trend and cycle trend and seasonality only cycle only seasonality non linearity

Question

       trend and cycle
       trend and seasonality
       only cycle
       only seasonality
       non linearity

You have a quarterly data series ACFs and the first four autocorrelation are significantly different from zero and the 4th lag autocorrelation is slightly above the 3rd lag autocorrelation. Also, the subsequent autocorrelations decreases slowly toward zero. In addition the autocorrelations for lag 8, 12 and 16 are significantly different from zero. What are your data autoregressive characteristics? (Points : 3)

Explanation / Answer

Examine the ACF and PACF of the differenced data (if differencing is necessary).

We’re using this information to determine possible models. This can be tricky going involving some (educated) guessing. Some basic guidance:

Non-seasonal terms: Examine the early lags (1, 2, 3, …) to judge non-seasonal terms. Spikes in the ACF (at low lags) indicate non-seasonal MA terms. Spikes in the PACF (at low lags) indicated possible non-seasonal AR terms.

Seasonal terms: Examine the patterns across lags that are multiples of S. For example, for quarterly data, look at lags 4,8,12 and 16 so on (probably won’t need to look at much more than the first two or three seasonal multiples). Judge the ACF and PACF at the seasonal lags in the same way you do for the earlier lags.

hence the anwer will be only seasonality.

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