The Autoregressive Conditional Root (ACR) Model

In this paper we propose and analyse the Autoregressive Conditional Root (ACR) timeseries model, which allows for endogenously generated regime switching between seemingly stationaryand non-stationary epochs. It proves to be an appealing alternative to existing nonlinear models suchas e.g. the threshold autoregressive or Markov switching classes of models, which are commonly used todescribe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditionson the parameters of the ACR process and its innovations, are shown to imply geometric ergodicity,stationarity and existence of moments. Furthermore, we establish consistency and asymptotic normalityof the maximum likelihood estimators in the ACR model. An application to French-German exchangerate data illustrate the conclusions and analysis.