Course Catalog Description
In this course the students will learn how to estimate financial data model and predict using time series models. The course will cover linear time series (ARIMA) models, conditional heteroskedastic models (ARCH type models), non-linear models (TAR, STAR, MSA), non-parametric models (kernel regression, local regression, neural networks), non-parametric methods of evaluating fit such as bootstrap, parametric bootstrap and cross-validation. The course will also introduce multivariate time series models such as VAR. Prerequisite: FE 541 or MA 331 or MA 541 or MA 612
- Review of Statistical Methods, Visual descriptors, Numerical Descriptors. Simple and multivariate regression, diagnostic checks.
- Characteristics of discrete time financial data, returns, kurtosis etc.
- Correlations, Dependence Autocorrelation
- Linear time series analysis (AR, MA, ARMA).
- Volatility modeling via conditional heteroscedastic models (ARCH, GARCH, EGARCH, etc.)
- Market Microstructure data analysis
- Nonlinear models and applications (TAR, STAR, MSA)
- Nonparametric methods: Kernel regression, local regression, Neural networks
- Value at risk (VaR), stress test, peak over threshold, expected shortfall
- Bootstrap, Parametric Bootstrap and simulation methods.
This is the main material. Provided enough time is left we may introduce the following topics
- Multivariate time series models.
- Multi-factor CAPM and APT.
- Principal Component Analysis and Application to Arbitrage Pricing Theory
A student graduating this course will be expected to have the following specific knowledge.
- A running knowledge of R that will help with any statistical (and not only) problem.
- The ability to approach and analyze any discrete time signal from a time series perspective.
- The ability to differentiate between various time series models.
- The ability to perform cross-validation of the model developed.
- The ability to forecast future observations of the time series.
- Analysis of Financial Time Series, by Ruey S. Tsay, 3rd edition, Wiley Series in Probability and Statistics, Aug 30 2010, ISBN: 9780470414354, ISBN-13: 978-0470414354 (primary textbook)
- Introductory Statistics with R, by Peter Daalgard, Springer; 2002. Corr. 3rd printing edition (January 9, 2004) ISBN-10: 0387954759 ISBN-13: 978-0387954752 (recommended text for R programming)
- Statistical Analysis of Time-Series Data in SPlus, by Renfine Carmona, Springer, March 4, 2004, ISBN: 0387202862 , ISBN-13: 978-0387202860 (recommended text)
- An Introduction to Analysis of Financial Data with R, by Ruey S. Tsay, John Wiley, 2013, ISBN 0470890813.
- We will use R throughout this course. Students will be expected to install and have the program running on their computers.
To understand the course material and get a good grade it is necessary (though not sufficient) to invest a substantial amount of time working on the assignments. Homework consisting of about 5-8 problems will be assigned in class and posted on the web every other week or so. They will be due on the specified due date at the specified time. No late homework will be accepted under any circumstances. I will grade two or three problems (selected by me) from each assignment which will count toward 60% of the homework grade, while casually reviewing the other problems for the remaining 40% of the homework grade.
You are encouraged to discuss homework; however, all written homework must be written by you. Copying solutions from other students in the class, former students, tutors, or any other source is strictly forbidden. Copying the solution of one or more problems from another source than your own brain is consider academic dishonesty/misconduct and will be dealt with according to the Stevens honor board policy. Please review the document posted on the website which details what is considered fair collaboration and what is considered academic misconduct. Your solutions must be those that you fully understand and can produce again (and solve similar problems) without help. The ideal model to follow is first to work independently, then to discuss issues with your fellow students, and then to prepare the final write-up individually. This is going to be an applied course. Therefore, I would expect any solution to a problem in this class to follow the steps bellow:
- Outline the steps and identify the mathematical techniques learned that pertain to the respective problem.
- If the problem needs a method first identify and describe the methodology you will apply. Comments about the first two steps. It is expected that in an applied course students spend most time on the next (third) step. However, the first two steps are equally important for a successful demonstration of understanding the course concepts. At the beginning of every course the problems are simple enough that the need for these two first steps seem unnecessary but by the end of the class the problems become complicated enough that this will not seem artificial (indeed it will be most helpful). It is equally important that you do these steps for the problems in midterm and the final. During a test students have sometime difficulties carrying out all the mathematical analysis to completely solve the problem. However, if I can determine that you understand the steps required and what to do to complete the problem, I can give more credit than in a situation when the problem is not completed or a wrong solution is given and the student does not tell me anything about what he/she is doing. Thus, a clearly written plan of your solution will help you earn a good test grade.
- Apply the methodology to the problem or the data under study. As a professional in a quantitative field you will be expected to carry out and provide answers involving real applications. However, in this class you must show an understanding of why and what of all of the steps involved . Explain what you are doing as if you are teaching it to someone. People who write journal articles often leave out most of the easy steps and just show the hardest steps. That is fine for journal articles, but it is not appropriate for a classroom situation where you need to be convincing the instructor that you understand the reasoning behind all the steps you are doing.
- Very important! Write a conclusion explaining if the application seems to support the method. This is the most important step. Oftentimes, an applied research article is judged from the contribution to the science as evident in the conclusion. Therefore, the clarity with which you expose this part is the most important step of solving the problem.
We will have one midterm and a final exam. The format will be decided at a later time. If in class you will be allowed to bring a handwritten page containing whatever you think is relevant for the exam. I have not yet decided at this time if you will be asked to do real applied problem that will require the use of a laptop pc. If you need to use a computer the exam will be open-books open-notes. The date for the midterm will be agreed on during the semester. The most weight for the final grade will be coming from the final examination.
There will be no individual make up exams. If you miss one of the exams, you may be allowed to take a comprehensive make up exam (location and time to be determined) at the end of the semester. To be allowed to take this make up exam you have to bring valid written documentation that explains the reason for the missed exam. The make up exam will replace at most one missing exam grade.