On the Sample Mean and Variance of a Long Memory Process.
Abstract
Some properties of the sample mean and sample variance of a long memory process are described. It is shown that for a particular class of long memory process the asymptotic relative efficiency of the k- decimated sample mean x bar sub n (K) (formed by taking the mean of every k -th observation) with respect to the sample mean x bar sub n of all n observations is 1, but that the deficiency (as defined by Hodges and Lehmann) of x bar sub n (K) with respect to x bar sub n is infinite. It is also shown that the sample variance S sub n to the 2nd power of a long memory process can be badly biased toward O: for any integer N and every epsilon > O there exists a long memory process with population variance such that Es sub n to the 2nd power < ep silon population variance for all sample sizes n < or = N. These properties of the sample mean and variance are not shared by ordinary stationary processes such as ARMA processes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1985
- Accession Number
- ADA176221
Entities
People
- Donald B. Percival
Organizations
- University of Washington