338
Views
4
CrossRef citations to date
0
Altmetric
Research Papers

Analyzing order flows in limit order books with ratios of Cox-type intensities

ORCID Icon &
Pages 81-98 | Received 08 Oct 2018, Accepted 20 Jun 2019, Published online: 21 Aug 2019

References

  • Abergel, F., Anane, M., Chakraborti, A., Jedidi, A. and Muni Toke, I., Limit Order Books, 2016 (Cambridge University Press: Delhi).
  • Bacry, E., Dayri, K. and Muzy, J.-F., Non-parametric kernel estimation for symmetric Hawkes processes. Application to high frequency financial data. Eur. Phys. J. B Condens. Matter Complex Syst., 2012, 85(5), 1–12.
  • Bacry, E., Delattre, S., Hoffmann, M. and Muzy, J.-F., Modelling microstructure noise with mutually exciting point processes. Quant. Finance, 2013, 13(1), 65–77.
  • Bouchaud, J.-P., Gefen, Y., Potters, M. and Wyart, M., Fluctuations and response in financial markets: The subtle nature of ‘random’ price changes. Quant. Finance, 2004, 4(2), 176–190.
  • Bouchaud, J.-P., Mézard, M. and Potters, M., Statistical properties of stock order books: Empirical results and models. Quant. Finance, 2002, 2(4), 251–256.
  • Bowsher, C.G., Modelling security market events in continuous time: Intensity based, multivariate point process models. J. Econom., 2007, 141, 876–912.
  • Bozdogan, H., Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 1987, 52(3), 345–370.
  • Chakraborti, A., Muni Toke, I., Patriarca, M. and Abergel, F., Econophysics review: I. Empirical facts. Quant. Finance, 2011, 11(7), 991–1012.
  • Cont, R., Stoikov, S. and Talreja, R., A stochastic model for order book dynamics. Oper. Res., 2010, 58(3), 549–563.
  • De Gregorio, A. and Iacus, S.M., Adaptive LASSO-type estimation for multivariate diffusion processes. Econ. Theory, 2012, 28(4), 838–860.
  • Fan, J. and Li, R., Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc., 2001, 96(456), 1348–1360.
  • Fan, J. and Li, R., Variable selection for Cox's proportional hazards model and frailty model. Ann. Stat., 2002, 30(1), 74–99.
  • Frank, L.E. and Friedman, J.H., A statistical view of some chemometrics regression tools. Technometrics, 1993, 35(2), 109–135.
  • Gould, M.D., Porter, M.A., Williams, S., McDonald, M., Fenn, D.J. and Howison, S.D., Limit order books. Quant. Finance, 2013, 13(11), 1709–1742.
  • Hansen, N.R., Reynaud-Bouret, P. and Rivoirard, V., Lasso and probabilistic inequalities for multivariate point processes. Bernoulli, 2015, 21(1), 83–143.
  • Huang, W., Lehalle, C.-A. and Rosenbaum, M., Simulating and analyzing order book data: The queue-reactive model. J. Am. Stat. Assoc., 2015, 110(509), 107–122.
  • Kinoshita, Y. and Yoshida, N., Penalized quasi-likelihood estimation for variable selection. Preprint, 2018.
  • Lallouache, M. and Challet, D., The limits of statistical significance of Hawkes processes fitted to financial data. Quant. Finance, 2016, 16(1), 1–11.
  • Lehalle, C.-A. and Mounjid, O., Limit order strategic placement with adverse selection risk and the role of latency. Market Microstructure Liquidity, 2017, 3(1), 1750009.
  • Lillo, F. and Farmer, J.D., The long memory of the efficient market. Stud. Nonlinear Dyn. Econom., 2004, 8(3), 1–33.
  • Lipton, A., Pesavento, U. and Sotiropoulos, M.G., Trade arrival dynamics and quote imbalance in a limit order book. arxiv preprint arxiv:1312.0514, 2013.
  • Muni Toke, I., Reconstruction of order flows using aggregated data. Market Microstructure Liquidity, 2016, 2(2), 1650007.
  • Muni Toke, I. and Pomponio, F., Modelling trades-through in a limited order book using Hawkes processes. Econ. J., 2012, 6, 22.
  • Muni Toke, I. and Yoshida, N., Modelling intensities of order flows in a limit order book. Quant. Finance, 2017, 17(5), 683–701.
  • Ogata, Y., The asymptotic behaviour of maximum likelihood estimators for stationary point processes. Ann. Inst. Stat. Math., 1978, 30(1), 243–261.
  • Ozaki, T., Maximum likelihood estimation of Hawkes' self-exciting point processes. Ann. Inst. Stat. Math., 1979, 31(1), 145–155.
  • Rio, E., Asymptotic Theory of Weakly Dependent Random Processes, Probability Theory and Stochastic Modelling, 2017 (Springer: Berlin).
  • Stoikov, S., The Micro-Price: A High Frequency Estimator of Future Prices. SSRN preprint, 2017.
  • Suzuki, T. and Yoshida, N., Penalized least squares approximation methods and their applications to stochastic processes. arXiv:1811.09016, 2018.
  • Tibshirani, R., Regression shrinkage and selection via the lasso. J. R. Stat. Soc. Ser. B Methodol., 1996, 58(1), 267–288.
  • Umezu, Y., Shimizu, Y., Masuda, H. and Ninomiya, Y., AIC for non-concave penalized likelihood method. arxiv preprint arxiv:1509.01688, 2015.
  • Wang, H. and Leng, C., Unified LASSO estimation by least squares approximation. J. Am. Stat. Assoc., 2007, 102(479), 1039–1048.
  • Yoshida, N., Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations. Ann. Inst. Stat. Math., 2011, 63(3), 431–479.
  • Yue, Y.R. and Loh, J.M., Variable selection for inhomogeneous spatial point process models. Canad. J. Statist., 2015, 43(2), 288–305.
  • Zou, H., The adaptive lasso and its oracle properties. J. Am. Stat. Assoc., 2006, 101(476), 1418–1429.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.