Limit theorems for the sample mean and sample autocovariances of continuous time moving averages driven by heavy-tailed Levy noise

作者：Drapatz Martin^*

来源：Alea (Rio de Janeiro): Latin American Journal of Probability and Mathematical Statistics , 2017, 14(1): 403-426.

DOI：10.30757/alea.v14-22

• continuous time moving average
• Levy process
• sample autocovariance
• sample mean

In this article we consider continuous time moving averages observed on a lattice, driven by an infinite variance Levy process with regularly varying tails with index alpha is an element of (0, 2). We show that the asymptotic distribution of the sample mean and sample autocovariance function is a stable law. The parameters of the stable limit distribution are explicitly given in terms of the kernel and characteristics of the Levy process.

• 出版日期2017