Question

5) The following MINITAB output is for ARIMA model of certain time series of size 132. Type AR 1 AR 2 SAR 12 -0.27124 0.0662 1.590.113 Constant 0.074870.08826 -3.07 0.0026 Coef 0.62993 0.07249 8.69 0.001 0.20816 0.07344 2.83 0.0053 SE Residuals: SS-0.0002323 MS- 0.001409, DE=117 Modified Box-Pierce (Ljung-Box) Chi-square statistio Lag Chi-Square 8.6 15.4 28.038.7 DE P-Value 0.3859 0.7635 0.7029 0.6014 12 24 36 8 7 31 43 Which parameters should be included in the model and why? Based on your decision, write the general model and the prediction equation. State all hypotheses for the adequacy of the model, and test them What type of difference yields to stationary data. Find the point forecast and 95% P. I. of Y133 given that Y132-2979 and Y120 = 2990. a) b) c) d)

Answer 1

a) AR1 and AR2 with intercept should be included in the model because this is statistical significant the model.

The general time series model is AR(2) model when seasonal is not effect

$y_{t}=0.07487+0.20816y_{t-1}+0.6299y_{t-2}$

If seasoanl is there then

$(1+0.2712B^{12})(1-0.6299B-0.20816B^{2})(y_{t}-0.0748)=w_{t}$

b) The Ljung-Box test (or Chi-squared test) tests are used for adequacy of the model and the following is the null hypothesis

$H_{0}:\rho _{1}=\rho _{2}=...=\rho _{k}$

The test result is describe in the table with different lag point. We can see that p-value is greater than 0.05. So, we fail to reject the null hypothesis.

c) The data is not need to difference because data is stationary data.