Alexander McNeil

Empirical Methods for Finance

Time and Place

WS 2003-04. Wednesday 15-16 in HG D7.2 and Thursday 15-17 in HG D1.2.

Target Audience

This course is mandatory for students of the Master of Advanced Studies in Finance program and is designed with these students in mind; it is however open to all students.

Required Knowledge

The course will assume prior knowledge of probability and statistics at least at the level of a first university course in a quantitative discipline. Masters students are certainly expected to be familiar with much of the content of the book "Mathematical Statistics and Data Analysis" by John A. Rice (see references below), and a detailed summary of the recommended preliminary reading from Rice is available.

The varied backgrounds of the Masters students will mean that some revision and repetition of basic concepts in statistics is necessary.

The course will be taught in English.

Course Description

This course will present a concise overview of empirical methods from various areas of statistics and econometrics which are relevant for financial modelling and quantitative risk management. The contents of the course will reflect the personal experience and tastes of the lecturer and should be considered as an introduction to a vast field.

The course will lead naturally into the SS04 course "Quantitative Methods for Risk Management", which is an optional specialisation for Masters students.

In style the course will offer a combination of theory, statistical methods and practical examples with real data using S-Plus and S+FinMetrics.

Essentials of statistical inference: a review.
- point estimation, likelihood theory, confidence intervals, hypothesis testing, asymptotic behaviour of estimators
Multivariate analysis.
- multivariate normal distribution, inference based on multivariate normal, principal components, factor analysis, elliptical and other multivariate distributions
Analysis of time series.
- basic concepts, ARMA models, inference in time domain
Models for changing volatility.
- models for asset returns, stylised facts of financial time series, ARCH and GARCH models, volatility prediction

Practical Exercises with S-Plus

A feature of the course will be the integration of practical examples using S-Plus and S+FinMetrics. This software is installed in the student computer rooms in E floor and is also available as part of the Neptun project (see also Maths department Neptun page) for installation on students' own notebook computers.

It is intended that students should be able to reproduce the analyses demonstrated in the lecture room.The vast majority of the analyses could also be performed in R, although some of the more advanced functionality of S+FinMetrics for modelling financial time series will not be available.

Students following the Masters will have some course work assignments, which will be voluntary for other students (but encouraged!).

Exercises for Downloading

Students following the course may download the following S program files, which contain the demonstrations shown in class. Note that scripts with stars (***) are not fully self-contained and require additional material which is listed below.

Additional Material

A summary of likelihood inference is found in the appendices of my forthcoming book.
The DowJones index returns are required for scripts 6 and 7. These can be found in the data download area.
Chapter on multivariate models from forthcoming book.
Chapter on time series from forthcoming book.

Assignments

Recommended Literature

1. Statistical Inference

Rice, J.A. (1995). Mathematical Statistics and Data Analysis. Duxbury Press, Belmont, California. Highly recommended basic text; much of the contents will be assumed to be prior knowledge.
Casella, G. & Berger, R. (2002). Statistical Inference. Duxbury Press, Pacific Grove, Calfornia. A very recent text at a more advanced level.
Hogg, R.V. & Craig, A.T. (1995, 5th edition). Introduction to Mathematical Statistics, Prentice Hall, Upper Saddle River, New Jersey.A classic text which is highly praised by reviewers at Amazon.

2. Multivariate Statistics

Mardia, K.V., Kent, J.T. & Bibby, J.M. (1995). Multivariate Analysis, Academic Press, Padstow, Cornwall. A standard reference for multivariate statistical analysis.

3. Time Series

Brockwell,P.J. & Davis,R.A. (2002, 2nd edition). Introduction to Time Series and Forecasting. Springer-Verlag, New York. The ideal introductory text for general theory and applications of time series.
Brockwell,P.J. & Davis,R.A. (1991, 2nd edition). Time Series: Theory and Methods. For those who want the full mathematics.

4. Econometric Models

Zivot,E. & Wang,J. (2002). Modeling Financial Time Series with S-Plus. Insightful + Springer Verlag, New York. Extremely useful book - highly recommended for this lecture course. Contains many relevant S-Plus examples.