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

• Autorzy: Ghodsi A. , Shitan M.
• Języki publikacji: EN

Abstrakty

EN

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 m^1/2(d^₁ − d₁) and m^1/2(d^₂ − d₂) are independent and identically distributed as N(0, π²/24), when m = o(n^4/5) and ln² n = o(m).

Słowa kluczowe

EN

spatial processes; FISSARMA models; asymptotic properties; GPH estimators; long-memory parameters

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 2
• Strony: 247--265
• Opis fizyczny: Bibliogr. 14 poz., rys., tab., wykr.

Twórcy

autor

Ghodsi A.

• Department of Statistics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran

autor

Shitan M.

• Department of Mathematics, Faculty of Science, University Putra Malaysia, Serdang, Malaysia

Bibliografia

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• [4] P. J. Brockwell and R. A. Davis, Introduction to Time Series and Forecasting, second edition, Springer, New York 2002.
• [5] J. Geweke and S. Porter-Hudak, The estimation and application of long memory time series models, J. Time Ser. Anal. 4 (1983), pp. 221-237.
• [6] A. Ghodsi and M. Shitan, Estimation of the memory parameters of the fractionally integrated separable spatial autoregressive (FISSAR(1, 1)) model: A simulation study, Comm. Statist. Simulation Comput. 38 (6) (2009), pp. 1256-1268.
• [7] A. Ghodsi and M. Shitan, Some properties of the normalized periodogram of a fractionally integrated separable spatial ARMA (FISSARMA) model, Comm. Statist. Theory Methods 42 (8) (2013), pp. 1515-1530.
• [8] H. Guo, C. Y. Lim, and M. Meerschaert, Local Whittle estimator for anisotropic random fields, J. Multivariate Anal. 100 (5) (2009), pp. 993-1028.
• [9] C. M. Hurvich and K. I. Beltrao, Automatic semiparametric estimation of the memory parameter of a long memory time series, J. Time Ser. Anal. 15 (1994), pp. 285-302.
• [10] C. M. Hurvich, R. Deo, and J. Brodsky, The mean squared error of Geweke and Porter-Hudak’s estimator of the memory parameter of a long-memory time series, J. Time Ser. Anal. 19 (1) (1998), pp. 19-46.
• [11] P. M. Robinson, Log-periodogram regression of time series with long range dependence, Ann. Statist. 23 (1995), pp. 1048-1074.
• [12] P. M. Robinson, Gaussian semiparametric estimation of long range dependence, Ann. Statist. 23 (1995), pp. 1630-1661.
• [13] M. Shitan, Fractionally integrated separable spatial autoregressive (FISSAR) model and some of its properties, Comm. Statist. Theory Methods 37 (2008), pp. 1266-1273.
• [14] L. Wang, Memory parameter estimation for long range dependent random fields, Statist. Probab. Lett. 79 (2009), pp. 2297-2306.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).