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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.

Suggested Citation

  • Rydén, Tobias & Teräsvirta, Timo & Åsbrink, Stefan, 1996. "Stylized Facts of Daily Return Series and the Hidden Markov Model," SSE/EFI Working Paper Series in Economics and Finance 117, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0117

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    References listed on IDEAS

    1. O'Donnell, Owen & Propper, Carol, 1991. "Equity and the distribution of UK National Health Service resources," Journal of Health Economics, Elsevier, vol. 10(1), pages 1-19, May.
    2. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    3. Wagstaff, Adam, 1986. "The demand for health : Some new empirical evidence," Journal of Health Economics, Elsevier, vol. 5(3), pages 195-233, September.
    4. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    5. Culyer, A. J. & van Doorslaer, Eddy & Wagstaff, Adam, 1992. "Utilisation as a measure of equity by Mooney, Hall, Donaldson and Gerard," Journal of Health Economics, Elsevier, vol. 11(1), pages 93-98, May.
    6. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    7. Muurinen, Jaana-Marja, 1982. "Demand for health: A generalised Grossman model," Journal of Health Economics, Elsevier, vol. 1(1), pages 5-28, May.
    8. Michael Grossman, 1972. "The Demand for Health: A Theoretical and Empirical Investigation," NBER Books, National Bureau of Economic Research, Inc, number gros72-1, January.
    9. van Doorslaer, Eddy & Wagstaff, Adam & van der Burg, Hattem & Christiansen, Terkel & De Graeve, Diana & Duchesne, Inge & Gerdtham, Ulf-G & Gerfin, Michael & Geurts, Jose & Gross, Lorna, 2000. "Equity in the delivery of health care in Europe and the US," Journal of Health Economics, Elsevier, vol. 19(5), pages 553-583, September.
    10. Cameron, A Colin & Trivedi, Pravin K, 1986. "Econometric Models Based on Count Data: Comparisons and Applications of Some Estimators and Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 1(1), pages 29-53, January.
    11. Cameron, A. Colin & Trivedi, Pravin K., 1990. "Regression-based tests for overdispersion in the Poisson model," Journal of Econometrics, Elsevier, vol. 46(3), pages 347-364, December.
    12. A. C. Cameron & P. K. Trivedi & Frank Milne & J. Piggott, 1988. "A Microeconometric Model of the Demand for Health Care and Health Insurance in Australia," Review of Economic Studies, Oxford University Press, vol. 55(1), pages 85-106.
    13. van Doorslaer, Eddy & Wagstaff, Adam, 1992. "Equity in the delivery of health care: some international comparisons," Journal of Health Economics, Elsevier, vol. 11(4), pages 389-411, December.
    14. Duan, Naihua, et al, 1983. "A Comparison of Alternative Models for the Demand for Medical Care," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(2), pages 115-126, April.
    15. Wagstaff, Adam & van Doorslaer, Eddy & Paci, Pierella, 1991. "On the measurement of horizontal inequity in the delivery of health care," Journal of Health Economics, Elsevier, vol. 10(2), pages 169-205, July.
    16. Le Grand, Julian, 1978. "The Distribution of Public Expenditure: The Case of Health Care," Economica, London School of Economics and Political Science, vol. 45(178), pages 125-142, May.
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    More about this item


    Higher-order dependence; mixture of normal distributions; nonlinear time series; parametric bootstrap; S&P 500; time series modelling;

    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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