MTB > Retrieve 'C:\MTBWIN\STUDENT9\CPI.MTW'.

MTB > print c2

Data Display

 

CPIChnge

1.7 1.0 1.0 1.3 1.3 1.6 2.9 3.1 4.2 5.5 5.7 4.4 3.2 6.2 11.0 9.1 5.8 6.5 7.6 11.3 13.5 10.3 6.2 3.2 4.3 3.6 1.9 3.6 4.1 4.8 5.4 4.2 3.0

MTB > TSPlot

  

 

MTB > %acf c2

  

 

MTB > %pacf c2

  

MTB > arima 1 0 1 c2;

SUBC> fore 5 c3 c4 c5;

SUBC> gser;

SUBC> gacf;

SUBC> gpacf;

SUBC> ghist;

SUBC> gnormal.

ARIMA Model

ARIMA model for CPIChnge

Estimates at each iteration

Iteration SSE Parameters

0 323.251 0.100 0.100 4.522

1 200.616 0.250 -0.050 3.745

2 182.146 0.184 -0.200 4.067

3 163.067 0.135 -0.350 4.308

4 142.864 0.107 -0.500 4.434

5 121.402 0.111 -0.650 4.407

6 99.668 0.150 -0.800 4.197

7 77.036 0.268 -0.950 3.590

8 67.550 0.418 -0.956 2.828

9 62.802 0.568 -0.964 2.062

10 62.108 0.637 -0.973 1.687

11 62.030 0.644 -0.979 1.619

12 62.003 0.647 -0.982 1.584

13 61.996 0.651 -0.985 1.549

14 61.996 0.651 -0.986 1.539

Unable to reduce sum of squares any further

Final Estimates of Parameters

Type Coef StDev T

AR 1 0.6513 0.1434 4.54

MA 1 -0.9857 0.0516 -19.11

Constant 1.5385 0.4894 3.14

Mean 4.412 1.403

Number of observations: 33

Residuals: SS = 61.8375 (backforecasts excluded)

MS = 2.0613 DF = 30

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48

Chi-Square 9.6(DF=10) 17.0(DF=22) * (DF= *) * (DF= *)

Forecasts from period 33

95 Percent Limits

Period Forecast Lower Upper Actual

34 3.1362 0.3216 5.9507

35 3.5810 -1.8180 8.9801

36 3.8708 -2.3061 10.0476

37 4.0594 -2.4192 10.5380

38 4.1823 -2.4201 10.7848

  

  

 

 

 

 

 

 

 

 

 

 

 MTB > cdf 9.6;

SUBC> chis 12.

Cumulative Distribution Function

Chi-Square with 12 DF

x P( X <= x)

9.6000 0.3490

MTB > cdf 17.0;

SUBC> chis 24.

Cumulative Distribution Function

Chi-Square with 24 DF

x P( X <= x)

17.0000 0.1513

MTB > arima 2 0 0 c2

Type Coef StDev T

AR 1 1.1872 0.1625 7.31

AR 2 -0.4657 0.1624 -2.87

Constant 1.3270 0.2996 4.43

Mean 4.765 1.076

Number of observations: 33

Residuals: SS = 88.6206 (backforecasts excluded)

MS = 2.9540 DF = 30

Modified Box-Pierce (Ljung-Box) Chi-Square statistic

Lag 12 24 36 48

Chi-Square 19.8(DF=10) 25.4(DF=22) * (DF= *) * (DF= *)

MTB >