Multivariate time series modelling.
This research is based on a detailed description of model building for multivariate time series models. Under the assumption of stationarity, identification, estimation of the parameters and diagnostic checking for the Vector Auto regressive (p) (VAR(p)), Vector Moving Average (q) (VMA(q)) and Vector Auto regressive Moving Average (VARMA(p, q) ) models are described in detail. With reference to the non-stationary case, the concept of cointegration is explained. Procedures for testing for cointegration, determining the cointegrating rank and estimation of the cointegrated model in the VAR(p) and VARMA(p, q) cases are discussed. The utility of multivariate time series models in the field of economics is discussed and its use is demonstrated by analysing quarterly South African inflation and wage data from April 1996 to December 2008. A review of the literature shows that multivariate time series analysis allows the researcher to: (i) understand phenomenon which occur regularly over a period of time (ii) determine interdependencies between series (iii) establish causal relationships between series and (iv) forecast future variables in a time series based on current and past values of that variable. South African wage and inflation data was analysed using SAS version 9.2. Stationary VAR and VARMA models were run. The model with the best fit was the VAR model as the forecasts were reliable, and the small values of the Portmanteau statistic indicated that the model had a good fit. The VARMA models by contrast, had large values of the Portmanteau statistic as well as unreliable forecasts and thus were found not to fit the data well. There is therefore good evidence to suggest that wage increases occur independently of inflation, and while inflation can be predicted from its past values, it is dependent on wages.