Page 221 - Contributed Paper Session (CPS) - Volume 2

CPS1834 Gumgum D. et al.
in rainfall are influenced by the gravity of the moon. Based on Tsubatsa
Kohyama's research, the authors consider the use of calendar based on the
rotation of the moon compared to the rotation of the Sun.
What is interesting to examine from the problems above is, whether
rainfall data using the Hijri calendar will provide good results compared to
rainfall data using the Gregorian calendar (AD). If the extent to which the
difference occurs if both are modelled with the same model (SARIMA).

2. Method
This research use Seasonal Model of ARIMA (autoregressive Integrated
moving Average),the general ARIMA model can be write as follows;

M K i d N

0 
  j ( ) (1 B i s ) =  +  k ( )a
−
B
B
t
j= 1 i= 1 k 1 =
Thus, the model may contain K differencing factors, M autoregressive
factors, and N moving average factors. This extension is useful in describing
many non-standard time series that, for example, may contain a mixture of
seasonal phenomena of different periods. Since it is this general form that
most time series software use, we now explain this general model in more
detail.
The ith differencing factor is
i d
−
(1 B i s )
With the order si (the power B) and the degree di. If K=0, then Z = t Z − t  .

Otherwise, Z = Z , as the mean of time series, does not exist. The parameter
t
t
 represents the deterministic trend and is considered only when K  . The
0
0
jth autoregressive factor
−
B =
−
... 
2
 j ( ) ( 1  1 j B  2 j B − − jp j B j p )
Contains one more autoregressive parameter,  jm . The kth moving average
factor is
2
 k ( ) (1B = −  k 1 B − k 2 B − ... − kq k B k q )
And contains one or more moving average parameter,  kn . In most
applications, the value of K, M and N are usually less than or equal to 2.
Parameters in autoregressive and moving average factors beyond the first
factor of each kind are normally considered seasonal parameters in the model.
The well-known Box Jenkins multiplicative seasonal ARIMA model
D
d
 P ( ) ( )(1B  s p B − B ) (1 B− s ) Z =  q ( ) ( ) a Q B s t
B
t
Where

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