Abstract
Generalized Space-Time Autoregressive (GSTAR) model is one of the models that usually used for modeling and forecasting space and time series data. The aim of this paper is to study further about the stationarity conditions for parameters in the GSTAR model and the relation to Vector Autoregressive (VAR) model. We focus on the theoretical study about stationarity condition in GSTAR(11) and the relation tothe stationarity condition of parameters in VAR(1). Then, we do an empirical study to give counter examples for the theorem of stationarity condition proposed by Borovkovaet al. The results show that the theorem of stationarity condition of parameters in GSTAR(11) model given by Borovkova et al. is incorrect. Additionally, the empirical results also show that GSTAR(11) model could always be represented in VAR(1) model by applying matrix operation to the space and time parameters. Hence, we can also conclude that VAR model, particularly VAR(1), is an extension of GSTAR(11) model with any possibility values of space and time parameters.DOI : http://dx.doi.org/10.22342/jims.13.1.90.115-122
Highlights
The time series data in many empirical studies consist of observations from several variables, known as multivariate time series data [2]
We will do a theoretical study about stationary condition of parameters in Generalized Space-Time Autoregressive (GSTAR) models related to a Vector Autoregressive (VAR) model
Stationarity condition of parameters at GSTAR(11) model proposed by Borovkova et al [1] as stated in Theorem 4.1. is incorrect
Summary
The time series data in many empirical studies consist of observations from several variables, known as multivariate time series data [2]. We frequently deal with the data that depend on time (with past observations) and on site or space, called spatial data. 2000 Mathematics Subject Classification: 62M45 Key words and Phrases: stationarity condition, GSTAR, VARIMA, space and time series model is a model that combines time and space dependence which affects certain multivariate time series data. This model firstly proposed by Pfeifer and Deutsch (see [7, 8]). Some previous comparison studies on the comparison of building model steps between GSTAR and VARIMA models can be found in [9]
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