Statistical aspects
Howell Tong · 1990
Abstract We have been looking at the ensemble properties, that is properties pertaining to the collection of all realizations/sample paths. Under ergodicity /stationarity, these properties will tell us about the long-run behaviour of each realization. Now, we are going to study the ‘inverse problem’ of inferring something about the ensemble properties from one, or more precisely part of one, single realization. This falls within the domain of statistical inference. Before performing any formal statistical procedure, it is always good practice to examine the data graphically. A number of graphical methods have been in routine use in time series modelling. For example, time series data plots, sample autocorrelation function plots, sample partial autocorrelation function plots, sample spectral density functions, histograms, plots of differenced data, plots of instantaneously transformed data, etc., have been used as standard practice.