In Sections 1.2 and 1.3 we introduced some commonly used stochastic time series models. In this section we turn our attention to actual time series data. These data can be obtained from real experiments or observations over time or generated from numerical simulations of specified time series models. We consider these data to be particular realizations of stochastic processes. Although we call both the stochastic process and its realization time series, we distinguish between them by using lower-case letters to denote the actual data and the corresponding upper-case letters to denote the random variables.

Several ways of transforming the raw data into a form suitable for modeling are presented in this section. These transformations include linear filtering, simple exponential smoothing, differencing, moving average, and the Box-Cox transformation. We demonstrate how to generate normally distributed random sequences and time series from specified models and also show how to read in data from a file and plot them.