 Aims
The aim of this course is to give a good comprehension of the theory and application of stochastic time series modelling, with a view towards prediction (forecasting).
Main themes
The principal subjects of this course on an introduction into time series analysis will include the modelling, estimation and prediction of two types of processes - linear processes and heteroscedastic models of non-linear processes. We follow basically a parametric approach - the student will learn how to quantify statistical uncertainty while estimating the model parameters for the problem of forecasting future values of the observedseries.
Content and teaching methods
Content
1. Modelling time series data: an introduction
2. Linear processes - simple parametric models (ARMA)
3. Estimation and prediction of ARMA models
4. Box-Jenkins analysis - (S)ARIMA models
5. Non-linear processes - heteroscedastic (G)ARCH models - applications to modelling financial data
Methods
Basic models of linear time series will be treated in the first part. The data analysis, i.e. estimation of the model parameters for forecasting, will be based predominantly on Box-Jenkins methods. In the second part of the course some elements of modelling financial data with the more recently developed ARCH and GARCH models will be given and included into the practical part of the course (done with the S-Plus software).
Other information (prerequisite, evaluation (assessment methods), course materials recommended readings, ...)
Prerequisites
A general knowledge of basic statistical concepts (on the
level of a first introductory course in statistics) is necessary.
Evaluation
The examination will be oral. An applied data analysis project
has to be prepared on the computer.
Teaching material
Course notes, von Sachs, R. and S. Van Bellegem, Script.
References :
Brockwell, P., Davis, R. : Introduction to Time Series and Forecasting. 1996, Springer, New York
Brockwell, P., Davis, R. : Times Series : Theory and Methods. 1991, Springer, New York
Gourieroux, Ch. : Modèles ARCH et applications financières. 1992, Economica, Paris
For more information:
http://www.stat.ucl.ac.be/cours/stat2414/index.html
http://www.stat.ucl.ac.be/cours/stat2414/index.html
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