NON-LINEAR TIME SERIES IN FINANCE: An econometric approach

Instructor: Dominique Guégan
1st  Semester
Number of credits: 3 ECTS
Hours: 6 lectures of 3 hours each

General Presentation
The modeling of time series in finance is an important task. It is useful for understanding the evolution of the assets themselves, for forecasting, for measuring the volatility on the markets, and for risk measurements purposes. This last topic including the measure of the risks associated to portfolio management, and also all the developments and extensions linked to the necessity of regulators to get robust risk measures, for the different risks encountered on the  market risks, like liquidity risks for instance. Thus to get a robust modeling for the time series which underline these notions is fundamental.
In this course we consider discrete time series and introduce several modeling permitting to take into account the main features which characterize the financial assets. We focus on the general class of GARCH models which take into account mainly the heteroscedasticity of the data sets. We introduce and develop the Markov switching models which permit to the data sets to evolve inside two different states which generally characterize respectively the quiet and the turmoil periods detected on the markets. Models which jumps and breaks will be also detailed in order to catch some specific extreme events: these models will include classes of Stop-Breaks models and Bilinear processes. All these processes will be introduced with their univariate version and then extended in a multivariate setting.
The objectives of this course is:
-  to have a good knowledge of the different non-linear features which exist on the markets,
- to introduce several methods to model them,
- to present and detail the econometric developments around these models
- to give an estimation theory and an adequacy test theory permitting to use these models in practice.

Evaluation: Oral presentation of an article with discussion with the classroom: the purpose of this exam based on the study of an article will be the opportunityfor the students  to understand the strength and the limit of the use of these models in practice.

References:
P.J. Brockwell, R.A. Davis (1988) Time Series: Theory and Methods, Springer Series in Statistics, Springer.

Campbell J., Lo A., MacKinlay (1997) The econometrics of financial markets, Princeton University press, Princeton, NJ.

R. Engle and D. McFadden eds, (1994) Handbook of Econometrics, 4, North Holland.


D Guégan (1994) Séries Chronologiques non Linéaires à Temps Discret, Economica,
Paris.

D. Gu´egan (2003) Les chaos en finance: approche statistique, Economica, Paris

H. Krolzig (2001) Markov-Switching Vector Autoregressions: Modelling, Statistical Inference, and Application to Business Cycle Analysis, Lecture Notes in Economics and Mathematical Systems, Springer Verlag.

D. Pe˜na, G.C. Tiao, R.S. Tsay (2001) A course in time series analysis, Wiley series in Probability and statistics, N.Y.

H. Tong (1990) Non-linear Time Series: a Dynamical Approach, Oxford Scientific Publications, Oxford.