Page 222 - Contributed Paper Session (CPS) - Volume 2

CPS1834 Gumgum D. et al.
 Z −  , if d = D = 0
Z =  t
t
 Z t , otherwise
For convenience, we often call  p ( ) and  p ( ) the regular
B
B
autoregressive and moving average factors (polynomial) and  ( ) and
s
B
P
 Q ( ) the seasonal autoregressive and moving average factors (or
s
B
plynomials), respectively. This model is often denoted as
ARIMA p ) ( , ,Q ) where the sub index s refers to the seasonal
( , , d q x P D
s
period.
For model selection, this research uses four types of models selections
there are MAPE (Mean Absolute Percentage Error, MAD (Mean Absolute
Deviation), MSE (Mean Square Error) and AIC (Akaike Information Criteria).
1. MAPE (Mean Absolute Percentage Error)
 1 M e 
MAPE =   t    x 100%
 M t= 1 Z n+ 1 
2. MSE (Mean Square Error)
1 M
MSE =  e
2
M t= 1 t
3. MAD (Mean Absolut Deviation)
1 M
MAD =  X − 
M t= 1 t
M is the number of out sample
4. AIC ( Akaike Information Criteria)

( ) = −
AIC K 2ln Maximum likelihood +
 2K

ˆ +
= n ln a 2 2K
K is the number of parameters in the models.

The optimal order of model is chosen by the value of M, which is a function
of p,q, so that AIC(K) is minimum.

3. Methodology
There are six step in comparison of SARIMA modelling based on Hijri and
Gregorian calendar. The first step is collecting data of rainfall data usually
available in Gregorian Calendar. The rainfall data obtained is secondary data
obtained at BMKG Aceh. The time series data obtained is daily data in the
Christian calendar. The researcher obtained data from March 1, 2000 to
December 31, 2017. Data processed for analysis is the sum of daily data into
monthly. The second step is converting rainfall data from Hijri to Gregorian
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