Question

Sample: 1983 2017 Included observations: 35 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 1 1 I 1 1 inta I 1 1 0.517 0.517 10.164 0.001 2 0.234 -0.044 12.318 0.002 3 0.234 0.178 14.526 0.002 4 0.158 -0.041 15.570 0.004 5 0.216 0.193 17.576 0.004 6 0.281 0.103 21.098 0.002 7 0.106 -0.144 21.619 0.003 8 -0.073 -0.164 21.873 0.005 9 -0.181 -0.192 23.497 0.005 10 -0.066 0.146 23.720 0.008 11 0.066 0.082 23.955 0.013 12 0.040 -0.007 24.046 0.020 1 1

explain which time series model is more likely to describe the time series, an AR(1), AR(2), MA(1) or MA(2) process? Justify your answer

Answer 1

Sol:

The PACF (Partial Autocorrelation) plot tells the number of AR terms to be added in the model for correcting the autocorrelation in the time series. On the other hand, ACF (Autocorrelation) plot tells the number of MA terms to be added in the model for correction of autocorrelation present in the data.

Since the PACF (Partial Autocorrelation) plot shows a significant spike at lag 1, this shows that the higher order autocorrelations will be explained by the lag 1 autocorrelation as in the question above. Meanwhile, ACF plot shows a sharp cut-off at lag 1 but slowly decays along the time-series.

Hence, according to significant lag at 1 in the Partial Autocorrelation plot, AR(1) is the time-series model which describes the above time-series.