Statistical Learning for Big Dependent Data

CHAPTER 2LINEAR UNIVARIATE TIME SERIES

In this chapter, we study methods for modeling and forecasting univariate time series. Our study is brief and focuses on the automatic analysis of large sets of time series. Interested readers can consult any of the many time series textbooks for further details. See, for instance, Peña et al. (2001), Box et al. (2015), Brockwell and Davis (2013), Cryer and Chan (2008), Shumway and Stoffer (2017), and Tsay (2010, 2014), among others.

Given a set of time series, the first step of the analysis is to visualize the data by plotting the series in order to understand their basic properties. One would also try to detect gross measurement errors that are quite common with data recorded in an automatic way. These errors may happen at some specific times in many series, or be concentrated in a few series making them different from the others. The graphical representations we present are designed to identify both cases of measurement errors. Once the set of time series has gone through some cleaning, we present statistical methods to model and forecast the series. The models most commonly used for stationary time series are the autoregressive moving-average (ARMA) models, that have proved to be useful in many scientific fields. Particular members of this family are the autoregressive (AR) models, where the series depends only on its first lagged values ...