Proceedings of the IConSSE FSM SWCU 2015, pp. SC.30–37 ISBN: 978-602-1047-21-7
SWUP
SC.30
The simulation studies for Generalized Space Time Autoregressive-X GSTARX model
Junta Dwi Kurnia
a
, Setiawan
b
, Santi Puteri Rahayu
c
a, b, c
Department of Statistics, Institut Teknologi Sepuluh Nopember Surabaya, Kampus ITS Sukolilo Surabaya 60111, Indonesia
Abstract
Generalized Space Time Autoregressive-X GSTARX is a model that involve the predictor variable X introduced by Pfeifer dan Deutsch. Generalized Space Time Autoregressive
GSTAR is one of multivariate time series models that combine elements of time and location or spatial data or time series. X Variable in GSTAR is a symbol that has a metric
and non-metric scale. For the case of univariate time series using the predictor X with metric scale called the Transfer Function Model, while for non-metric scale called the
Intervention Model and Calendar Variations. The literature studies showed that studies regarding the approach of multivariate time series by using GSTAR-X is still limited to
models involving variable X with non-metric scale, so that in this research restricted use a variable X with a metric scale. GSTAR-X estimation method for using the Generalized
Least Square GLS, as well as the estimation method on the model Seemingly Unrelated Regression SUR that introduced by Zellner. The purpose of this research is to obtain a
parameter estimation from GSTAR-X model with simulation study. Results of the simulation study showed that, if the residual of simulation are correlated, it will generate
a error standard of parameters estimate values are small in GSTARX-SUR model than GSTARX-OLS so it can be said that the parameter estimation using GSTARX-SUR is more
efficient than GSATRX-OLS.
Keywords GSTARX-SUR, GSTARX-OLS, metric, predictor
1. Introduction
GSTAR is one of multivariate time series models that involve more than one response and correlated. GSTAR is the development of models Space Time Autoregressive STAR
introduced by Pfeifer Deutsch 1980. This model is a model that combines elements with the elements of the spatial dependency of time or location. STAR model itself is a
development of the Model Vector Autoregressive Integrated Moving Average VARIMA, but the VARIMA model has not been paying attention time with spatial dependencies. Therefore
developed a method that combines elements of time and location dependencies multivariate with spatially heterogeneous elements which was then called the method GSTAR Ruchjana,
2002
GSTAR method involving the predictor variables called GSTARX. Variable X in GSTAR is a symbol that has a metric and non-metric scale. For the case of univariate time series using
the predictor X with metric scale called the Transfer Function Model, while for non-metric scale called the Intervention Model and Variations Calendar. Research on Transfer Function
Model can be seen in Wu Tsay 2003 on the role of test statistics on a limited sample case through simulations using Transfer Function Model. For research on intervention models
have been widely applied, one by Suhartono 2007 on the effect of the first Bali bombing against a five-star hotel occupancy. While one study on Variation Model Calendar conducted
by Lee et al. 2010 for the sales data male Muslim clothing by adding the effect of Ramadhan.
J.D. Kurnia, Setiawan, S.P. Rahayu
SWUP
SC.31
While research has been conducted by GSTARX Suhartono et al., 2015 concerning GSTARX model for forecasting the data spatio temporal in the case of inflation of four cities in East
Java with X-scale non-metric, ie Eid events and factors rise in fuel prices, as well as research by Oktanindya 2014 regarding the intervention model GSTARX and a step pulse is applied
to the case of foreign tourists forecasting. Studies of multivariate time series approach using GSTARX is still limited to models involving variable X with non-metric scale.
GSTARX estimation method using the GLS, as well as the estimation method on the model equations SUR. Ordinary Least Square method OLS can not be used for multivariate
model consisting of multiple equations that are correlated because it will produce a estimator is less efficient, in the sense that the resulting variance would be very large.
Based on the description that has been described above, in this study will be conducted further studies on multivariate time series model with variable X metric using GLS estimation.
The aim of this study is to obtain estimates of the model parameters GSTARX through simulation studies.
2. Materials and methods
