Non-stationary time series models

In this section, we will look at some models that are non-stationary but nonetheless have certain properties that allow us to either derive a stationary model or model the non-stationary behavior.

Autoregressive integrated moving average models

The random walk process is an example of a time series model that is itself non-stationary, but the differences between consecutive points, Y_t and Y_t+1, which we can write as ∆Y_t, is stationary. This differenced sequence was nothing but the white noise sequence, which we know to be stationary.

If we were to take the difference between consecutive output points of the differenced sequence, we would again obtain another sequence, which we call a second order differenced sequence.

Generalizing this notion of differencing, we can say that a d^th order difference is obtained by repeatedly computing differences between consecutive terms d times, to obtain a new sequence with points, W_t, from an original sequence, Y_t. We can...