AISM 52, 71-83
(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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