ABSTRACT
This chapter concerns functional data observed sequentially over time. Pollution on a given day will be affected by pollution on previous days, so the curves will be dependent. A daily pollution pattern will be different on Sunday and on Monday, so the curves will not have the same distribution every day. The chapter introduces the most extensively used functional time series model, the autoregressive process of order 1, the FAR(I) model. It then considers forecasting methods for functional time series which are implemented in easy to use R packages, and discusses the long-run covariance function. While the covariance function is appropriate for iid functions, many inferential procedures for functional time series are based on the long-run covariance function. The chapter illustrates the application of this concept in the context of stationarity tests. It reviews fundamental concepts of time series analysis. The chapter concludes with two elaborations on the FAR(I) model.
