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Multivariate modelling of time series count data: an autoregressive conditional Poisson model

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  • HEINEN, Andreas
  • RENGIFO, Erick

Abstract

This paper introduces a new multivariate model for time series count data. The Multivariate Autoregressive Conditional Poisson model (MACP) makes it possible to deal with issues of discreteness, overdispersion (variance greater than the mean) and both auto- and cross-correlation. We model counts as Poisson or double Poisson and assume that conditionally on past observations the means follow a Vector Autoregression. We use a copula to introduce contemporaneous correlation between the series. An important advantage of this model is that it can accommodate both positive and negative correlation among variables. As a feasible alternative to multivariate duration models, the model is applied to the submission of market orders and quote revisions on IBM on the New York Stock Exchange. We show that a single factor cannot explain the dynamics of the market process, which confirms that time deformation, taken as meaning that all market events should accelerate or slow down proportionately, does not hold. We advocate the use of the Multivariate Autoregressive Conditional Poisson model for the study of multivariate point processes in finance, when the number of variables considered simultaneously exceeds two and looking at durations becomes too difficult.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2003025.

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Date of creation: 00 Mar 2003
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Handle: RePEc:cor:louvco:2003025

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Related research

Keywords: count data; time series; copula; market microstructure;

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References

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  1. Robert F. Engle & Asger Lunde, 2003. "Trades and Quotes: A Bivariate Point Process," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(2), pages 159-188.
  2. 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.
  3. Lee, Charles M C & Ready, Mark J, 1991. " Inferring Trade Direction from Intraday Data," Journal of Finance, American Finance Association, vol. 46(2), pages 733-46, June.
  4. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 422, October.
  5. 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.
  6. Harvey, Andrew C & Fernandes, C, 1989. "Time Series Models for Count or Qualitative Observations," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 407-17, October.
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Citations

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Cited by:
  1. Heinen, Andréas & Rengifo, Erick, 2008. "Multivariate reduced rank regression in non-Gaussian contexts, using copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2931-2944, February.
  2. Quoreshi, Shahiduzzaman, 2005. "Modelling High Frequency Financial Count Data," UmeÃ¥ Economic Studies 656, Umeå University, Department of Economics.
  3. Jung, Robert C. & Kukuk, Martin & Liesenfeld, Roman, 2006. "Time series of count data: modeling, estimation and diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2350-2364, December.
  4. Snyder, Ralph D. & Ord, J. Keith & Beaumont, Adrian, 2012. "Forecasting the intermittent demand for slow-moving inventories: A modelling approach," International Journal of Forecasting, Elsevier, vol. 28(2), pages 485-496.
  5. Kurt Brannas & A. M. M. Shahiduzzaman Quoreshi, 2010. "Integer-valued moving average modelling of the number of transactions in stocks," Applied Financial Economics, Taylor & Francis Journals, vol. 20(18), pages 1429-1440.
  6. Feigin, Paul D. & Gould, Phillip & Martin, Gael M. & Snyder, Ralph D., 2008. "Feasible parameter regions for alternative discrete state space models," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2963-2970, December.
  7. GRAMMIG, Joachim & HEINEN, Andréas & RENGIFO, Erick, 2004. "Trading activity and liquidity supply in a pure limit order book market," CORE Discussion Papers 2004058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Ghahramani, M. & Thavaneswaran, A., 2009. "On some properties of Autoregressive Conditional Poisson (ACP) models," Economics Letters, Elsevier, vol. 105(3), pages 273-275, December.
  9. Weiß, Christian H., 2010. "INARCH(1) processes: Higher-order moments and jumps," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1771-1780, December.

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