MODELING OF INDONESIA CONSUMER PRICE INDEX USING MULTI INPUT INTERVENTION MODEL
P. W. Novianti 1 Suhartono 2
IV. EMPIRICAL RESULT
IV.2. Intervention Modeling of Indonesia CPI
First intervention event which affected Indonesia CPI is monetary crisis in 1997/ 1998. It is a step function intervention. Based on Figure (IV.6), data pattern of ARIMA model forecasting (green line) is different from data pattern before intervention (red line). It indicates that intervention occurs and has significant effect.£The first step in intervention modeling is identifying the value of b, s, and r. This identification is done by evaluating into residual bar chart of pre intervention model (Figure IV.6(b)).
Based on Figure IV.6(b), we got b=2, s=[1,4,5,6,7], and r=0. The result of parameter estimation and signification test show that all of parameters are significant, so intervention model is written as
(IV.19)
87
Modeling of Indonesia Consumer Price Index Using Multi Input Intervention Model
Model (IV.19) shows that monetary crisis gives positive escalation. Two months after intervention occurred, the magnitude of intervention is 0.2. This escalation is become 7.7 in the ninth month after intervention. The detail of monetary crisis effects is shown in Table IV.2.
Figure IV.6
(a) Time Series Plot (b) Bar Chart Residual of Pre Intervention Model
(a) (b)
Table IV.2
Effects of Monetary Crisis to Indonesia CPI
T+2 September 1997 0.2
T+3 - T+5 October-December 1997 0.2+0.3=0.5
T+6 January 1998 0.2+0.3+0.2=0.7
T+7 February 1998 0.2+0.3+0.2+3.7=4.4
T+8 March 1998 0.2+0.3+0.2+3.7+1.8=6.2
T+9 April 1998 0.2+0.3+0.2+3.7+1.8+1.5=7.7
Time (t) Month Effect»s Magnitude
Time Series Plot Data Aktual, Fit, dan Forecast
Month Year
T 40
35 30 25 20 15
Data Variable Aktual fit for
Jan Jan Jan Jan Jan Jan Jan
1989 1990 1992 1995 1996 1997 1998
Jan 1994 Jan 1993 Jan
1991
T
Bar Chart Residual Hasil Pemodelan Pre Intervensi Residual
-0.27 0.27
T 10
8 6 4 2 0
9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
Figure IV.7
(a) Time Series Plot (b) Residual Bar Chart of Intervention Model because of Monetary Crisis
(a) (b)
Time Series Plot Data Aktual, Fit, dan Forecast Hasil Pemodelan Intervensi 1
Month Year
50
40
30
20
10 Data
Variable Aktual fit-kris for_kris
Jan Jan Jan Jan Jan Jan Jan
1989 1990 1992 1995 1996 1997 1998
Jan 1994 Jan 1993 Jan 1991
Jan 1999
Bar Chart Residual Hasil Pemodelan Intervensi 1 Residual T
-0.30 0.30 T
14 12 10 8 6
0 4 2
9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
-8 10 111213 14 1516
The second intervention is fuel price rising on May 1998 (25-71.43%). It gives additional escalations to Indonesia CPI. Based on the results in Figure 7(b), we got b=0, s=4, and r=0.
Intervention model is
and the impacts are presented in Table IV.3. These results show that the government policy had direct impact to CPI. In the first month (the same month as this event occurred), CPI rose for almost 2 points and would be 3.8 points in the following month. Furthermore, CPI on September 1998 was 12.4 points higher than a month before this regulation had been applied. It shows that the fuel price rising which happened in the crisis era has quite big effect to CPI.
Table IV.3
Effects of Fuel Price Rising on May 1998 to Indonesia CPI
T May 1998 1.9
T+1 June 1998 1.9+1.9 =3.8
T+2 July 1998 1.9+1.9+3.8 =7.6
T+3 August 1998 1.9+1.9+3.8+2.9 =10.5
T+4 September 1998 1.9+1.9+3.8+2.9+1.9 =12.4
Time (t) Month Effect»s Magnitude
Modeling of multi input intervention is continued by detecting the order for the next intervention, independence of Timor-Timur. Theoretically, Timor-Timur was not being part of Indonesia in 2002, but BPS has not included Dili (former capital city of Timor√Timur) in CPI»s calculating since October 1999. Therefore, we assume that independence of Timor-Timor happened on October 1999. As the previous intervention, order detection is done by evaluating on to residual bar chart of the previous intervention model.
89
Modeling of Indonesia Consumer Price Index Using Multi Input Intervention Model
Thus, we got the new multi input intervention model as follows
Based on that model, the impact is written as in Table IV.4. The independence of Timor-Timur started to affect CPI dataset in two months after it occurred. The escalation remained stable during December 1999 - June 2000, but there was a slight increase in Indonesia CPI on July and August 2000.
