Question

A stationary time series of length 121 produced sample partial autocorrelation of

φ^11 = 0.8, φ^22 = −0.6, φ^33 = 0.08, and φ^44 = 0.00. Based on this information alone, what model would we tentatively specify for the series?

Answer 1

A stationary time series of length 121 produced sample partial autocorrelation of

φ^11 = 0.8, φ^22 = −0.6, φ^33 = 0.08, and φ^44 = 0.00.

Based on this information alone, ARIMA(0,1,0) model would we tentatively specify for the series.

In this the autocorrelation function of first is positive, then negative, then positive similarly this sequence is occur. therefore the model is ARIMA(0,1,0).

which is an ARIMA(0,1,0) without constant forecasting equation with θ₁ = 1-α. This means that you can fit a simple exponential smoothing by specifying it as an ARIMA(0,1,0) model without constant, and the estimated MA(1) coefficient corresponds to 1-α in the SES formula.