AISM 52, 71-83

Testing for unit roots in a nearly nonstationary spatial autoregressive process

B.B. Bhattacharyya1, X. Li2, M. Pensky2 and G. D. Richardson2

1Department of Statistics, North Carolina State University, Raleigh, NC 27695-8203, U.S.A.
2Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364, U.S.A.

(Received May 20, 1996; revised June 30, 1998)

Abstract.    The limiting distribution of the normalized periodogram ordinate is used to test for unit roots in the first-order autoregressive model Zst = alpha Zs-1,t+beta Zs,t-1 - alpha beta Zs-1,t-1+ epsilonst. Moreover, for the sequence alphan = e c/n, betan = ed/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.

Key words and phrases:    First-order autoregressive process, unit roots, nearly nonstationary, periodogram ordinate, local Pitman-type alternatives, Ornstein-Uhlenbeck process.

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