Figure IV.8
(a) Time Series Plot (b) Residual Bar Chart of Intervention Model because of Fuel Price Rising on May 1998
(a) (b)
Time Series Plot Data Aktual, Fit, dan Forecast Hasil Pemodelan Intervensi 2
Month Year
50
40
30
20
10 Data
Variable Aktual fit_B98 for_B98
Jan Jan Jan Jan Jan Jan Jan
1989 1990 1992 1995 1996 1997 1998 Jan
1994 Jan 1993 Jan 1991
Jan 1999
Jan 2000
Residual Hasil Peramalan dengan Model Intervensi Tahap 2 Residual T
-0.408 0.408
T 3.0
2.5 2.0 1.5 1.0 0.5 0.0 -0.5
9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
-8 10 11
-9 -10 -11 -12 -13 -14 -15 -16 -17
Table IV.4
Effects of Independence of Timor-Timur to Indonesia CPI
T+2 - T+8 December 1999-June 2000 0.6
T+9 July 2000 0.6+0.7 = 1.3
T+10 August 2000 0.6+0.7+0.4 = 1.7
T+11 September 2000 0.6+0.7+0.4 = 1.7
Time (t) Month Effect»s Magnitude
Based on the result at Table IV.1, the next intervention is fuel price rising on October 2000. By using the same step as the previous intervention, we got the new intervention model.
Then, we applied that model to identify the order of the next intervention event, base year changing on 2002. In each base year changing, BPS always magnifies the number of commodities and cities. To know the effect of this addition, we consider that it is an intervention event.
Figure IV.9 shows that an intervention event effects CPI dataset. Estimation and signification test for parameter yields intervention model as follows
Government raised the price of fuel on January 2003. The percentage of this rising is 3 until 28 percent. Surprisingly, this government»s policy was not affected to CPI. It can be seen in Figure IV.10, where there is no residual which out of the confidence interval. However, residuals on t=175 and t>180 are out of the limit. It indicates that there are other intervention effects in CPI dataset. Having included those observations and re-estimates parameters coefficients, the model is re-written as
Figure IV.9
(a) Time Series Plot (b) Residual Bar Chart of Intervention Model because of Fuel Price Rising on October 2000
(a) (b)
Time Series Plot of IHK_1, Fits, for BB M00
Month Year
50 40 30 20 10
Data Variable IHK_1 Fits ForBBM00
Jan Jan Jan
1989 1995 1997
Jan 1993 Jan 1991
Jan 1999
Jan 2001 60
70
Residual Hasil Peramalan dengan Model Intervensi Tahap 2 Residual T
-0.419 0.419
T 5
4 3 2 1 0
9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
-8 10 11
-9 -10
91
Modeling of Indonesia Consumer Price Index Using Multi Input Intervention Model
Model (IV.20) is used to obtain the order of Tsunami disaster, which is the next intervention event. The new model for intervention after included this intervention event is
That model gives information that Tsunami disaster affected to CPI only in the first month after that event happened. The increasing of CPI is 0.5 on January 2005.
By using the same steps, modeling of intervention with all of intervention events on Table (IV.1) produces multi input intervention model as follows
(IV.20)
Figure IV.10
(a) Time Series Plot (b) Residual Bar Chart of Intervention Model because of base year changing on 2002
(a) (b)
Time Series Plot of Aktual,fits, for
Month Year
50 40 30 20 10
Data Variable Aktual fits for
Jan Jan Jan
1989 1995 1997
Jan 1993 Jan 1991
Jan 1999
Jan 2003 60
80 70
Jan 2001
Bar Chart Residual Hasil Pemodelan Tadas 02 Residual T
-0.452 0.452
T 3
2
1
0
9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7
-8 10 11
-9 -10 -1
1213 1415 1617 1819 20 2122
Multi input intervention Model (IV.21) has high value of kurtosis. It can be caused by a lot of residual which have zero value. RMSE of this multi input intervention model is 0.184.
Besides those events which were written on Table IV.1, Equation (IV.21) shows that Ied on January 1999 (X121), events on December 2005 and September 2008 (X237) give positive impact in Indonesia CPI. Whereas, events on April 2002 (X160) and July 2003 (X175) yield negative effect to Indonesia CPI. Table IV.2 gives details information about each event»s effect. Fuel price risings tend to give direct and positive effect to CPI. During research period, there is only one of fuel price raisings that not affecting CPI which happened on January 2003. Conversely, the highest percentage of fuel price rising happened on October 2005 (125 percent), as a result, CPI rose more than 6 points in that month.
Fuel price risings do not have big impact during Orde Baru era. However, it gives quite big impact in Reformation era. For instance, there was a slight increase in CPI because of fuel price rising on January 1993 (27 percent), but this regulation yields high rising on CPI when the percentage of escalation was only 30 percent (March 2005). It shows that CPI is more sensitive by fuel price rising in Reformation Era than Orde Baru era.
(IV.21)
93
Modeling of Indonesia Consumer Price Index Using Multi Input Intervention Model
Monetary crisis in 1997/1998 gave positive and permanent effect to CPI. Though the effect was felt six months after it started, the CPI increased gradually in that month, 1.2. Other event, independence of Timor-Timur is also give positive and permanent impact.