Unit Roots Test: Spatial Model With Long Memory Errors

Keywords

Autoregressive spatial process; Fractional Brownian sheet; Unit roots

Abstract

A test for unit roots in the autoregressive model Yij=αYi−1,j+βYi,j−1−αβYi−1,j−1+ϵij is developed whenever the error structure is assumed to have long range dependence. Whenever α=β=1, the limiting distribution of the sequence of normalized Fourier coefficients of the Y− process is shown to be a function of a two parameter fractional Brownian motion process on [0,1]×[0,1]. This result is used to find the limiting distribution of the periodogram ordinate of the Y-process under the null hypothesis that α=β=1.

Publication Date

9-1-2018

Publication Title

Statistics and Probability Letters

Volume

140

Number of Pages

126-131

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.spl.2018.05.003

Socpus ID

85047240269 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85047240269

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