Co-integrated time series: Structure, forecasting and testing

The first chapter provides a comprehensive summary of the dissertation.; The second chapter investigates the structure and representations of cointegrated time series. Assuming the transfer function of a vector time series is rational, the well known Smith-McMillan form is used as a basic tool. This form separates out the pole(s) and zero(s) of the transfer function making the analysis simple and clear. The analysis restricts neither the locations nor the multiplicities of the explosive pole(s) and zero(s) of the time series. To handle such situations, the idea of a 'polynomial cointegrating vector' is introduced, allowing for dynamic long run relationships. A generalized error correction model is also proposed which allows for dynamic error correcting terms with possibly different degrees of nonstationarity. The analysis includes cointegration at seasonal frequencies and cointegration of explosive time series as interesting.; The third chapter examines forecasting and testing in cointegrated systems. It is established that the long term forecasts of a cointegrated time series satisfy the cointegrated relationship exactly. The forecast error variance is shown to be finite in spite of the fact that individual series have infinite series have infinite variance. The forecasting performances of two competing representations, a correctly specified unrestricted vector autoregression and an error correction model, are compared by simulation. It is found that the error correction model performs substantially better for long term horizons. The limiting distribution of the Engle-Granger (EG) test statistic for non-cointegration is derived and extended critical values are tabulated by Monte Carlo study.; The final chapter examines the limiting distribution of the EG statistic in a general framework. The EG testing procedure is then extended to test for the cointegratedness of variables which possibly have linear deterministic trends in addition to I(1) components (or stochastic trend components). Critical values for the extended EG test are also provided.