On the asymptotics of residuals in autoregressive moving average processes with one autoregressive unit root

Chul Gyu Park; Dong Wan Shin

doi:10.1016/0167-7152(95)00095-X

On the asymptotics of residuals in autoregressive moving average processes with one autoregressive unit root

Chul Gyu Park, Dong Wan Shin

Department of Statistics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In the autoregressive moving average (ARMA) model with one autoregressive unit root, limiting distribution of the residual autocorrelations depends only on parameters other than the parameter corresponding to the unit root and is the same as that in the corresponding stationary ARMA process. On the other hand, limiting distribution of the partial sum process of residuals does not depend on parameter other than the parameter corresponding to the unit root and is the same as that in AR(1) with autoregressive coefficient one.

Original language	English
Pages (from-to)	341-346
Number of pages	6
Journal	Statistics and Probability Letters
Volume	27
Issue number	4
DOIs	https://doi.org/10.1016/0167-7152(95)00095-X
State	Published - 1 May 1996

Bibliographical note

Funding Information:
The research is supported by a grant from Korea Research Foundation.

Keywords

ARMA process
Brownian motion
Nonstationary process
Partial sums of residuals
Residual autocorrelations

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10.1016/0167-7152(95)00095-X

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abstract = "In the autoregressive moving average (ARMA) model with one autoregressive unit root, limiting distribution of the residual autocorrelations depends only on parameters other than the parameter corresponding to the unit root and is the same as that in the corresponding stationary ARMA process. On the other hand, limiting distribution of the partial sum process of residuals does not depend on parameter other than the parameter corresponding to the unit root and is the same as that in AR(1) with autoregressive coefficient one.",

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AB - In the autoregressive moving average (ARMA) model with one autoregressive unit root, limiting distribution of the residual autocorrelations depends only on parameters other than the parameter corresponding to the unit root and is the same as that in the corresponding stationary ARMA process. On the other hand, limiting distribution of the partial sum process of residuals does not depend on parameter other than the parameter corresponding to the unit root and is the same as that in AR(1) with autoregressive coefficient one.

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KW - Nonstationary process

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On the asymptotics of residuals in autoregressive moving average processes with one autoregressive unit root

Abstract

Bibliographical note

Keywords

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