Due to high and low volatility periods, time series of absolute returns experience temporary level shifts which differ in length and size. In this paper we modify the basic Censored Latent Effects Autoregressive [CLEAR] model, such that it can describe and forecast the location and size of such level shifts. For our particular application, we assume that technical trading variables may have explanatory value for future level shifts, where these effects may differ across upward- or downward-tending markets. A natural competitor of the resultant switching regime CLEAR [SR-CLEAR] model is a long-memory model, which is known to pick up neglected level shifts. Hence, when we apply the SR-CLEAR model to nine stock markets and document its good fit and forecasting ability, we compare it with a long-memory model.