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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 is that 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 straight forward extensions Our application to US unemployment shows that the model ts very well A linear combination of lagged dierenced industrial production oil price interest spread and stock returns amounts to an adequate indicator of an upcoming recession which corresponds with explosive behavior of unemployment Also the outofsample forecasts from our model oftentimes improve those from linear and other nonlinear models Keywords asymmetric persistence nonlinear time series business cycle censored regressio