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Modeling and Forecasting Stock Return Volatility Using a Random Level Shift Model

  • Yang K. Lu

    ()

    (Boston University)

  • Pierre Perron

    ()

    (Boston University)

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 process which is 0 with some probability (1-a) and is a random variable with probability a. Our estimation method transforms such a model into a linear state space with mixture of normal innovations, so that an extension of Kalman filter algorithm can be applied. We apply this random level shift model to the logarithm of absolute returns for the S&P 500, AMEX, Dow Jones and NASDAQ stock market return indices. Our point estimates imply few level shifts for all series. But once these are taken into account, there is little evidence of serial correlation in the remaining noise and, hence, no evidence of long-memory. Once the estimated shifts are introduced to a standard GARCH model applied to the returns series, any evidence of GARCH effects disappears. We also produce rolling out-ofsample forecasts of squared returns. In most cases, our simple random level shifts model clearly outperforms a standard GARCH(1,1) model and, in many cases, it also provides better forecasts than a fractionally integrated GARCH model.

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Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number wp2008-012.

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Length: 36
Date of creation: Sep 2008
Handle: RePEc:bos:wpaper:wp2008-012
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