Limit Theory for the Sample Autocovariance for Heavy Tailed Stationary Infinitely Divisible Processes Generated by Conservative Flows

2013/02/01 by Owada, Takashi
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1302.0058

Abstract

This study aims to develop the limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case where the infinitely divisible process has heavy tail marginals and is generated by a conservative flow. Interestingly, the growth rate of the sample autocovariances is determined by not only heavy tailedness of the marginals but also memory length of the process. Although this feature was first observed by \citeresnick:samorodnitsky:xue:2000 for some very specific processes, we will propose a more general framework from the viewpoint of infinite ergodic theory. Consequently, the asymptotics of the sample autocovariances can be more comprehensively discussed.

Related

• Limit theorems for the sample autocovariance of a continuous-time moving average process with long memory
• Large sample autocovariance matrices of linear processes with heavy\n tails
• Functional central limit theorem for negatively dependent heavy-tailed stationary infinitely divisible processes generated by conservative flows
• Asymptotic Inference of Autocovariances of Stationary Processes
• Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes