We address the issue of time varying persistence of shocks to macroeconomic time series variables by proposing a new and parsimonious time series model. Our model assumes that this time varying persistence depends on a linear combination of lagged explanatory variables, where this combination characterizes the business cycle regimes. The key feature of our model isthat an autoregressive parameter takes larger values only when this indicator variable exceeds a stochastic threshold. The parameters and the(lags of the) variables that constitute the indicator variable have to be determined from the data. Other forms of censoring amount to straightforward extensions. Our application to US unemployment shows that the model fitsvery well. A linear combination of lagged (differenced) industrial production, oil price, interest spread and stock returns amounts to anadequate indicator of an upcoming recession, which corresponds with explosive behavior of unemployment. Also, the out-of-sample forecasts from our model oftentimes improve those from linear and other nonlinear models.business cycle;censored regression;nonlinear time series;asymmetric persistence
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