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Stylized Facts of Daily Return Series and the Hidden Markov Model

  • Rydén, Tobias

    (Department of Mathematical Statistics)

  • Teräsvirta, Timo


    (Department of Economic Statistics)

  • Åsbrink, Stefan

    (Department of Economic Statistics)

In two recent papers, Granger and Ding (1995a, b) considered long return series that are first differences of logarithmed price series or price indices. They established a set of temporal and distributional properties for such series and suggested that the returns are well characterized by the double exponential distribution. The present paper shows that a mixture of normal variables with zero mean can generate series with most of the properties Granger and Ding singled out. In that case, the temporal higher-order dependence observed in return series may be described by a hidden Markov model. Such a model is estimated for ten subseries of the well-known S&P 500 return series of about 17000 daily observations. It reproduces the stylized facts of Granger and Ding quite well, but the parameter estimates of the model sometimes vary considerably from one subseries to the next. The implications of these results are discussed.

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Paper provided by Stockholm School of Economics in its series SSE/EFI Working Paper Series in Economics and Finance with number 117.

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Length: 50 pages
Date of creation: Jun 1996
Date of revision:
Publication status: Published in Journal of Applied Econometrics, 1998, pages 217-244.
Handle: RePEc:hhs:hastef:0117
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