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


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:

  1. 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.
  2. Nonlinear models: ARCH, GARCH, and more general volatility models.
  3. Applications: market microstructure, transaction cost modeling, and optimal trading strategies for both agency and principal trading.


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


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.


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


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


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.