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Forecasting limit order book liquidity supply-demand curves with functional AutoRegressive dynamics

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  • Chen, Ying
  • Chua, Wee Song
  • Härdle, Wolfgang Karl

Abstract

Limit order book contains comprehensive information of liquidity on bid and ask sides. We propose a Vector Functional AutoRegressive (VFAR) model to describe the dynamics of the limit order book and demand curves and utilize the tted model to predict the joint evolution of the liquidity demand and supply curves. In the VFAR framework, we derive a closed-form maximum likelihood estimator under sieves and provide the asymptotic consistency of the estimator. In application to limit order book records of 12 stocks in NASDAQ traded from 2 Jan 2015 to 6 Mar 2015, it shows the VAR model presents a strong predictability in liquidity curves, with R2 values as high as 98.5 percent for insample estimation and 98.2 percent in out-of-sample forecast experiments. It produces accurate 5-, 25- and 50- minute forecasts, with root mean squared error as low as 0.09 to 0.58 and mean absolute percentage error as low as 0.3 to 4.5 percent

Suggested Citation

  • Chen, Ying & Chua, Wee Song & Härdle, Wolfgang Karl, 2016. "Forecasting limit order book liquidity supply-demand curves with functional AutoRegressive dynamics," SFB 649 Discussion Papers 2016-025, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2016-025
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    References listed on IDEAS

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    1. Benston, George J. & Hagerman, Robert L., 1974. "Determinants of bid-asked spreads in the over-the-counter market," Journal of Financial Economics, Elsevier, vol. 1(4), pages 353-364, December.
    2. Mourid, Tahar & Bensmain, Nawel, 2006. "Sieves estimator of the operator of a functional autoregressive process," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 93-108, January.
    3. Härdle, Wolfgang Karl & Hautsch, Nikolaus & Mihoci, Andrija, 2012. "Modelling and forecasting liquidity supply using semiparametric factor dynamics," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 610-625.
    4. Philippe C. Besse & Herve Cardot & David B. Stephenson, 2000. "Autoregressive Forecasting of Some Functional Climatic Variations," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 673-687, December.
    5. Umut Çetin & Robert A. Jarrow & Philip Protter, 2008. "Liquidity risk and arbitrage pricing theory," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 8, pages 153-183, World Scientific Publishing Co. Pte. Ltd..
    6. Tarun Chordia & Asani Sarkar & Avanidhar Subrahmanyam, 2003. "An empirical analysis of stock and bond market liquidity," Staff Reports 164, Federal Reserve Bank of New York.
    7. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    8. Wolfgang K. Härdle & Nikolaus Hautsch & Andrija Mihoci, 2015. "Local Adaptive Multiplicative Error Models for High‐Frequency Forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 529-550, June.
    9. Antoniadis, Anestis & Sapatinas, Theofanis, 2003. "Wavelet methods for continuous-time prediction using Hilbert-valued autoregressive processes," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 133-158, October.
    10. Guillas, Serge, 2001. "Rates of convergence of autocorrelation estimates for autoregressive Hilbertian processes," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 281-291, December.
    11. Kerry Cooper, S. & Groth, John C. & Avera, William E., 1985. "Liquidity, exchange listing, and common stock performance," Journal of Economics and Business, Elsevier, vol. 37(1), pages 19-33, February.
    12. Peter Gomber & Uwe Schweickert & Erik Theissen, 2015. "Liquidity Dynamics in an Electronic Open Limit Order Book: an Event Study Approach," European Financial Management, European Financial Management Association, vol. 21(1), pages 52-78, January.
    13. Michael J. Fleming & Eli M. Remolona, 1999. "Price Formation and Liquidity in the U.S. Treasury Market: The Response to Public Information," Journal of Finance, American Finance Association, vol. 54(5), pages 1901-1915, October.
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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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