Summary

In this chapter, we've considered the task of analyzing discrete time series: sequential observations taken at fixed intervals in time. We've seen how the challenge of modeling such a series can be made easier by decomposing it into a set of components: a trend component, a seasonal component, and a cyclic component.

We've seen how ARMA models decompose a series further into autoregressive and moving-average components, each of which is in some way determined by past values of the series. This conception of a series is inherently recursive, and we've seen how Clojure's natural capabilities for defining recursive functions and lazy sequences lend themselves to the algorithmic generation of such series. By determining each value of the series as a function of the previous values, we implemented a recursive ARMA generator that was capable of simulating a measured series and forecasting it forwards in time.

We've also learned about expectation maximization: a way of reframing solutions...