Testing for unit roots in a nearly nonstationary spatial autoregressive process

    Authors

    B. B. Bhattacharyya; X. Li; M. Pensky;G. D. Richardson

    Comments

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    Abbreviated Journal Title

    Ann. Inst. Stat. Math.

    Keywords

    first-order autoregressive process; unit roots; nearly nonstationary; periodogram ordinate; local Pitman-type alternatives; Ornstein-Uhlenbeck; process; ASYMPTOTIC INFERENCE; TIME-SERIES; Statistics & Probability

    Abstract

    The limiting distribution of the normalized periodogram ordinate is used to test for unit roots in the first-order autoregressive model Z(st) = alpha Z(s-1,t) + beta Z(s,t - 1) - alpha beta Z(s-1,t-1) + epsilon(st). Moreover, for the sequence alpha(n) = e(c/n), beta(n) = e(d/n) of local Pitman-type alternatives, the limiting distribution of the normalized periodogram ordinate is shown to be a linear combination of two independent chi-square random variables whose coefficients depend on c and d. This result is used to tabulate the asymptotic power of a test for various values of c and d. A comparison is made between the periodogram test and a spatial domain test.

    Journal Title

    Annals of the Institute of Statistical Mathematics

    Volume

    52

    Issue/Number

    1

    Publication Date

    1-1-2000

    Document Type

    Article

    Language

    English

    First Page

    71

    Last Page

    83

    WOS Identifier

    WOS:000086965600006

    ISSN

    0020-3157

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