Parameter estimates for fractional autoregressive spatial processes
Y. Boissy, B. B. Bhattacharyya, X. Li, G. D. Richardson
The Annals of Statistics · 2005 · Volume 33 · Issue 6
DOI: 10.1214/009053605000000589
Abstract
A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular, it is shown that $\hat{d}_{N}-d=O_{P}(\frac{(\operatorname{Log}N)^{3}}{N})$, where d=(d1,d2) denotes the long memory parameter.
Keywords
62F12, 62M30, autoregressive spatial process, long memory, Parameter estimation, spectral density function
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