To model real data sets using second order stochastic processes imposes that the data sets verify the second order stationarity condition. This stationarity condition concerns the unconditional moments of the process. It is in that context that most of models developed from the sixties' have been studied; We refer to the ARMA processes (Brockwell and Davis, 1988), the ARCH, GARCH and EGARCH models (Engle, 1982, Bollerslev, 1986, Nelson, 1990), the SETAR process (Lim and Tong, 1980 and Tong, 1990), the bilinear model (Granger and Andersen, 1978, Guegan, 1994), the EXPAR model (Haggan and Ozaki, 1980, the long memory process (Granger and Joyeux, 1980, Hosking, 1981, Gray, Zang and Woodward, 1989, Beran, 1994, Giraitis and Leipus, 1995, Guegan, 2000), the switching process (Hamilton, 1988). For all these models, we get an invertible causal solution under speci¯c conditions on the parameters, then the forecast points and the forecast intervals are available. Thus, the stationarity assumption is the basis for a general asymptotic theory for identification, estimation and forecasting. It guarantees that the increase of the sample size leads to more and more information of the same kind which is basic for an asymptotic theory to make sense.

About the speaker: Domenique Guegan is Professor at the Centre d'Economie de la Sorbonne (CES) at the University Paris1 Pantheon-Sorbonne. Her research interests are: non-linear time series modelling, risk measures in finance, financial markets, parametric and non-parametric statistical methods with application in finance, and deterministic chaotic systems.


Professor Dominique Guegan

Research Area

Statistics Seminar


Professor Dominique Guegan


Wed, 04/03/2009 - 11:00am