1. (a) Explain the di?erence between an autoregressive and a moving-average process.
(b) Why are AR and MA processes referred to as stationary processes?
2. (a) Autoregression is a process in which a proportion of yt is carried forward to the next period, then a proportion of ytþ1 is carried to the next, and so forth. Since some of yt is in ytþ1 when it is carried forward, we say that autoregression is long-lasting. A high observation at time t will be carried
forward inde?nitely in smaller and smaller proportions. The moving-average process, on the other hand, carries forward "t, the random component of yt, so previous observations are not perpetuated.
(b) Both the AR process (given that jy1j 1), and the MA process eventually revert back to their original means after a positive or negative shock. In the AR process, the shock eventually dies out. In the MA process, the shock leaves after a number of periods greater than the number of lags in the MA process. Since both of these processes stay around their means, they are stationary.