Time Series Analysis and Statistical Arbitrage
G63.2707, Fall 2009

Outline

How do we analyse historical financial data to develop profitable and low-risk trading strategies? This course is an introduction to time series analysis as used in finance, and trading strategies relevant to both buy-side and sell-side market participants. The course will be roughly divided into three parts:

Linear models: AR and MA for scalar and vector processes, and simple volatility and covariance estimation. Model evaluation and residual analysis. Cointegration and its application in risk modeling and pairs trading strategies.
Nonlinear models: ARCH, GARCH, and more general volatility models.
Applications: market microstructure, transaction cost modeling, and optimal trading strategies for both agency and principal trading.

Instructors

Instructors:	Robert Almgren and Robert Reider
Assistant:	Lin Li, ll1084 at nyu

Prerequisites

The course is intended for second-year students in the Courant Institute's MS Program on Mathematics in Finance. Such students are expected to have an excellent foundation in mathematics applied to finance (stochastic calculus and PDEs), a reasonable background in finance (portfolio theory and risk management) and in computing, but not necessarily an intensive knowledge of statistics. Students with comparable preparation may enroll if space is available.

Work

About 5 homework sets (40% total), one quiz (30%), and a final project (30%).

References

We have a class account at Wharton Research Data Services. Login information will be given in class.

Carol Alexander, Market Models.
James D. Hamilton, Time Series Analysis, Princeton University Press 1994.
Joel Hasbrouck, Empirical Market Microstructure, Oxford University Press 2006 (more info on Hasbrouck's page).
Stephen J. Taylor, Asset Price Dynamics, Volatility, and Prediction, Princeton University Press 2005.
Ruey S. Tsay, Analysis of Financial Time Series, 2nd Edition, Wiley 2005.
Research articles will be made available as needed.

Schedule

Monday evenings, 7:10 to 9 PM in Silver 713, from Sept. 14 through Dec. 7 or 14. (There is no Columbus Day holiday this year.) The schedule and the outline below are subject to change depending on how the course develops, and on the instructors' travel demands.

1	Sept 14	Introduction to time series modeling. Notes 1, HW 1. Data files: A, B, C
2	Sept 21	Moving average and autoregressive models. Notes 2. R codes used in class: cplot.R, demean.R.
3	Sept 28	Linear models. Notes 3, HW 2.
4	Oct 5	Application to financial data. Supplementary Notes 4. Codes used in class: expav.R, gettemp.R, tfit.R, utils.R, vplot.R, cmevlm.csv, mktmpr
5	Oct 12	Quiz (Columbus Day seems no longer to be an NYU holiday)
6	Oct 19	Reider -- Volatility Forecasting: GARCH-type models. Notes 1
7	Oct 26	Reider -- Volatility Forecasting: stochastic volatility models. Notes 2, HW, Data: XLS, CSV
8	Nov 2	Almgren -- State space models and the Kalman filter. Notes 5. HW 3 (new due date: Nov 23).
9	Nov 9	Almgren -- Multidimensional models and particle methods. Notes 6.
10	Nov 16	Reider -- Trading strategies 1
11	Nov 23	Reider -- Trading strategies 2
12	Nov 30	Reider -- Trading strategies 3
13	Dec 7	Almgren -- Market microstructure and high-frequency data. HW 4, Slides from class, Notes 7.
14	Dec 14	Final project due -- no class planned.

Time Series Analysis and Statistical Arbitrage G63.2707, Fall 2009