 要 】

This paper deals with issues pertaining to estimating the spectral density of a stationary harmonizable a-stable process, where 0 < alpha < 2. The estimator we consider is obtained by smoothing the periodogram, which has a similar flavor as the usual kernel spectral density estimator for a second-order stationary process. We derive the basic asymptotic properties of the estimator and show how to pick the optimal smoothing parameter for a in different intervals of (0, 2). At the heart of these derivations is the theoretical problem of finding the asymptotic distribution of a weighted average of \Y(u)\(p) over an increasing interval, where 0 < p < infinity and Y is a nearly stationary moving average alpha-stable process. Our results partially extend the limit theorems in Davis (1983) and LePage et al. (1981).

【 授权许可】

Free