Empirical ?ndings related to the time series properties of stock returns volatility indicate autocorrelations that decay slowly at long lags. In light of this, several long-memory models have been proposed. However, the possibility of level shifts has been advanced as a possible explanation for...

We consider the estimation of a random level shift model for which the series of interest is the sum of a short memory process and a jump or level shift component. For the latter component, we specify the commonly used simple mixture model such that the component is the cumulative sum of a...