Discrete time models

Discrete time models, such as the ones we have been looking at so far, separate time into slices at regular intervals. For us to be able to predict future values of time slices, we assume that they are dependent on past slices.

Note

Time series can also be analyzed with respect to frequency rather than time. We won't discuss frequency domain analysis in this chapter but the book's wiki at http://wiki.clojuredatascience.com contains links to further resources.

In the following, let y_t denote the value of an observation at time t. The simplest time series possible would be one where the value of each time slice is the same as the one directly preceding it. The predictor for such a series would be:

This is to say that the prediction at time t + 1 given t is equal to the observed value at time t. Notice that this definition is recursive: the value at time t depends on the value at t - 1. The value at t - 1 depends on the value at t - 2, and so on.

We could model this...