Spectral Methods in the Identification of Time Series

The analysis of time series is a very important element in much of the systems work carried out at IIASA and elsewhere. The basic principles of time series analysis were laid down by Box and Jenkins in 1970 in an approach which divided model building into three stages: model identification, parameter estimation and model validation. However, while there are many formal approaches to parameter estimation and several formal methods for model validation, the only available tool for model identification is currently visual inspection of the time series plot and autocorrelation function. This is evidently the weakest point of the Box-Jenkins methodology. In an attempt to remedy this, Andrzej Lewandowski proposes here a new approach to Box-Jenkins model identification. In contrast to the existing tools, this approach is based on spectral methods and involves frequency analysis of ARMA models. It differs from the standard spectral approach presented in textbooks on time series analysis, although it is based on a principle well known in control engineering and circuit theory. This method provides a means of analyzing time series in some depth using only a pencil, a piece of paper, and a pocket calculator.