Absorption of shocks in nonlinear autoregressive models

It generally is difficult, if not impossible, to fully understand and interpret nonlinear time series models by considering the estimated values of the model parameters only. To shed light on the characteristics and implications of a nonlinear model it can then be useful to consider the effects of shocks on the future patterns of the time series variable. Most interest in such impulse response analysis has concentrated on measuring the persistence of shocks, or the magnitude of their (ultimate) effect. A framework is developed and implemented that is useful for measuring the rate at which this final effect is attained, or the rate of absorption of shocks. It is shown that the absorption rate can be used to examine whether the propagation of different types of shocks, such as positive and negative shocks or large and small shocks follows different patterns. The nonlinear floor-and-ceiling model for US output growth is used to illustrate the various concepts. The presence of substantial asymmetries in both persistence and absorption of shocks is documented, with interesting differences arising across magnitudes of shocks and across regimes in the model. Furthermore, it appears that asymmetry became much less pronounced due to a large decline in output volatility in the 1980s.