multivariate analysis/ARIMA/Bootstrap

1. ABSTRACT
Trisnawati, 2012.-- ARIMA MODEL PARAMETER ESTIMATION OF
COMPOSITE STOCK EXCHANGE INDEX USING BOOTSTRAP METHOD (i –
xiv; 105 pages) (Supervisors : I Gde Ekaputra Gunartha and Mustika Hadijati)
The study aims to find the composite stock exchange index (CSEI) ARIMA model
using bootstrap method and to determine the amount of replication (B) which has a
significantly minimum bootstrap standard error. The data used in this study are data
CSEI on period of January 3 to June 30, 2011.
This study consists of several stages, namely: ARIMA model identification,
parameter estimation, estimation of parameter model selected using bootstrap
methods, and diagnostic checking. From model identification stage was selected
CSEI ARIMA model (2,1,0) without constant. Model parameters were estimated by
Ordinary Least Square method (OLS) and Maximum Likelihood Estimation (MLE)
using the software Minitab 15. The standard error (SE) of ARIMA model selected
then compared with the estimation results using the bootstrap method. The number
of replication (B) examined to obtain a significant minimum SE were 1000, 1100,
1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, and
2500 replicate. The analysis used the S-Plus 2000.
The results of study showed ARIMA model for periodic data of CSEI using bootstrap
methods as follows:
1. For the OLS algorithm obtained ARIMA model:
X t  X t 1  0,1717 X t 1  X t  2   0,1698 X t  2  X t 3 
ˆ
2. For the MLE algorithm obtained ARIMA model:
X t  X t 1  0,6659 X t 1  X t  2   0,3402 X t  2  X t 3 
ˆ
Bootstrap method can reduce the standard error of 39.91% in the ARIMA model with
OLS. While the MLE, the bootstrap method is not great influence on changes in the
value of its SE. Thus the bootstrap method is very well applied to the ARIMA model-
based estimates of OLS.
Based on the results of standard error calculation for each model above obtained the
number of B in the re-sampling process of bootstrap methods that has a significantly
minimum of SE is 1000 replicate.
Keywords: ARIMA, bootstrap, resampling
©
Program Studi Matematika – FMIPA Universitas Mataram (2012)