Skip to main content
SpringerLink
Log in

Bayesian estimation and inference for log-ACD models

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

This paper adapts Bayesian Markov chain Monte Carlo methods for application to some auto-regressive conditional duration models. Subsequently, the properties of these estimators are examined and assessed across a range of possible conditional error distributions and dynamic specifications, including under error mis-specification. A novel model error distribution, employing a truncated skewed Student-t distribution is proposed and the Bayesian estimator assessed for it. The results of an extensive simulation study reveal that favourable estimation properties are achieved under a range of possible error distributions, but that the generalised gamma distribution assumption is most robust and best preserves these properties, including when it is incorrectly specified. The results indicate that the powerful numerical methods underlying the Bayesian estimator allow more efficiency than the (quasi-) maximum likelihood estimator for the cases considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

References

  • Allen D, Chan F, McAleer M, Peiris MS (2008) Finite sample properties of the QMLE for the log-ACD model: application to Australian stocks. J Econom 147:163–185

    Article  MathSciNet  Google Scholar 

  • Bauwens L, Giot P (2000) The logarithmic ACD model: an application to the bid ask quote process of three NYSE stocks. Annales D’Economie et de Statistique 60:117–145

    Google Scholar 

  • Bauwens L, Giot P, Grammig J, Veredas D (2004) A comparison of financial duration models via density forecasts. Int J Forecast 20:589–609

    Article  Google Scholar 

  • Bauwens L, Veradas D (2004) The stochastic conditional duration model: a latent variable model for the analysis of financial durations. J Econom 119:381–412

    Article  MathSciNet  MATH  Google Scholar 

  • Bollerslev T (1986) Generalized autoregressive conditional heteroskedasticity. J Econom 31:307–327

    Article  MathSciNet  MATH  Google Scholar 

  • Bollerslev T (1987) A conditionally heteroskedastic time series model for speculative prices and rates of return. Rev Econom Stat 69(3):542–547

    Article  Google Scholar 

  • Chen CWS, Gerlach R, Lin EMH (2008) Volatility forecasting using threshold heteroskedastic models of the intra-day range. Comput Stat Data Anal 52(6):2990–3010

    Article  MathSciNet  MATH  Google Scholar 

  • Drost, Werker (2004) Semiparametric duration models. J Bus Econom Stat 22(1):40–50

    Article  MathSciNet  Google Scholar 

  • Engle RF, Manganelli S (2004) CAViaR: conditional autoregressive value at risk by regression quantiles. J Bus Econom Stat 22:367–381

    Article  MathSciNet  Google Scholar 

  • Engle RF, Russell JR (1997) Forecasting the frequency of changes in quoted foreign exchange prices with the autoregressive conditional duration model. J Empir Finance 4:187–212

    Article  Google Scholar 

  • Engle RF, Russell JR (1998) Autoregressive conditional duration: a new model for irregularly spaced transactions data. Econometrica 66:1127–1162

    Article  MathSciNet  MATH  Google Scholar 

  • Fernandes M, Grammig J (2006) A family of autoregressive conditional duration models. J Econom 130:1–23

    Article  MathSciNet  Google Scholar 

  • Gerlach R, Chen CWS (2008) Bayesian inference and model comparison for asymmetric smooth transition heteroskedastic models. Stat Comput 18:391–408

    Article  MathSciNet  Google Scholar 

  • Gerlach R, Chen CWS, Chan NYC (2011) Bayesian time-varying quantile forecasting for value-at-risk in financial markets. J Bus Econom Stat 29(4):481–492

    Article  MathSciNet  Google Scholar 

  • Giordani P, Kohn R (2010) Adaptive independent Metropolis–Hastings by fast estimation of mixtures of normals. J Comput Gr Stat 19(2):243–259

    Article  MathSciNet  Google Scholar 

  • Hansen BE (1994) Autoregressive conditional density estimation. Int Econom Rev 35(3):705–730

    Article  MATH  Google Scholar 

  • Hoogerheide LF, Kaashoek JF, van Dijk HK (2007) On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks. J Econom 139:154–180

    Article  MathSciNet  Google Scholar 

  • Meitz M, Terasvirta T (2006) Evaluating models of autoregressive conditional duration. J Bus Econom Stat 24:104–124

    Article  MathSciNet  Google Scholar 

  • Smith M, Kohn R (1996) Nonparametric regression using Bayesian variable selection. J Econom 75(2):317–343

    Article  MATH  Google Scholar 

  • Strickland C, Forbes C, Martin G (2006) Bayesian analysis of the stochastic conditional duration model. Comput Stat Data Anal 50:2247–2267

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang MY, Russell JR, Tsay RS (2001) A nonlinear autoregressive conditional duration model with applications to financial transaction data. J Econom 104:179–207

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Business School, The University of Sydney, Sydney, NSW, 2006, Australia

    Richard Gerlach

  2. School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia

    Shelton Peiris

  3. Institute of Statistical Science, Academica Sinica, Taipei, 11529, Taiwan

    Edward M. H. Lin

Authors
  1. Richard Gerlach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shelton Peiris
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Edward M. H. Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Richard Gerlach.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gerlach, R., Peiris, S. & Lin, E.M.H. Bayesian estimation and inference for log-ACD models. Comput Stat 31, 25–48 (2016). https://doi.org/10.1007/s00180-015-0576-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-015-0576-8

Keywords

Search

Navigation