The acf is clearly declining very slowly in this case, which is consistent with their being an autoregressive part to the appropriate model. The pacf is clearly significant for lags one and two, but the question is does it them become insignificant for lags 2 and 4, indicating an AR(2) process, or does it remain significant, which would be more consistent with a mixed ARMA process? Well, given the huge size of the sample that gave rise to this acf and pacf, even a pacf value of 0.001 would still be statistically significant. Thus an ARMA process is the most likely candidate, although note that it would not be possible to tell from the acf and pacf which model from the ARMA family was more appropriate. The DGP for the data that generated this plot was y_t = 0.9 y_(t-1) - 0.3 u_(t-1) + u_t.
-If a series, y, is described as "mean-reverting", which model from the following list is likely to produce the best long-term forecasts for that series y?
A) A random walk
B) The long term mean of the series
C) A model from the ARMA family
D) A random walk with drift

Question

Quizplus · Accepted Answer

Given the description of the series as "mean-reverting," the best model for long-term forecasts would be one that predicts a return to a long-term mean, hence option B. Mean reversion implies that the series tends to move back towards its average value over time, making the long-term mean a suitable forecast.

The Acf Is Clearly Declining Very Slowly in This Case