Autoregressive models

An autoregressive model can be used to represent a time series with the goal of forecasting future values. In such a model, a variable is assumed to depend on its previous values. The relation is also assumed to be linear and we are required to fit the data in order to find the parameters of the data. The mathematical formula for the autoregressive model is as follows:

In the preceding formula, c is a constant and the last term is a random component also known as white noise.

This presents us with the very common problem of linear regression. For practical reasons, it's important to keep the model simple and only involve necessary lagged components. In machine learning jargon, these are called features. For regression problems, the Python machine learning scikit-learn library is a good, if not the best, choice. We will work with this API in Chapter 10, Predictive Analytics and Machine Learning.

In regression setups, we frequently encounter the problem of overfitting...