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Asymptotic properties of GPH estimators of the memory parameters of the fractionally integrated separable spatial ARMA (FISSARMA) models. (English) Zbl 1359.62398

Summary: In this article, we first extend Theorem 2 of P. M. Robinson [Ann. Stat. 23, No. 3, 1048–1072 (1995; Zbl 0838.62085)] from one dimension to two dimensions. Then the theoretical asymptotic properties of the means, variances, covariance and MSEs of the regression/GPH (GPH states for Geweke and Porter-Hudak’s) estimators of the memory parameters of the FISSARMA model are established. We also performed simulations to study MSE and covariances for finite sample sizes. We found that through the simulation study the MSE values of the memory parameters tend to the theoretical MSE values as the sample size increases. It is also found that \(m^{1/2}(\hat{d}_1-d_1)\) and \(m^{1/2}(\hat{d}_2-d_2)\) are independent and identically distributed as \(N(0,\pi^2/24)\), when \(m = o (n^{4/5})\) and \(\ln^2n = o(m)\).

MSC:

62M30 Inference from spatial processes
62M15 Inference from stochastic processes and spectral analysis
62G20 Asymptotic properties of nonparametric inference
62G05 Nonparametric estimation

Citations:

Zbl 0838.62085

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