ASYMPTOTIC PROPERTIES OF GPH ESTIMATORS OF THE MEMORY
PARAMETERS OF THE FRACTIONALLY INTEGRATED SEPARABLE
SPATIAL ARMA (FISSARMA) MODELS
Alireza Ghodsi
Mahendran Shitan
Abstract: 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 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 and
are independent and identically distributed as , when and
.
2010 AMS Mathematics Subject Classification: Primary: 62M30; Secondary: 62M15,
62G20, 62G05.
Keywords and phrases: Spatial processes, FISSARMA models, asymptotic properties,
GPH estimators, long-memory parameters.