Modeling and forecasting stock return volatility using a random level shift model

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Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices (2010, methodology): “Lu and Perron (2008) present a method to directly estimate a level shift model using an extension of the Kalman filter and apply it to the logarithm of squared returns for the S&P 500, AMEX, Dow Jones and NASDAQ stock market return indices.”
MEMORY PARAMETER ESTIMATION IN THE PRESENCE OF LEVEL SHIFTS AND DETERMINISTIC TRENDS (2013, unknown): “We also examined DGPs calibrated to stock market volatility data by Lu and Perron (2010) with results not reported as they are very similar to those discussed earlier.”
Modified local Whittle estimator for long memory processes in the presence of low frequency (and other) contaminations (2014, methodology): “These specifications were also used by McCloskey and Perron (2013) so that we can make direct comparisons of the relative performance of our estimators with theirs (the sample sizes they used are 1000 and 2000 but the minor differences in T should not be of concern given the rather large differences”