An Application of Multiple Time Series Methods to Canadian Economic Data

Abstract

This work outlines several aspects of multiple time series analysis, which are then demonstrated on a large set of data. After introducing the general autoregressive integrated moving average model, discussion is restricted to a canonical form: the pure autoregressive process of order p (AR(p)). Methods for identifying and fitting the AR(p) process using quasi-partial correlation matrices and Akaike's AIC criterion are discussed. The AR model can then be used to make forecasts by taking conditional expectations at the origin time. Probability limits on the forecasts are also defined. A method for canonical analysis of AR processes is described which can indicate possible reductions in the dimensionality of the problem. Using computer programs developed for this project, the above methods are applied to an 11-dimensional set of Canadian economic data and the results are discussed.