Forecasting with an ARMA model

In the previous chapter, Chapter 4, Simple Predictive Analytics with NumPy, we learned about autoregressive models. ARMA is a generalization of these models that adds an extra component—the moving average. ARMA models are frequently used to predict values of a time-series. These models combine autoregressive and moving-average models. Autoregressive models predict values by assuming that a linear combination is formed by the previously encountered values. For instance, we can consider a linear combination, which is formed from the previous value in the time-series and the value before that. This is also named an AR(2) model since we are using components that lag two periods. In our case, we would be looking at the number of sunspots one year before and two years before the period we are predicting. In an ARMA model, we try to model the residues that we cannot explain from the previous period data (also known as unexpected components). Here, a linear combination...