Testing for Unit Roots in a Nearly Nonstationary Spatial Autoregressive Process |
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Authors: | B B Bhattacharyya X Li M Pensky G D Richardson |
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Institution: | (1) Department of Statistics, North Carolina State University, Raleigh, NC, 27695-8203, U.S.A.;(2) Department of Mathematics, University of Central Florida, Orlando, FL, 32816-1364, U.S.A. |
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Abstract: | The limiting distribution of the normalized periodogram ordinate is used to test for unit roots in the first-order autoregressive model st= s-1,t+s,t-1- s-1,t-1+st. Moreover, for the sequence
n
= e
c/n
,
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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Keywords: | First-order autoregressive process unit roots nearly non-stationary periodogram ordinate local Pitman-type alternatives Ornstein-Uhlenbeck process |
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