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

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  • Yang K. Lu

    ()
    (Boston University)

  • Pierre Perron

    ()
    (Boston University)

Abstract

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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Bibliographic Info

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
Date of revision:
Handle: RePEc:bos:wpaper:wp2008-012

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Keywords: structural change; forecasting; GARCH models; long-memory;

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Citations

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Cited by:
  1. Georges Dionne & Olfa Maalaoui Chun, 2013. "Default and liquidity regimes in the bond market during the 2002-2012 period," Canadian Journal of Economics, Canadian Economics Association, vol. 46(4), pages 1160-1195, November.
  2. Grassi, Stefano & Santucci de Magistris, Paolo, 2014. "When long memory meets the Kalman filter: A comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 301-319.
  3. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(06), pages 1196-1237, December.
  4. Morel, Christophe & Michel, Thierry & Michel, Laurent, 2010. "A Volatility-Driven Asset Allocation (VDAA)," Economics Papers from University Paris Dauphine 123456789/5954, Paris Dauphine University.
  5. Claudio Morana, 2014. "Factor Vector Autoregressive Estimation of Heteroskedastic Persistent and Non Persistent Processes Subject to Structural Breaks," Working Papers 273, University of Milano-Bicocca, Department of Economics, revised May 2014.
  6. Pierre Perron & Zhongjun Qu, 2008. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-004, Boston University - Department of Economics.
  7. Francesco Battaglia & Mattheos Protopapas, 2012. "Multi–regime models for nonlinear nonstationary time series," Computational Statistics, Springer, vol. 27(2), pages 319-341, June.

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