Monthly Archives: February 2011

Giacomo Bormetti, “Minimal model of financial stylized facts”

Tuesday February 15 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Giacomo Bormetti
Scuola Normale Superiore – Pisa

Abstract
In this seminar I will present joint work with D. Delpini from the University of Pavia. We afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatilitiy of financial returns. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the emergence of fat tails, and of the relevant correlation functions. We also propose a systematic methodology for estimating the model parameters, and we describe the empirical analysis of the Standard & Poor 500 index daily returns, confirming the ability of the model to capture many of the established stylized fact as well as the scaling properties of empirical distributions over different time horizons.

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Sylvain Arlot, “Advanced Course on Statistics”

Monday February 14 2011, 14.00 – 16.00 Aula Bianchi

Tuesday February 15 2011, 9.00 – 11.00 Aula Fermi

Thursday February 17 2011, 14.00 – 16.00 Aula Fermi

Tuesday February 22 2011, 14.00 – 16.00 Aula Dini

Wednesday February 23 2011, 9.00 – 11.00 Aula Bianchi

Scuola Normale Superiore

SYLVAIN ARLOT
CNRS-INRIA and ENS, Paris

Advanced Course on Statistics

Lecture 1. (Monday February 14) Statistical learning

  • the statistical learning learning problem
  • examples: prediction, regression, classification, density estimation
  • estimators: definition, consistency, examples
  • universal learning rates and No Free Lunch Theorems [1]
  • the estimator selection paradigm, bias-variance decomposition of the risk
  • data-driven selection procedures and the unbiased risk estimation principle

Lecture 2. (Tuesday February 15) Model selection for least-squares regression

  • ideal penalty, Mallows’ Cp
  • oracle inequality for Cp (i.e., non-asymptotic optimality of the corresponding model selection procedure), corresponding learning rates [2]
  • the variance estimation problem
  • minimal penalties and data-driven calibration of penalties: the slope heuristics [3,4]
  • algorithmic and other practical issues [5]

Lecture 3. (Thursday February 17) Linear estimator selection for least-squares regression [6]

  • linear estimators: (kernel) ridge regression, smoothing splines, k-nearest neighbours, Nadaraya-Watson estimators
  • bias-variance decomposition of the risk
  • the linear estimator selection problem: CL penalty
  • oracle inequality for CL
  • data-driven calibration of penalties: a new light on the slope heuristics

Lecture 4. (Tuesday February 22) Resampling and model selection

  • regressograms in heteroscedastic regression: the penalty cannot be a function of the dimensionality of the models [7] 
  • resampling in statistics: general heuristics, the bootstrap, exchangeable weighted bootstrap [8]  
  • study of a case example: estimating the variance by resampling  
  • resampling penalties: why do they work for heteroscedastic regression? oracle-inequality. comparison of the resampling weights [9]

Lecture 5. (Wendsday February 23) Cross-validation and model/estimator selection [10]  

  • cross-validation: principle, main examples 
  • cross-validation for estimating of the prediction risk: bias, variance  
  • cross-validation for selecting among a family of estimators: main properties, how should the splits be chosen?  
  • illustration of the robustness of cross-validation: detecting changes in the mean of a signal with unknown and non-constant variance [11]  
  • correcting the bias of cross-validation: V-fold penalization. Oracle-inequality. [12] Continue reading →

Lucio M. Calcagnile, “Misurare l’efficienza informativa dei mercati finanziari”

Wednesday February 2 2011
13:00
Scuola Normale Superiore
Aula Bianchi

Lucio M. Calcagnile
Scuola Normale Superiore

Abstract
Un mercato finanziario è detto “efficiente” se è efficiente nel processare l’informazione disponibile, se – cioè – gli agenti che lo compongono assimilano e incorporano immediatamente nei prezzi tutte le informazioni rilevanti. È possibile stabilire se un mercato è efficiente in senso assoluto ovvero quantificare il grado di efficienza relativa di un mercato rispetto a un altro? Esporrò alcuni lavori recenti in letteratura che con metodi diversi tentano di misurare l’efficienza relativa. Presenterò esperimenti e analisi condotti su serie temporali finanziarie ad alta frequenza usando il contesto della teoria dell’informazione e l’entropia di Shannon quale strumento per misurare l’efficienza. Illustrerò infine alcuni vantaggi e svantaggi che si presentano nell’analisi di serie ad alta frequenza.

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