Year: 2025
Type: article
Abstract: ABSTRACT We consider a borderline case: The central limit theorem for a strictly stationary time series with infinite variance but a Gaussian limit. In the i.i.d. case, a well‐known sufficient condition for this central limit theorem is regular variation of the marginal distribution with tail index . In the dependent case, we assume the stronger condition of sequential regular variation of the time series with tail index . We assume that a sample of size from this time series can be split into blocks of size such that as and that the block sums are asymptotically independent. Then we apply classical central limit theory for row‐wise i.i.d. triangular arrays. The necessary and sufficient conditions for such independent block sums will be verified by using large deviation results for the time series. We derive the central limit theorem for ‐dependent sequences, linear processes, stochastic volatility processes and solutions to affine stochastic recurrence equations whose marginal distributions have infinite variance and are regularly varying with tail index .
Source: Journal of Time Series Analysis
DOI: 10.1111/jtsa.70020
Authors: Muneya Matsui, Thomas Mikosch
Institutions: Nanzan University, University of Copenhagen
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414949034