Limit Theory for the Sample Covariance and Correlation Functions of Moving Averages.
Abstract
Document describes a moving average process which have regularly varying tail probabilities with index alpha > 0. The limit distribution of the sample covariance function is derived in the case that the process has a finite variance but an infinite variance but an infinite fourth moment. Furthermore, in the infinite variance case (0 < alpha < 2), the sample correlation function is shown to converge in distribution to the ratio of two independent stable random variables with indices alpha and alpha/2, respectively. This result immediately gives the limit distribution for the least squares estimates of the parameters in an autoregressive process. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1984
- Accession Number
- ADA145488
Entities
People
- Russ E. Davis
- S. Resnick
Organizations
- University of North Carolina at Chapel Hill