Many models that we come across involve observing a process of some sort over a period of time in order to learn to predict how that process will behave in the future. As we are dealing with a process that generates observations indexed by time, we refer to these models as time series models. Classic examples of time series are stock market indexes, volume of sales of a company's product over time, and changing weather attributes such as temperature and rainfall during the year.

In this chapter, we will focus on univariate time series, that is to say, time series that involve monitoring how a single variable fluctuates over time. To do this, we begin with some basic tools for describing time series, followed by an overview of a number of fundamental examples. It turns out that there is a wide variety of different approaches to modeling time series; in this chapter, we will focus primarily on ARIMA models, but we will also provide pointers on a few alternatives...