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Time-Deformation Modeling Of Stock Returns Directed By Duration Processes

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Author Info
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)

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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.

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Paper provided by University of Waterloo, Department of Economics in its series Working Papers with number 08010.

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Date of creation: Dec 2008
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Handle: RePEc:wat:wpaper:08010

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Related research
Keywords: Duration process; Ergodicity; Method of simulated moments; Return process; Stationarity.;

Find related papers by 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

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References listed on IDEAS
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  1. Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics. [Downloadable!]
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  2. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Dingan Feng, 2004. "Stochastic Conditional Duration Models with "Leverage Effect" for Financial Transaction Data," Journal of Financial Econometrics, Oxford University Press, vol. 2(3), pages 390-421. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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 328-52, July.
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  8. Renault, E. & Werker, B.J.M., 2004. "Stochastic volatility models with transaction time risk," Discussion Paper 24, Tilburg University, Center for Economic Research. [Downloadable!]
  9. 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. [Downloadable!] (restricted)
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