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Modelling Stock Market Excess Returns by Markov Modulated Gaussian Noise

  • Jonathan Manton
  • Anton Muscatelli
  • Vikram Krishnamurthy
  • Stan Hurn

A basic analysis of stock market excess return data shows both linear and non-linear dependence present. Previous papers have used this to argue that it must therefore be possible to predict future values. However, this paper shows that the linear and non-linear dependence can be explained by simply allowing the mean and variance of Gaussian noise to be modulated by a (typically 3 state) hidden Markov model. Attempting to fit a Markov modulated AR process proved fruitless; the conclusion is that there is no AR-predictability present in excess return data.

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Paper provided by Business School - Economics, University of Glasgow in its series Working Papers with number 9806.

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Handle: RePEc:gla:glaewp:9806
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  1. Gallant, A Ronald & Rossi, Peter E & Tauchen, George, 1992. "Stock Prices and Volume," Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 199-242.
  2. Hentschel, Ludger & Campbell, John, 1992. "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns," Scholarly Articles 3220232, Harvard University Department of Economics.
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  5. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-313, September.
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  7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
  8. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  9. Sentana, Enrique & Wadhwani, Sushil, 1991. "Semi-parametric Estimation and the Predictability of Stock Market Returns: Some Lessons from Japan," Review of Economic Studies, Wiley Blackwell, vol. 58(3), pages 547-63, May.
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  12. Gallant, A.R. & Hsieh, D. & Tauchen, G., 1988. "On Fitting A Recalcitrant Series: The Pound/Dollar Exchange Rate, 1974- 83," Papers 88-60, Chicago - Graduate School of Business.
  13. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  14. James M. Poterba & Lawrence H. Summers, 1987. "Mean Reversion in Stock Prices: Evidence and Implications," NBER Working Papers 2343, National Bureau of Economic Research, Inc.
  15. Crato, Nuno & de Lima, Pedro J. F., 1994. "Long-range dependence in the conditional variance of stock returns," Economics Letters, Elsevier, vol. 45(3), pages 281-285.
  16. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
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