Consistent estimation and order selection for nonstationary autoregressive processes with stable innovations

Peter Burridge; Daniela Hristova

doi:10.1111/j.1467-9892.2008.00579.x

Consistent estimation and order selection for nonstationary autoregressive processes with stable innovations

Peter Burridge, Daniela Hristova

Economics

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

Abstract

A possibly nonstationary autoregressive process, of unknown finite order, with possibly infinite-variance innovations is studied. The ordinary least squares autoregressive parameter estimates are shown to be consistent, and their rate of convergence, which depends on the index of stability, alpha, is established. We also establish consistency of lag-order selection criteria in the nonstationary case. A small experiment illustrates the relative performance of different lag-length selection criteria in finite samples.

Original language	English
Pages (from-to)	695-718
Number of pages	24
Journal	Journal of Time Series Analysis
Volume	29
Issue number	4
DOIs	https://doi.org/10.1111/j.1467-9892.2008.00579.x
Publication status	Published - Jul 2008

Keywords

consistent estimation
infinite-variance innovations
unit-root AR processes
consistent order-selection criteria
INFINITE-VARIANCE
TIME-SERIES
UNIT-ROOT
INFORMATION CRITERION
MOVING AVERAGES
MODEL SELECTION
LIMIT THEORY
REGRESSION

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10.1111/j.1467-9892.2008.00579.x

http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9892.2008.00579.x/abstract

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abstract = "A possibly nonstationary autoregressive process, of unknown finite order, with possibly infinite-variance innovations is studied. The ordinary least squares autoregressive parameter estimates are shown to be consistent, and their rate of convergence, which depends on the index of stability, alpha, is established. We also establish consistency of lag-order selection criteria in the nonstationary case. A small experiment illustrates the relative performance of different lag-length selection criteria in finite samples.",

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KW - consistent estimation

KW - infinite-variance innovations

KW - unit-root AR processes

KW - consistent order-selection criteria

KW - INFINITE-VARIANCE

KW - TIME-SERIES

KW - UNIT-ROOT

KW - INFORMATION CRITERION

KW - MOVING AVERAGES

KW - MODEL SELECTION

KW - LIMIT THEORY

KW - REGRESSION

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EP - 718

JO - Journal of Time Series Analysis

JF - Journal of Time Series Analysis

IS - 4

ER -

Consistent estimation and order selection for nonstationary autoregressive processes with stable innovations

Abstract

Keywords

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