statistika/matematika/metode ARIMA/time series analysis

1. ABSTRACT
Sri Hartati Ningsih, 2011.-- FORECASTING OF MONTHLY RAINFALL IN
RAINFED AREAS OF LOMBOK ISLAND USING ARIMA METHODS (i – xv; 169
pages) (Supervisors : I Gde Ekaputra Gunartha and I Gede Adhitya Wisnu
Wardhana)
This study aims to find the best models for forecasting the monthly rainfall in rainfed
areas of Lombok Island using ARIMA methods, and then to predict the monthly
rainfall for the year of 2010. Four sets of data from January 2000 until Desember
2009 were analyzed to construct the models, i.e. the monthly rainfall data of Sikur
District (East Lombok), Mujur District (Central Lombok), Sekotong District (West
Lombok), and the Bayan District (North Lombok). So, there are 120 points of
monthly rainfall data were modeled.
In the study, the ARIMA modeling was done through five stages, namely stationary
of data, model identification, parameter estimation, model verification, and
implementing the selected models for forecasting.
The results found that the best model for forecasting the monthly rainfall in the four
rainfed regions of Lombok Island, are as follows:
1. The rainfall in the District of Sikur is modeled well by using ARIMA (1,1,1)
(1,0,1)12 without constant, with the form of equation :
Yt  Yt-1  1Yt 1  1Yt 2   1Yt 12   1Yt 13  1 1Yt 13  1 1Yt 14
ˆ
-  1et 1  1et 12  11et 13
2. In District of Mujur using ARIMA (0,1,1)(1,0,1)12 without constant, with the
form of equation :
Yt  Yt-1   1Yt 12   1Yt 13  1et 1  1et 12  11et 13
ˆ
3. In District of Sekotong using ARIMA (0,1,1)(0,1,1)12 without constant, with the
form of equation :
Yt  Yt-1  Yt 12  Yt 13  1et 1  11et 1  1et 12
ˆ
4. Whereas in District of Bayan using ARIMA (0,1,1)(1,1,1)12 without constant,
with the form of equation :
Yt  Yt-1  Yt 12   1Yt 12  Yt 13   1Yt 13   1Yt  24   1Yt  25
ˆ
-  1et 1  1et 12   11et 13
©
Program Studi Matematika – FMIPA Universitas Mataram (2011)

2. Using the models obtained above show that the forecasts and the actual monthly
rainfall data of 2010 at four locations studied spread within the 95% confidence
interval lines. This means that the selected models follow the distribution patterns of
actual data.
Key words: forecasting, monthly rainfall, and ARIMA methods
©
Program Studi Matematika – FMIPA Universitas Mataram (2011)