Time series forecasting as regression
A time series, as we saw in Chapter 1, Introducing Time Series, is a set of observations taken sequentially in time. And typically, time series forecasting is about trying to predict what these observations will be in the future. Given a sequence of observations of arbitrary length of history, we predict the future to an arbitrary horizon.
We saw that regression, or machine learning to predict a continuous variable, works on a dataset of examples, and each example is a set of input features and targets. We can see that regression, which is tasked with predicting a single output provided with a set of inputs, is fundamentally incompatible with forecasting, where we are given a set of historical values and asked to predict the future values. This fundamental incompatibility between the time series and machine learning regression paradigms is why we cannot use regression for time series forecasting directly.
Moreover, time series forecasting...
