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Stylized facts of daily return series and the hidden Markov model


  • Tobias Rydén

    (Department of Mathematical Statistics, Lund University, Box 118, S-221 00 Lund, Sweden)

  • Timo Teräsvirta

    (Department of Economic Statistics, Stockholm School of Economics, Box 6501, S-113 83 Stockholm, Sweden)

  • Stefan Åsbrink

    (Trygg Hansa, Equities, S-106 26 Stockholm, Sweden)


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 17,000 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. © 1998 John Wiley & Sons, Ltd.

Suggested Citation

  • Tobias Rydén & Timo Teräsvirta & Stefan Åsbrink, 1998. "Stylized facts of daily return series and the hidden Markov model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(3), pages 217-244.
  • Handle: RePEc:jae:japmet:v:13:y:1998:i:3:p:217-244

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    References listed on IDEAS

    1. Quah, Danny & Vahey, Shaun P, 1995. "Measuring Core Inflation?," Economic Journal, Royal Economic Society, vol. 105(432), pages 1130-1144, September.
    2. Roger Beaton & Paul Fisher, 1995. "The Construction of RPIY," Bank of England working papers 28, Bank of England.
    3. Joanna Paisley & Chris Salmon, 1995. "How Cyclical is the PSBR?," Bank of England working papers 34, Bank of England.
    4. Francis Breedon & Ian Twinn, 1995. "Valuation of underwriting agreements for UK rights issues: evidence from the traded option market," Bank of England working papers 39, Bank of England.
    5. Andy Haldane & Bennett McCallum & Chris Salmon, 1996. "Base Money Rules in the UK," Bank of England working papers 45, Bank of England.
    6. Quah, Danny & Vahey, Shaun P, 1995. "Measuring Core Inflation?," Economic Journal, Royal Economic Society, vol. 105(432), pages 1130-1144, September.
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods


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