Keynote speakers

TITLE OF THE TALK:    FRACTIONAL INTEGRATION AND COINTEGRATION IN FINANCIAL TIME SERIES DATA

Summary: We examine financial time series modeling using new approaches based on the concepts of fractional integration and cointegration. With respect to the univariate work, these methods depart from the conventional approaches based on stationary I(0) and nonstationary I(1) by allowing the number of differences to be a fractional value. We extend these models in several fronts, including structural breaks, non-linearities, seasonality, cyclicity, volatilities, etc. An overview of the applications of these techniques to financial time series will also be conducted. In particular, we examine variables such as stock market prices, returns, and their associated volatilities measured in terms of squared and absolute value returns; dividens, earnings, a consumer price index and a long term interest rate. With  respect to the multivariate work, the most recent techniques based on fractional cointegration will be examined, including stationary and nonstationary weak and strong cointegration.

TITLE OF THE TALK:     OFFLINE AND ONLINE MULTIPLE CHANGE DETECTION FOR CAUSAL TIME SERIES

Summary: consider time series belonging to a large class of causal models including, AR(∞), ARCH(∞), TARCH(∞), ARMA-GARCH(∞) processes. We first suppose that certain parameters of a fixed model change at each break-point and that there is a number K of changes, K unknown. It can be underlined that after a change-point, the model depends on previous data built with other parameters. Therefore between two successive break-points, the time series is generally not stationary. All the unknown parameters (K, the change dates and the successive parameters of the model) are estimated using a penalized contrast built from a Gaussian quasi-likelihood. Under conditions, we show that we obtain the same convergence rates that in the case of independent random variables. Numerically, we added a data-driven procedure of choice of the penalty which allows to obtain extremely convincing results. We secondly consider a sequential procedure for detecting changes in parameters of causal time series. In this framework, we construct a test statistics based on Gaussian log-likelihood and we study its asymptotic behavior. Simulations are also realized.

(Joint works with William Kengne (Cergy) and Olivier Wintenberger (Paris 6))