1) The following output is for the ARIMA model of a monthly time series of size

Question

1)    The following output is for the ARIMA model of a monthly time series of size 178:

Type         Coef      SE Coef      T      P

AR    1    -0.1716      0.0774     -2.22 0.028

AR    2     0.2118      0.6098      3.030 0.003

MA    1     0.1053      0.0662      1.590   0.113    

SMA 12     0.4652      0.0712      6.530   0.000

Constant    0.07526    0.06650    1.130 0.259

Number of observations: Original series 178, after differencing 165

Residuals:    SS = 282.4 (backforecasts excluded)

              MS = 1.765 DF = 160

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

Lag            12     24     36     48

Chi-Square    7.7   19.4   34.4   48.0

DF              9     21     33     45

P-Value     0.567 0.558 0.398 0.353

What type of difference transformation used in this model and name ARIMA?Test the significance of the estimates of the parameters?Write the general forecasting equation in terms of Y?Perform a diagnostic checking?

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Explanation / Answer

1. The model has used RA lagged by 1,2 and 3 months and SMA lagged by 12 months

2. At 0.05 level, we can see that p calues for RA1, RA2 and SMA are significant

3. Y_t = 0.07526 -0.1716RA_t-1 + 0.2118RA_t-2 +0.1053RA_t-3 +0.4652SMA_t-12

4. Diagnostic check is performed using the Box-Ljung test, used to test the lack of fit of a time series model. It is used to examine autocorrelations of the residuals after fitting the time series model. From the results we can see that the p value is more than 0.05 in all the cases and hence null hypothesis that the model does not exhibit lack of fit cannot be rejected.

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