Time Series

This chapter focuses on time series in discrete time. It expresses that the time series is either stationary in some sense or may be reduced to stationarity by a combination of elementary differencing operations and regression trend removal. Two types of stationarity are in common use, second‐order stationarity and strict stationarity. A strictly stationary time series with finite second moments is obviously second‐order stationary. Outliers in time series are more complex than in the situations, where there is no temporal dependence in the data. Time series outliers can have an arbitrarily adverse influence on parameter estimators for time series models, and the nature of this influence depends on the type of outlier. The chapter describes several probability models for time series outliers, including additive outliers, replacement outliers and innovations outliers. It also describes the properties of classical estimators of the parameters of an autoregression model.