Discussion
The sample autocorrelation of certain time series data was found to be significant at lags one and five, whereas the sample partial autocorrelations were not significants for first 30 lags. What model would you suggest for such a time series ?
Answer: C
The suggested model is MA(5).
The signature of a moving average process of order \(q\) is an autocorrelation function that cuts off after lag \(q\), with partial autocorrelations that tail off. Significant autocorrelations at lags 1 and 5 only, with none of the partial autocorrelations significant, point to an MA model of order 5, with the coefficients at lags 2 to 4 possibly zero.
An AR(5) model would show the reverse pattern: partial autocorrelations cutting off after lag 5. The mixed ARMA models would show both functions tailing off, and significant partial autocorrelations would be expected.
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