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Time-Deformation Modeling Of Stock Returns Directed By Duration Processes

Author

Listed:
  • Dingan Feng

    (CIBC, Toronto)

  • Peter X.-K. Song

    (Department of Biostatistics, University of Michigan School of Public Health)

  • Tony S. Wirjanto

    (Department of Economics, University of Waterloo)

Abstract

This paper presents a new class of time-deformation (or stochastic volatility) models for stock returns sampled in transaction time and directed by a generalized duration process. Stochastic volatility in this model is driven by an observed duration process and a latent autoregressive process. Parameter estimation in the model is carried out by using the method of simulated moments (MSM) due to its analytical feasibility and numerical stability for the proposed model. Simulations are conducted to validate the choices of the moments used in the formulation of the MSM. Both the simulation and empirical results obtained in this paper indicate that this approach works well for the proposed model. The main empirical findings for the IBM transaction return data can be summarized as follows: (i) the return distribution conditional on the duration process is not Gaussian, even though the duration process itself can marginally function as a directing process; (ii) the return process is highly leveraged; (iii) a longer trade duration tends to be associated with a higher return volatility; and (iv) the proposed model is capable of reproducing return whose marginal density function is close to that of the empirical return.

Suggested Citation

  • Dingan Feng & Peter X.-K. Song & Tony S. Wirjanto, 2008. "Time-Deformation Modeling Of Stock Returns Directed By Duration Processes," Working Papers 08010, University of Waterloo, Department of Economics.
    • Handle: RePEc:wat:wpaper:08010
    as

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    File URL: http://economics.uwaterloo.ca/documents/TW-tdrt-051208_000.pdf
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    References listed on IDEAS

    as
    1. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
    2. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    3. Grammig, Joachim & Wellner, Marc, 2002. "Modeling the interdependence of volatility and inter-transaction duration processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 369-400, February.
    4. John Knight & Cathy Q. Ning, 2008. "Estimation of the stochastic conditional duration model via alternative methods," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 593-616, November.
    5. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    6. Dingan Feng, 2004. "Stochastic Conditional Duration Models with "Leverage Effect" for Financial Transaction Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(3), pages 390-421.
    7. Renault, E. & Werker, B.J.M., 2004. "Stochatic Volatility Models with Transaction Time Risk," Discussion Paper 2004-24, Tilburg University, Center for Economic Research.
    8. Thierry Ané & Hélyette Geman, 2000. "Order Flow, Transaction Clock, and Normality of Asset Returns," Journal of Finance, American Finance Association, vol. 55(5), pages 2259-2284, October.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Duration process; Ergodicity; Method of simulated moments; Return process; Stationarity.;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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