Unit roots test: Spatial model with long memory errors

A test for unit roots in the autoregressive model Yij=αYi−1,j+βYi,j−1−αβYi−1,j−1+ϵij is developed whenever the error structure is assumed to have long range dependence. Whenever α=β=1, the limiting distribution of the sequence of normalized Fourier coefficients of the Y− process is shown to be a function of a two parameter fractional Brownian motion process on [0,1]×[0,1]. This result is used to find the limiting distribution of the periodogram ordinate of the Y-process under the null hypothesis that α=β=1.