Introduction PROS Andria PD, Suhartono Two level parameter fulltext

Proceedings of the IConSSE FSM SWCU 2015, pp. SC.12–20 ISBN: 978-602-1047-21-7 SWUP SC.12 Two-level parameter estimates GSTARX-GLS model Andria Prima Ditago and Suhartono Statistics Department, Sepuluh November of Institute Technology, Surabaya 60119, Indonesia Abstract GSTAR is a special form of the VAR model and is one of the commonly used models for modeling and forecasting time series data and location. At GSTAR modeling, estimation method used is OLS, the method is considered to have a weakness, which will result in an inefficient estimator. Thus, one appropriate method is GLS. In this study, conducted modeling GSTARX two levels by adding a predictor of calendar variation model. Parameter estimation of the first level models made of predictors with a linear regression model, while the second level models using error models which is done on first level with GSTAR model. Calendar variation model discussed is the impact of Ramadhan effect. Results of the simulation study showed that GSTAR-GLS models produces a more efficient estimator than GSTAR-OLS, seen from the obtained standard error smaller. Keywords calendar variations, efficient, GLS, GSTARX, Ramadhan, two-level

1. Introduction

One approach that can be used to handle the data space-time is a Generalized Space Time Autoregressive models GSTAR. The model provides a more flexible and is an extension of the model STAR Borovkova et al., 2008. Different from STAR models, GSTAR does not require that the values of the same parameters for all locations. Therefore GSTAR more realistic, because in reality is more found models with different parameters for different locations. Theoretical studies relating to the nature of the parameters GSTAR asymptotically and weighting between locations given Lopuhaa Borovkova, 2005. Implementation of GSTAR has been done on the production of oil and Gross Domestic Product GDP in 16 Western European countries Nurani, 2002. In addition, research on comparison of between VARMA with GSTAR models Suhartono, 2005 showed that the fore- casting is more accurate GSTAR model. However, in the model building process in terms of theoretical and applied by the statistical program package was found that the model is more flexible and perfect VARMA. In addition, studies related to GSTAR especially for parameter estimation is still limited to using Ordinary Least Square OLS Borovkova et al., 2008 and Maximum Likelihood method Terzi, 1995. Parameter estimation using OLS in the multivariate model with residual correlated assessed as having a weakness, which will result in inefficient estimators. However, over the years, developed Generalized Least Square GLS estimation method. GLS methods commonly applied to the model Seemingly Unrelated Regression SUR, because one of the approaches that can be used to estimate the parameters in the model SUR is the GLS method Baltagi, 1980. SUR is a system of equations that consist of multiple regression equations, where each equation has a different response and possible predictors have different also. Advantages of system of equations SUR is able to accommodate the correlation between the error equation with the other equations. SUR models were first A.P. Ditago, Suhartono SWUP SC.13 applied in the case of gross investment demand in the two companies Zellner, 1962. The results obtained are the estimated parameters by GLS for the overall model is more efficient than the OLS parameter estimates for each model. In addition, SUR models are also applied to the spatio-temporal domains Wang Kockelman, 2007. SUR models were applied to estimate the parameters GSTAR provide assurance that the error of the model is a multivariate white noise Wutsqa Suhartono, 2010. Along with its development, GSTAR model can be expanded to GSTARX. In this case X is a notation for a predictor or input. Predictors can be a metric and or non-metric scale form. For this form metric, predictor will be conducted by transfer function model, whereas for the form of non-metric conducted by dummy variables. In the case of non-metric, the variable may be the effect of the intervention, outliers and calendar variations. This research will be used predictor of the calendar variation model to capture of Ramadhan effects. Implementation of the GSTARX model in this study will be discussed through a simulation study with the aim to get the right model building procedure according with the conditions of real data.

2. Materials and methods