"Autoregressive conditional root model"
	
Anders Rahbek, 

	
Department of Statistics and Operations Research, University of Copenhagen, 
Universitetsparken 5, DK-2100 Copenhagen, Denmark 
		
Neil Shephard,
Nuffield College, Oxford OX1 1NF, UK.
	

Abstract: In this paper we develop a time series model which allows long-term disequilibriums 
to have epochs of non-stationarity, giving the impression that long term relationships between 
economic variables have temporarily broken down, before they endogenously collapse back 
towards their long term relationship. This autoregressive root model is shown to be ergodic 
and covariance stationary under some rather general conditions. We study how this model can be 
estimated and tested, developing appropriate asymptotic theory for this task. Finally we apply 
the model to assess the purchasing power parity relationship.
	
Keywords:  Cointegration; Equilibrium correction model; GARCH; Hidden Markov model; Likelihood; 
Regime switching; STAR model; Stochastic break; Stochastic unit root; Switching regression; 
Real Exchange Rate; PPP; Unit root hypothesis.