Multi-scale statistical analysis and modeling of financial time series

E. Bacry

*15 hour course in February and March *

The purpose of this course is twofold. The first is to familiarize the student with the microstructure of markets and the construction and manipulation of high frequency financial data. Secondly, we analyse the statistical properties of these data at very different time scales. We build a scale-invariant model to account for most of these properties. An application to risk prediction is presented.

Forecasting program :

  • Market microstructure : order books, bid-ask spread, transaction price, transaction cost, overnight effect, close price, tick by tick series
  • High frequency series Interpolation problem Treatment of rolls (for futures/forwards) Returns - Volume - Trading frequency Realised volatility - Microstructure noise
  • Some basic notions in estimation theory Estimation of a probability distribution Extreme value theory - Tail exponent Estimation of moments, correlation
  • Seasonality of volatility Daily/weekly seasonality Seasonality overnight Public holidays Seasonal adjustment - Construction of stationary series
  • Some stylized facts and ‘‘classical’’ models Skewness and kurtosis thick tails Correlation of volatility, long-range dependence, heteroscedasticity ARCH-type models Stochastic volatility models Link with trading volume/frequency Leverage effect
  • Scale invariance of financial series Stylized facts of scale invariance Modelling the seasonality of volatility Modelling returns with a scale invariant model Application to risk prediction Fundamental problems in parameter estimation


  • An Introduction to High-Frequency Finance by Michael Dacorogna, Ramazan Gencay and Ulrich A Muller

  • Bouchaud J.-Ph. et Potters M., Théorie des risques financiers, Alea Saclay, 1997.

  • Campbell, J.Y., A.W. Lo and A.C. MacKinlay, 1997The econometrics of financial markets. Princeton University Press.

Quelques autres éléments de bibliographie

  • Price dynamics in a Markovian limit order market , R. Cont, A. de Larrard, preprint, 2010

  • A Random Order Placement Model of Price Formation in the Continuous Double Auction, J. D. Farmer, L. Gillemot, G. Iori, S. Krishnamurthy, D.E. Smith, M.G. Daniels, The Economy as an Evolving Complex System, III,eds. L. Blume and S. Durlauf, 133-173. New York: Oxford University Press, 2005

  • Modeling microstructure noise with mutually exciting point processes E. Bacry, S. Delattre, M. Hoffmann, J.F. Muzy, preprint, 2010

  • Log-Normal continuous cascades: aggregation properties and estimation. Application to financial time-series download E.Bacry, A.Kozhemyak, J.F.Muzy, preprint, 2008

  • How markets slowly digest changes in supply and demand, J.P. Bouchaud, J.D. Farmer, F.Lillo, 2008, Quantitative Finance Papers 0809.0822,