24 Graphics for time series analysis
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Time series analysis is arguably the most graphical area of statistics. There is a long and rich history of attempts to graphically display the information contained in a set of data observed over time. This chapter considers the plots that have become a standard part of the analysis of univariate and multivariate time series in both the time and frequency domains and describes the essential features of an ideal time series graphics package. This package have three basic features: (1) it is interactive; it allows a user to point at a region of the screen and obtain information about the quantities being there; (2) it is dynamic; the values of certain parameters determining what is being displayed or the way it is displayed can be varied quickly with a corresponding updating of the display, and (3) it is linked; changing the plot of one quantity on the screen will automatically change any other plots as well. Many time series analysis methods rely on transforming data until the result has certain characteristics. Spectral density estimation is another part of time series analysis where dynamic graphics is very useful as the two major methods for spectral estimation have a smoothing parameter. The first method is known variously as window estimation or kernel estimation, or nonparametric estimation. The second major method for spectral estimation consists of (1) choosing a model from the class of autoregressive moving average time series models, (2) estimating the parameters of that model, and (3) substituting the estimates of the parameters into the formula for the true spectral density of that ARMA model.
