Non-stationarity in garch models: A bayesian analysis
Article first published online: 7 NOV 2006
Copyright © 1993 John Wiley & Sons, Ltd.
Journal of Applied Econometrics
Volume 8, Issue S1, pages S41–S61, December 1993
How to Cite
Kleibergen, F. and van Dijk, H. K. (1993), Non-stationarity in garch models: A bayesian analysis. J. Appl. Econ., 8: S41–S61. doi: 10.1002/jae.3950080505
- Issue published online: 7 NOV 2006
- Article first published online: 7 NOV 2006
- Manuscript Revised: MAY 1993
- Manuscript Received: SEP 1992
First, the non-stationarity properties of the conditional variances in the GARCH(1, 1) model are analysed using the concept of infinite persistence of shocks. Given a time sequence of probabilities for increasing/decreasing conditional variances, a theoretical formula for quasi-strict non-stationarity is defined. The resulting conditions for the GARCH(1,1) model are shown to differ from the weak stationarity conditions mainly used in the literature. Bayesian statistical analysis using Monte Carlo integration is applied to analyse both stationarity concepts for the conditional variances of the US 3-month treasury bill rate. Interest rates are known for their weakly non-stationary conditional variances but, using a quasi-strict stationarity measure, it is shown that the conditional variances are likely to be stationary. Second, the level of the treasury bill rate is analysed for non-stationarity using Bayesian unit root methods. The disturbances of the GARCH model for the treasury bill rate are t-distributed. It is shown that the unit root parameter is negatively correlated with the degrees-of-freedom parameter. Imposing normally distributed disturbances leads therefore to underestimation of the non-stationarity in the level of the treasury bill rate.