Note: This page is kept on the web for students who are trying to get a feel for the aim of Statistics 956. The course will be offered again in Spring 2007, and the content will change --- but only to the tune of about 25%. Looking over these assingments should still be useful for "shoppers." (See also, the home page for Stat 957-Spring 2007)
In the 2007 course I plan to move a bit more quickly. This Spring we will use the book Time Series Analysis and Its Applications by Shumway and Stoffer. I will add topics that are more finacially oriented. We will also use R more intensively. In particular, I hope that we can collectively write some useful R packages.
As assignments are completed, the old assignments will be moved down to this section. This transition usually takes place over the weekend.
No.1. This assignment provides an initial experience with writing S-Plus functions. The main task is to conduct a simulation experiment to assesses the approximate normality of the sample autocorrelation coefficient for a time series that is generated by the AR(1) model.
No. 2. This assignment provides more experience with S functions and plotting, but it is mainly an invitation to explore the notions of stability and stationarity. It focuses on the AR(2) process, but one sees similar phenomena in all AR(p) models.
No. 3. This assignment deals with the theoretical notion of white noise and the physical reality of actual returns. This is the first assignment for which you will need to use WRDS. If you are not a Wharton student, you will need to set up a Wharton account; it's free and easy. Everyone will need to become familiar with the mechanisms for WRDS access.
No. 4. This assignment covers some of the basic technology of ARMA simulation and fitting. It also provides a caricature of a trading system. If you're favorably predisposed to such things, they can send a tingle down your spine. Dash Hammet might have called them "the stuff that dreams are made of."
No. 5. This assignment invites you to fit two univariate AR(2) models to see how they compare to a bivariate AR(1) model. These fits are used to guess the signs of tomorrow's returns, and we then consider making bets on our guesses. Naturally, the bet sizes are guided by the Kelly-Breiman criterion. Incidentally, this assignment introduces the plan of dividing your data into training sets and testing sets. It also explicitly encourages the use of the "Executive Summary" report style.
No. 6. Half of this assignment provides bread-and-butter experience with the fitting of GARCH models, but the other half has room for some honest back-to-basics creativity. You can even dip into the well of ultimate understanding: How does one understand dependence in a sequence of coin flips? This question will be taken up in earnest over the next few assignments.
No. 7 continues with our back-to-basics approach to understanding "persistence of volatility." The main tasks include the writing of loopless S-functions to compute transition matrices from state occupancy vectors and the evaluation of the estimates. An important part of the exercise is to create a "story" out of your estimates. The exercise invites you to assess the precision of your estimates in accordance with your individual experience with Markov chains and hypothesis testing.
No. 8 addresses two issues. First it considers the problem of inter-temporal aggregation of real stock returns. Do the standard deviations follow the natural square root law, or is there some subtle dependence that lead to another power law? Second, the assigment considers the rolling regression tools of S-Plus and examines the time dependence of alpha and beta in the CAPM. This assigment is due Monday March 28.
No. 9. This assignment invites you to explore one of the less well-known of the stylized facts of return series, "the coarse-fine volitility estimate correlation." More generally, it also suggests how one can begin the exploration of any observation that is advanced as stylized fact. The second part of the assigment suggests a way to "jump start" your work on your final project. Part of this assigment is to browse the resources on stylized facts.
Assigment No. 9 is the last of regular homework assigments. The remaining assigments will be directed toward the formulation and design of your final project. Most of the class on Monday April 18 will be devoted to the group discussion of your proposals. Our last class is on Wednesday April 20.