Statistical Learning for Big Dependent Data

CHAPTER 4HANDLING HETEROGENEITY IN MANY TIME SERIES

Empirical time series are often affected by multiple occasional events that produce different causes of heterogeneity. The impacts of these events should be considered in the modeling process because they may lead to biased parameter estimates and/or model misspecification, resulting in poor forecasting performance. The first class of events we consider consists of a known cause such as strikes on a set of production series, a leap year on monthly sales series, a tariff change on import and export series, or an extreme climatological event on air pollution indexes. The second class of events deals with missing values in a time series caused by instrument failure or human errors. Here we assume that the missing values occur at random and, for a vector series, the whole data point or some elements of the vector may be missing. For these two types of events, we know their time of occurrence and want to remove its impact from the set of time series under study. How to carry out such adjustments is the focus of the first part of this chapter.

There are other situations in which we do not know if any atypical event has occurred, nor the time of its occurrence, if any. However, from the aberrant observations of the data, we can infer that some unexpected events did occur during the sampling period. Those aberrant data points are commonly referred to as outliers and were first studied in time series by Fox (1972). They happen often ...