ABSTRACT
In this chapter we will discuss some of the important models that are used to describe the behavior of a time series. Of particular interest will be the AR, MA, and ARMA models. These models were made popular by George Box and Gwilym Jenkins in their classic time series book, the current edition of which is Box et al. (2008). These models have become fundamental to the theory and applications of time series. While several example based on real data are examined in this chapter, we make extensive use of simulated realizations in this chapter because we are focusing on the properties and developing an understanding of known models. Also, unless otherwise specified, the autocorrelations and spectral densities illustrated in this chapter are the theoretical quantities for the models being studied. In later chapters, we will use the lessons learned in this chapter as we analyze actual time series data.
