Testing for Unit Roots in a Nearly Nonstationary Spatial Autoregressive Process

The limiting distribution of the normalized periodogram ordinate is used to test for unit roots in the first-order autoregressive model Ζst=α Ζs-1,t+βΖs,t-1-αβ Ζs-1,t-1+ɛst. Moreover, for the sequence αn = ec/n, βn = 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.