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Dynamic discrete mixtures for high frequency prices

Author

Listed:
  • Leopoldo Catania
  • Roberto Di Mari
  • Paolo Santucci de Magistris

Abstract

The tick structure of the financial markets entails that price changes observed at very high frequency are discrete. Departing from this empirical evidence we develop a new model to describe the dynamic properties of multivariate time-series of high frequency price changes, including the high probability of observing no variations (price staleness). We assume the existence of two independent latent/hidden Markov processes determining the dynamic properties of the price changes and the excess probability of the occurrence of zeros. We study the probabilistic properties of the model that generates a zero-inflated mixture of Skellam distributions and we develop an EM estimation procedure with closed-form M step. In the empirical application, we study the joint distribution of the price changes of four assets traded on NYSE. Particular focus is dedicated to the precision of the univariate and multivariate density forecasts, to the quality of the predictions of quantities like the volatility and correlations across assets, and to the possibility of disentangling the different sources of zero price variation as generated by absence of news, microstructural frictions or by the offsetting positions taken by the traders.

Suggested Citation

  • Leopoldo Catania & Roberto Di Mari & Paolo Santucci de Magistris, 2019. "Dynamic discrete mixtures for high frequency prices," Discussion Papers 19/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:19/05
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    File URL: https://www.nottingham.ac.uk/research/groups/grangercentre/documents/19-05.pdf
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    1. Eduardo Rossi & Paolo Santucci de Magistris, 2018. "Indirect inference with time series observed with error," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(6), pages 874-897, September.
    2. Neil Shephard & Justin J. Yang, 2017. "Continuous Time Analysis of Fleeting Discrete Price Moves," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1090-1106, July.
    3. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    4. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    5. Jan Bulla & Christophe Chesneau & Maher Kachour, 2015. "On the Bivariate Skellam Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(21), pages 4552-4567, November.
    6. Brownlees, C.T. & Gallo, G.M., 2006. "Financial econometric analysis at ultra-high frequency: Data handling concerns," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2232-2245, December.
    7. Geert Bekaert & Campbell R. Harvey & Christian Lundblad, 2007. "Liquidity and Expected Returns: Lessons from Emerging Markets," The Review of Financial Studies, Society for Financial Studies, vol. 20(6), pages 1783-1831, November.
    8. Siem Jan Koopman & Rutger Lit & André Lucas, 2017. "Intraday Stochastic Volatility in Discrete Price Changes: The Dynamic Skellam Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1490-1503, October.
    9. Lesmond, David A., 2005. "Liquidity of emerging markets," Journal of Financial Economics, Elsevier, vol. 77(2), pages 411-452, August.
    10. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    11. Jeroen K. Vermunt & Rolf Langeheine & Ulf Bockenholt, 1999. "Discrete-Time Discrete-State Latent Markov Models with Time-Constant and Time-Varying Covariates," Journal of Educational and Behavioral Statistics, , vol. 24(2), pages 179-207, June.
    12. Torben G. Andersen & Martin Thyrsgaard & Viktor Todorov, 2019. "Time-Varying Periodicity in Intraday Volatility," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1695-1707, October.
    13. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    14. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    15. Lo, Andrew W. & Craig MacKinlay, A., 1990. "An econometric analysis of nonsynchronous trading," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 181-211.
    16. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
    17. John Geweke & Gianni Amisano, 2011. "Hierarchical Markov normal mixture models with applications to financial asset returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 1-29, January/F.
    18. Katarzyna Bien & Ingmar Nolte & Winfried Pohlmeier, 2011. "An inflated multivariate integer count hurdle model: an application to bid and ask quote dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(4), pages 669-707, June.
    19. Nikolaus Hautsch & Peter Malec & Melanie Schienle, 2014. "Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 89-121.
    20. Ole E. Barndorff-Nielsen & David G. Pollard & Neil Shephard, 2012. "Integer-valued L�vy processes and low latency financial econometrics," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 587-605, January.
    21. Tina Hviid Rydberg & Neil Shephard, 2003. "Dynamics of Trade-by-Trade Price Movements: Decomposition and Models," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 2-25.
    22. Francesco Bartolucci & Alessio Farcomeni, 2015. "A discrete time event-history approach to informative drop-out in mixed latent Markov models with covariates," Biometrics, The International Biometric Society, vol. 71(1), pages 80-89, March.
    23. Bartolucci, Francesco & Farcomeni, Alessio, 2009. "A Multivariate Extension of the Dynamic Logit Model for Longitudinal Data Based on a Latent Markov Heterogeneity Structure," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 816-831.
    24. Antonello Maruotti, 2011. "Mixed Hidden Markov Models for Longitudinal Data: An Overview," International Statistical Review, International Statistical Institute, vol. 79(3), pages 427-454, December.
    25. Roman Liesenfeld & Ingmar Nolte & Winfried Pohlmeier, 2008. "Modelling financial transaction price movements: a dynamic integer count data model," Studies in Empirical Economics, in: Luc Bauwens & Winfried Pohlmeier & David Veredas (ed.), High Frequency Financial Econometrics, pages 167-197, Springer.
    26. Siem Jan Koopman & André Lucas & Marcel Scharth, 2015. "Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State-Space Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 114-127, January.
    27. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    28. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    29. 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.
    30. Andrew Harvey & Ryoko Ito, 2017. "Modeling time series with zero observations," Economics Papers 2017-W01, Economics Group, Nuffield College, University of Oxford.
    31. Atchison, Michael D & Butler, Kirt C & Simonds, Richard R, 1987. "Nonsynchronous Security Trading and Market Index Autocorrelation," Journal of Finance, American Finance Association, vol. 42(1), pages 111-118, March.
    32. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    33. Brockwell, A.E., 2007. "Universal residuals: A multivariate transformation," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1473-1478, August.
    34. Siem Jan Koopman & Rutger Lit & André Lucas & Anne Opschoor, 2018. "Dynamic discrete copula models for high‐frequency stock price changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 966-985, November.
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    Keywords

    Dynamic Mixtures; Skellam Distribution; Zero-inflated series; EM Algorithm; High frequency prices; Volatility;
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