UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.2 43.1 42.2 42.1 41.2 41.1 40.2
40.1 39.2 39.1 38.2 38.1 37.2 37.1
36.2 36.1 35.2 35.1 34.2 34.1 33.2
33.1 32.2 32.1 31.2 31.1 30.2 30.1
29.2 29.1 28.2 28.1 27.2 27.1 26.2
26.1 25.2 25.1 24.2 24.1 23.2 23.1
22.2 22.1 21.2 21.1 20.2 20.1 19.2
19.1 18.2 18.1 17.2 17.1 16.2 16.1
15 14.2 14.1 13.2 13.1 12.2 12.1
11.2 11.1 10.2 10.1 9.2 9.1 8
7.2 7.1 6.2 6.1 5.2 5.1 4.2
4.1 3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 36, Fasc. 2,
pages 247 - 265
 

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 m1∕2(dˆ - d) 1 1 and m1∕2(ˆd - d ) 2 2 are independent and identically distributed as N (0,π2∕24) , when m = o(n4∕5) and ln2n = o(m) .

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.

Download:    Abstract    Full text   Abstract + References