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1.6: Summary

In this chapter, the classical decomposition (1.1.1) of a time series into a drift component, a seasonal component and a sequence of residuals was introduced. Methods to estimate the drift and the seasonality were provided. Moreover, the class of stationary processes was identified as a reasonably broad class of random variables. Several ways were introduced to check whether or not the resulting residuals can be considered to be independent, identically distributed. In Chapter 3, the class of autoregressive moving average (ARMA) processes is discussed in depth, a parametric class of random variables that are at the center of linear time series analysis because they are able to capture a wide range of dependence structures and allow for a thorough mathematical treatment. Before, properties of the sample mean, sample ACVF and ACF are considered in the next chapter.