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Bounds for the probability distribution function of the linear ACD process

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  • Fernandes, Marcelo

Abstract

This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p,q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.

Suggested Citation

  • Fernandes, Marcelo, 2004. "Bounds for the probability distribution function of the linear ACD process," Statistics & Probability Letters, Elsevier, vol. 68(2), pages 169-176, June.
    • Handle: RePEc:eee:stapro:v:68:y:2004:i:2:p:169-176
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    References listed on IDEAS

    as
    1. Drost, Feike C & Werker, Bas J M, 2004. "Semiparametric Duration Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 40-50, January.
    2. repec:dau:papers:123456789/5478 is not listed on IDEAS
    3. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(1), pages 17-39, February.
    4. Luc Bauwens & Pierre Giot, 2000. "The Logarithmic ACD Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks," Annals of Economics and Statistics, GENES, issue 60, pages 117-149.
    5. Fernandes, Marcelo & Grammig, Joachim, 2006. "A family of autoregressive conditional duration models," Journal of Econometrics, Elsevier, vol. 130(1), pages 1-23, January.
    6. Gourieroux, Christian & Jasiak, Joanna & Le Fol, Gaelle, 1999. "Intra-day market activity," Journal of Financial Markets, Elsevier, vol. 2(3), pages 193-226, August.
    7. repec:adr:anecst:y:2000:i:60:p:05 is not listed on IDEAS
    8. Joachim Grammig & Kai-Oliver Maurer, 2000. "Non-monotonic hazard functions and the autoregressive conditional duration model," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 16-38.
    9. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    10. M. Pawlak & W. Schmid, 2001. "On the Distributional Properties of GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(3), pages 339-352, May.
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    Cited by:

    1. Maria Pacurar, 2008. "Autoregressive Conditional Duration Models In Finance: A Survey Of The Theoretical And Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 711-751, September.

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