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

Ghodsi A., Shitan M.

Probability and Mathematical Statistics

2016

Vol. 36, Fasc. 2

247--265

In this article, we first extend Theorem 2 of Robinson [11] 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 performer 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 m1/2(d^1 − d1) and m1/2(d^2 − d2) are independent and identically distributed as N(0, π2/24), when m = o(n4/5) and ln2 n = o(m).