Page 14 - ASBIRES-2017_Preceedings

A CASE STUDY ON THE QUALITY OF ALUMINIUM CABLES AND FORECASTING THE DEMAND OF
ALUMINIUM CABLES

According to the Figure 1, the series Table 5: Final estimates of parameters

is not stationary as a trend and seasonal Coefficient T P
variation is visible. To make the series
stationary a seasonal differencing has been Model A
performed. SAR 12 0.1053 -4.53 0.000
Constant 7.696 5.03 0.000
The correlogram and the partial
correlogram of the stationary series are Model B
shown in Figure 2 and Figure 3 respectively. SMA 12 0.0871 9.6 0.000
Constant 1.772 14.5 0.000

2The Modified Box-Pierce (Ljung-
Box) Chi-Square statistic for the both
models is presented in Table 6.

Table 6: Modified box-pierce (Ljung-Box)
Chi-Square statistic
Model A
Lag 12 24 36
Chi-Square 6.2 17.6 23.9

Figure 2: ACF of the stationary series DF 10 22 34
P-Value 0.8 0.73 0.901

Model B
Lag 12 24 36
Chi-Square 8.3 12 23.2
DF 10 22 34
P-Value 0.6 0.957 0.918

As depicted in Table 5, the residuals
can be assumed to be random at 5% level of
significance, because all the p-values are
greater than 0.05. The Normality of the
residuals is checked by using the normal
Figure 3: PACF of the stationary series
probability plot. The Normal probability
As illustrated in Figure 2 and Figure plots for both of the models are shown in
3, autocorrelations cuts off at seasonal lag 1 Figure 4. As shown in Figure 4, it can be
and partial autocorrelations cuts off at assumed that there is a straight line.
Therefore the residuals are normally
seasonal lag 1. distributed.

Therefore the identified models are Model B
Model A
Model A: SARIMA (0, 0, 0) (1, 1, 0)12

Model B: SARIMA (0, 0, 0) (0, 1, 1)12.

The summary of the parameter
estimation of the two models are represented
in Table 4.

According to the Table 5 all the
parameters are significant at 5% level of
significance in both models.

4