NON-STATIONARITY IN GARCH MODELS - A BAYESIAN-ANALYSIS

First, the non-stationarity properties of the conditional variances in the GARCH(1, 1) model are analysed using the concept of infinite pers istence of shocks. Given a time sequence of probabilities for increasi ng/decreasing conditional variances, a theoretical formula for quasi-s trict non-stationarity is defined. The resulting conditions for the GA RCH(1, 1) model are shown to differ from the weak stationarity conditi ons mainly used in the literature. Bayesian statistical analysis using Monte Carlo integration is applied to analyse both stationarity conce pts for the conditional variances of the US 3-month treasury bill. rat e. Interest rates are known for their weakly non-stationary conditiona l variances but, using a quasi-strict stationarity measure, it is show n that the conditional variances are likely to be stationary. Second, the level of the treasury bill rate is analysed for non-stationarity u sing Bayesian unit root methods. The disturbances of the GARCH model f or the treasury bill rate are t-distributed. It is shown that the unit root parameter is negatively correlated with the degrees-of-freedom p arameter. Imposing normally distributed disturbances leads therefore t o underestimation of the non-stationarity in the level of the treasury bill rate.