# Stat 434 Financial Time Series --- Syllabus

A statistics course
committed to honest data analysis,
focused on mastery of best-practice models,
and obsessed with the dynamics of financial markets

## Syllabus for Financial Time Series (Wharton Statistics 434)

### Course Description

This course introduces students to the time series methods and practices which are most relevant to the analysis of financial time series--- especially series of equity returns, interest rates, and exchange rates.

The course begins with an introduction to the statistical programming language S-Plus and the tools for exploratory data analysis of time series, including the sample autocorrelation and partial autocorrelation functions. It continues with the methodology of linear modeling of time series including autoregressive models, moving average models, and their generalizations.

The course then addresses the more individual features of financial series, especially techniques for understating time dependent volatility. Empirical observations motivate the ARCH-GARCH family of models, and these become a central theme of the course. After engaging GARCH models in some detail, the course looks at general issues of model building with financial time series --- including methods of risk-adjustment and methods of multiple comparison.

### Course Attitude

More than other courses, this course tries to deal with the genuine subtlety of honest data analysis and the often misunderstood role that mathematical models play in our understanding of empirical data.

Students will be given fundamental grounding in the use of some widely used tools, but much of the energy of the course is focus on individual investigation of time series. Active participation in the class is very important. This class is more about the opportunity for individual and team discoveries than it is about mastering a fixed set of techniques.

### Prerequisites

The BARE MINIMUM is Statistics 101 and 102 or Statistics 431.

Simply having good grades in these courses may not be enough. You should really have some honest mastery of the material, say from use outside of classes.

On the "theory" side, If you cannot define "density" and "distribution" --- and the difference between the two --- this is not the course for you. If you cannot define "mean" and "variance" and explain the difference between the population values and the sample estimates --- this course is not for you.

On the" practice" side, you MUST have experience with programming. We will be working intensively with the statistical programming language S-Plus. If you have no experience with programming, you will be at a HUGE comparative disadvantage to the class members who do have such experience.

Bottom LIne: The better your preparation, the more you can get out of the class --- and the more fun you can have. Perhaps the most important prerequisite is a genuine curiosity about the dynamics of financial markets --- but by itself, this is not enough, however much one might hope it could be.

### Required Text (or better ... Semi-required)

• Modeling Financial Time Series with S-Plus by Eric Zivot and Jiahui Wang.

### Recommended Texts (Not Required)

• The Basics of S-Plus, Third Edition, by Andreas Krause and Melvin Olson. Springer 2002.
• Market Models: A Guide to Financial Data Analysis by C. Alexander. John-Wiley and Sons 2002.

Grades will be based on weekly assignments (40%), a project proposal presented in class (10%) and a final project (50%) which is typically fifteen to twenty pages. These projects are done in teams of size two --- never any bigger, only smaller by desire or parity.

### Week-by-Week Plan (with Likely Variations):

Week 1: Introduction to Exploratory Data Analysis (EDA) with S-Plus. Sketch of the "Big Picture" and introduction to the philosophical challenges of modeling. (Short week)

Week 2: Introduction to white noise and its simplest alternative, the AR(1) model. The notion of stationarity. The implications of dependence on the "volatility" of a series with dependence. Writing SPlus functions and for-loops. Introduction to simulation. Review of qqplots.

Week 3: The autocorrelation function and its uses as a diagnostic. The theoretical ACF for the AR(1) model. A general measure of dependence, the Ljung-Box test. Introduction to the general class of Autoregressive and Moving Average Models, the ARMA (p,q) models. The Wold representation for AR(1) processes and how it helps us to "see" stationarity.

Week 4: Discussion of the notion of model adequacy, including residual analysis, evaluation of forecast accuracy, outlier detection, model sensitivity, and portmanteau tests of model adequacy such as the Ljung-Box test.

Week 5: A richer discussion of model adequacy including the questions of long range dependence and the technology of unit root tests. We cover most of Chapter 4 of Zivot and Wang, but some details may be set aside in favor of discussing the article "Is it really long memory we see in financial returns?" by Mikosch and Starica in Extremes and Integrated Risk Management, P. Embrechts et al (eds.), Risk Books, 2000.

Week 6: Time series regression models. We will cover Zivot and Wang Chapter 6 together with additional material on the robust estimation of covariance matrices.

Week 7: Introduction to the theory and practice of GARCH models. We will deal in some detail the motivation for these models and the methods used to fit them. (Sections 7.1-7.4 of Zivot and Wang)

Week 8: Deeper discussion of GARCH models including the question of model selection within the GARCH family. We will also examine the quality of predictions from these models in comparison to simpler alternatives. (Sections 7.5-7.10 of Zivot and Wang)

Week 9: Rolling Analysis of Time Series. Forecasting versus filtering, cross validation, and the use of out-of-sample testing. (Sections 9.1-9.2 of Zivot and Wang)

Week 10: Technical trading and methods of back-testing (Sections 9.3- 9.5 of Zivot and Wang may be supplemented by discussion of the article by Diebold and Mariano "Comparing Predictive Accuracy," J. Business and Economic Statistics 13, 253-263)

Week 11: (Tentative) Vector Autoregressive Models for Multivariate Time Series (Chapter 11 of Zivot and Wang)

Weeks 12: (Tentative) Cointegration (Chapter 12 of Zivot and Wang), plus selected readings on statistical arbitrage. Discussion of the advance brief for the 2002 Bank of Sweden Prize in Honor of Alfred Nobel.

Weeks 13: (Tentative) Multivariate GARCH Modeling --- Chapter 13 of Zivot and Wang. Suggestions for price-based volatility estimate. Comparison with implied volatilities. Weeks 14: State Space Models and Financial Time Series (Chapter 14 of Zivot and Wang together with supplementary material on hidden Markov models and the change point problem).

### Expected Variations

For the first ten weeks, we will probably track the syllabus rather closely, but since the classes tend to become larger over the years, one can expect that the last three weeks will be a little more mellow than this syllabus suggests. Conintegration will be discussed in some detail, but the material on multivariate AR models and multivariate GARCH will probably have to give way to time for student project proposals and detailed discussions of the design of the final projects.

You can get some sense of the variation by looking at the course blogs for earlier year that you can find from links from the landing page.

### Our Text

Modeling Financial Time Series with S-Plus, 2nd Ed, by Eric Zivot and Jiahui Wang.. This is available in the bookstore, and it will be used throughout the course. Nevertheless, we will only cover about one-fourth of the book. You can regard it as semi-required.

### Our Software

S-Plus and Finmetrics. The method of distribution may change, but most recently this was distributed in class. We may have a web based method shortly.

### Why Not Use R?

I'd love to use R--- It's free and it runs on all platforms.

Unfortunately, R is not as bullet proof or as well documented as S. Thus, for a first time exposure, we will save ourselves some anxiety by using S-Plus.

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