The following output is for none-seasonal ARIMA model of certain time series aft
ID: 3375276 • Letter: T
Question
The following output is for none-seasonal ARIMA model of certain time series after second difference: 6) Type MA 1 MA 2 0.6569 0.0630 -10.42 0.000 Constant 35.1822 0.2223 158.23 0.000 Coef SE 0.52370.0631 8.29 0.000 Residuals: Ss 845.701 MS5.753 DE 147 Modified Box-Pierce (Ljung-Box) Chi-Square statistic Lag Chi-Square 10.4 22.5 27.3 38.0 DF P-Value 12 24 36 48 21 45 0.318 0.369 0.7450.760 a) Write a paragraph to explain the model b) Test the invertibility of the model c) Write a forecast equation in terms of Y. d) Find the point forecast and 95% P1 for T 151 (Y148-33.1, Y149-332, Y?50 33.5)Explanation / Answer
Answer
Part a)
Here we can see that here our model is ARIMA with order (0,0,2) .
From the above first table we see that all the p-values are less than 0.05
Conclusion - All our parameters are significant.
From the avobe mentioned second table data we see that all the p values are greater than 0.05
Hence,
Conclusion-------Residuals cant capture any pattern of the model and thereby all the patterns are captured by the model itself.
Part b)
Yes, the given model is invertible because the ARIMA(0,0,2) model can be written as MA(2) model that is moving average model.
Part c)
The model can be written as follows:
Zt=35.1822+Yt-1+0.5237Yt-2-0.6569Yt-3
Part d)
The point forecast for T=151 is given by putting the value of T in the above fromulae .
We got as
Z151=35.182+33.5+0.5237*33.2-0.6569*33.1
=64.3254
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