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Nonstationary autoregressive conditional duration models

Author

Listed:
  • Mishra Anuj

    (Department of Statistics and Centre for Advanced Studies, Savitribai Phule Pune University, Pune, Maharashtra, 411 007, India)

  • Ramanathan Thekke Variyam

    (Department of Statistics and Centre for Advanced Studies, Savitribai Phule Pune University, Pune, Maharashtra, 411 007, India)

Abstract

Recently, there has been a growing interest in studying the autoregressive conditional duration (ACD) models, originally introduced by (Engle, R. F., and J. R. Russell. 1998. “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data. Econometrica 66: 1127–1162). ACD models are useful for modeling the time between the events, especially, in financial context, the time between trading of stocks. In this paper, we propose a specific type of nonstationary ACD model, viz., time varying ACD model (tvACD), by allowing the parameters of the usual ACD model to vary as functions of time. Some probabilistic and inferential aspects of such models have been investigated. We also develop a local polynomial procedure for the estimation of the parameter functions of the proposed tvACD model. Asymptotic properties of the estimators have been investigated, including the asymptotic normality. The asymptotic distribution being dependent on the parameters of the original distribution, a weighted bootstrap estimator is suggested and its validity is established. Simulation study and empirical analysis using high frequency data (HFD) from National Stock Exchange (NSE, INDIA) illustrate the application of the proposed tvACD model.

Suggested Citation

  • Mishra Anuj & Ramanathan Thekke Variyam, 2017. "Nonstationary autoregressive conditional duration models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(4), pages 1-22, September.
    • Handle: RePEc:bpj:sndecm:v:21:y:2017:i:4:p:22:n:2
    DOI: 10.1515/snde-2015-0057
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    References listed on IDEAS

    as
    1. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    2. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2008. "Normalized least-squares estimation in time-varying ARCH models," LSE Research Online Documents on Economics 25187, London School of Economics and Political Science, LSE Library.
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    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.
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    6. 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.
    7. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    8. Neelabh Rohan & T. V. Ramanathan, 2013. "Nonparametric estimation of a time-varying GARCH model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(1), pages 33-52, March.
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