Asymmetric and common absorption of shocks in nonlinear autoregressive models

A key feature of many nonlinear time series models is that they allow for the possibility that the model structure experiences changes, depending on for example the state of the economy or of the financial market. A common property of these models is that it generally is not possible to fully understand the structure of the model by considering the estimated values of the model parameters only. Put differently, it often is difficult to interpret a specific nonlinear model. To shed light on the characteristics of a nonlinear model it can then be useful to consider the effect of shocks on the future patterns of a time series variable. Most interest in such impulse response analysis has concentrated on measuring the persistence of shocks, or the magnitude of the (ultimate) effect of shocks. Interestingly, far less attention has been given to measuring the speed at which this final effect is attained, that is, how fast shocks are 'absorbed' by a time series. In this paper we develop and implement a framework that can be used to assess the absorption rate of shocks in nonlinear models. The current-depth-of-recession model of Beaudry and Koop (1993), the floor-and-ceiling model of Pesaran and Potter (1997) and a multivariate STAR model are used to illustrate the various concepts.