Invertibility of Generalized Space-Time Autoregressive Model with Random Weight

Yundari Yundari, Setyo Wira Rizki

Abstract


The generalized linear process accomplishes stationarity and invertibility properties. The invertibility property must be having a series of convergence conditions of the process parameter. The generalized Space-Time Autoregressive (GSTAR) model is one of the stationary linear models therefore it is necessary to reveal the invertibility through the convergence of the parameter series. This article studies the invertibility of model GSTAR(1;1) with kernel random weight. The result shows that the model GSTAR(1;1) under kernel random weight fulfills the invertibility property and obtains a finite order of Generalized Space-Time Moving Average (GSTMA) process. The other result obtained is the time order of the finite orde  . On the Triangular kernel resulted in the relatively great value n, so that it does not apply to the kernel with a finite value n.


Keywords


invertibility; generalized linear process; autoregression process; stationarity.

Full Text:

PDF

References


G. Box, G. Jenkins and G.Reinsel, Time Series Analysis, forecasting and Control, 3rd edition, New Jersey: Prentice Hall, 1994.

R. Tsay, Multivariate Time Series Analysis With R and Financial Application, New Jersey: John Willey & Sons, 2014.

Y. Yundari, U. S. Pasaribu, U. Mukhaiyar and M.N.Heriawan, "Spatial Weight Determination of GSTAR(1;1) Model by Using Kernel Function," in IOP Conf, Series: Journal of Physics , 2018.

Y. Yundari, U. Pasaribu and U.Mukhaiyar, "Assumption Errors of Generalized STAR Model," J. Math. Fund. Sci., vol. 49, no. 2, pp. 136-155, 2017.

U. Mukhaiyar and U.S.Pasaribu, "A New Procedure of Generalized STAR Modelling using IAcM Approach," ITB J. Sci., vol. 44A, no. 2, pp. 179-192, 2012.

S. Borovkova, B. Ruchjana and H. Lopuhaa, "Least Squares Estimation of Generalized Space Time AutoRegressive (GSTAR) Model and Its Properties," in AIP Conf. Proc. , 2012.

D. Masteriana, M. Riani and U.Mukhaiyar, "Generalized STAR(1;1) with outlier-Case Study of Begal in Medan, North Sumatera," in J.Phys.:Conf. Ser., 2019.

H. Bonar, B. Ruchjana and G. Darmawan, "Development of generalized space time autoregressive integrated with ARCH galat (GSTARI-ARCH) model based on consumer price index phenomenon at several cities in North Sumatera province," in AIP Conference Proceedings, 2013.

A. Iriany, Suhariningsih, B. Ruchjana and Setiawan, "Prediction of Precipitation Data at Batu Town using the GSTAR(1,p)-SUR Model," Journal of Basic and Applied Scietific Research, vol. 3, no. 1, pp. 860-865, 2013.

M. Wand and M. Jones, Kernel Smoothing, New York: Springer- Science+Business Media B.V, 1995.

M. Michalack, "Time series pediction with periodic kernels," Pattern Analitic Application, vol. 14, no. 0, pp. 283-293, 2011.

R. Horn and C. Johnson, Matrix analysis, 2nd, New York: Cambridge Univesity Press, 2013.




DOI: https://doi.org/10.18860/ca.v6i4.11254

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Yundari Yundari, Setyo Wira Rizki

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.