A time series is just a sequence of random variables, Y₁, Y₂, …, Y_T, indexed by an evenly spaced sequence of points in time. Time series are ubiquitous in everyday life; we can observe the total amount of rainfall in millimeters over yearly periods for consecutive years, the average daytime temperature over consecutive days, the price of a particular share in the stock market at the close of every day of trading, or the total number of patients in a doctor's waiting room every half hour. As we can see, examples abound.

To analyze time series data, we use the concept of a stochastic process, which is just a sequence of random variables that are generated via an underlying mechanism that is stochastic or random, as opposed to deterministic. From the perspective of the predictive modeler, our goal is to study time series in order to build a model that best describes the behavior of a finite set of samples that we have obtained, in order for us to predict how...