Asymptotic distribution of the autoregressive estimates of the inverse correlation function
type: Item
instance of: scholarly article
title: Asymptotic distribution of the autoregressive estimates of the inverse correlation function
zbMATH Open document ID: 0574.62025
author: R. J. Bhansali
published in: Metron
publication date: 1984-01-01T00:00:00Z
review text: We consider a one-sided, infinite moving average process, with absolutely summable coefficients, of independent identically distributed random variables, \(\epsilon_ t\), with 0 mean and finite fourth moment. The spectral density of the process is also assumed to be non-vanishing. Using observations \(X_ 1,...,X_ T\) from \(x_ t\), an autoregression of order k, where \(k\to \infty\), \(k^ 3/T\to 0\) as \(T\to \infty\), is assumed to be fitted for estimating the inverse covariance and correlation functions of \(x_ t\). By further assuming that k is asymptotically sufficient to overcome the bias in approximating an infinite order autoregressive process by a process with finite order, the joint asymptotic normality of the estimated inverse covariance and correlation functions is established.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 3917446
zbMATH Keywords: one-sided, infinite moving average process
zbMATH Keywords: absolutely summable coefficients
zbMATH Keywords: spectral density
zbMATH Keywords: autoregression
zbMATH Keywords: estimating the inverse covariance and correlation functions
zbMATH Keywords: infinite order autoregressive process
zbMATH Keywords: joint asymptotic normality
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3917446