Abstract
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 α n = e c/n, β 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.
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Bhattacharyya, B.B., Li, X., Pensky, M. et al. Testing for Unit Roots in a Nearly Nonstationary Spatial Autoregressive Process. Annals of the Institute of Statistical Mathematics 52, 71–83 (2000). https://doi.org/10.1023/A:1004184932031
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DOI: https://doi.org/10.1023/A:1004184932031