Autoregressive spectral estimates under ignored changes in the mean

Periodogram‐based‐40 estimators of the spectral density are known to exhibit distorted behavior in neighborhoods of the origin in case of so‐called low frequency contamination, mimicking long‐range dependence. This note quantifies the behavior of the estimator based on autoregressive approximations...

Full description

Saved in:
Bibliographic Details
Published in:Journal of time series analysis 2022-03, Vol.43 (2), p.329-340
Main Authors: Demetrescu, Matei, Hosseinkouchack, Mehdi
Format: Article
Language:English
Subjects:
Density
long autoregression
Neighborhoods
Spectra
Spectral density
spurious pole
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Periodogram‐based‐40 estimators of the spectral density are known to exhibit distorted behavior in neighborhoods of the origin in case of so‐called low frequency contamination, mimicking long‐range dependence. This note quantifies the behavior of the estimator based on autoregressive approximations of order increasing with the sample size. Not surprisingly, the autoregressive spectral estimator is not consistent at the origin under ignored changes in the mean, but turns out to be consistent at non‐zero frequencies. We furthermore show how a specific trimming of the fitted long autoregression can be used to restore consistency in the vicinity of the origin.
ISSN:0143-9782
1467-9892
DOI:10.1111/jtsa.12612