Abstract
This paper studies a nonlinear least squares estimation method for the logarithmic autoregressive conditional duration (Log-ACD) model. We establish the strong consistency and asymptotic normality for our estimator under weak moment conditions suitable for applications involving heavy-tailed distributions. We also discuss inference for the Log-ACD model and Log-ACD models with exogenous variables. Our results can be easily translated to study Log-GARCH models. Both simulation study and real data analysis are conducted to show the usefulness of our results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Allen, D., Chan, F., McAleer, M., Peiris, S. Finite Sample Properties of the QMLE for the Log-ACD Model: Application to Australian Stocks. Working paper, 2006
Amemiya, T. Advanced Econometrics. Harvard University Press, Cambridge, Massachusetts,1985
Bauwens, L., Giot, P. 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 (2000)
Bauwens, L., Giot, P. Econometric Modelling of Stock Market Intraday Activity. Boston: Kluwer Academic Publishers, 2001
Bauwens, L., Galli, F. and Giot, P. The Moments of Log-ACD Models, CORE Discussion Paper. Available at SSRN: https://doi.org/ssrn.com/abstract=375180 or DOI: 10.2139/ssrn.375180, 2003
Billingsley, P. Convergence of Probability Measures. New York: Wiley, 1999
Dufour, A., Engle, R. F. The ACD Model: Predictability of the Time between Consecutive Trades. Discussion papers in Finance. Zurich: ISMA Centre, 59
Engle, R., Russell, J. Autoregressive Conditional Duration: A New Model for Irregularly Spaced Data. Econometrica, 66(5): 1127–1162 (1998)
Geweke, J. Modeling the Persistence of Conditional Variances: A Comment. Econometric Reviews, 5: 57–61 (1986)
Pantula, S.G. Modeling the Persistence of Conditional Variances: A Comment. Econometric Reviews, 5: 71–74 (1986)
Straumann, D. Estimation in Conditionally Heteroscedastic Time Series Models, Lecture Notes in Statistics. Heidelberg: Springer, 2005
Zhang, M.Y., Russell, J.R., Tsay, R.S. A Nonlinear Autoregressive Conditional Duration Model with Applications to Financial Transaction Data. Journal of Econometrics, 104: 179–207 (2001)
Author information
Authors and Affiliations
Corresponding author
Additional information
The research was supported by the National Natural Science Foundation of China (11690014, 11690015, 10871188), by the Research Funds of Renmin University of China (No.16XNB025), the Social Science Foundation of Beijing (No. 17GLB022).
Rights and permissions
About this article
Cite this article
Chen, Z., Liu, W., Wang, C.D. et al. Nonlinear Least Squares Estimation of Log-ACD Models. Acta Math. Appl. Sin. Engl. Ser. 34, 516–533 (2018). https://doi.org/10.1007/s10255-018-0766-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10255-018-0766-6