General description
Many of the most important uses of time series analysis concern the relationships between two or more series. The ARIMA models introduced in the module on Time Series and Forecasting will be extended to cater for interventions and transfer functions and to multiple ARIMA models. The module includes a short project.

Aims
To study models for relating two or more time series and to gain practical experience of their analysis by means of a project.

Learning outcomes
On completion of this module, a student should be able to:

• describe and analyse transfer function noise models;
• use a computer package to identify, estimate and check models relating two time series;
• construct forecasts using transfer function/noise models;
• explain the need for pre-whitening in the identification of transfer functions;
• analyse low order multivariate ARMA models;
• describe cointegration and explain its implications.

Syllabus
1. TRANSFER FUNCTIONS AND INTERVENTION ANALYSIS: Regression-autogression models; ordinary least squares estimation and the Mann-Wald theorem. Transfer functions: interventions; impulse response function; stability and gain; crosscorrelation function, prewhitening, identification of transfer functions; estimation and diagnostic checking. Forecasting.
2. MULTIPLE TIME SERIES: The multivariate ARMA model; stationarity and invertibility, marginal models, equivalent models. Cross-covariance matrices. Co-integration.