Description
This course deals with advanced topics in statistics/econometrics. It is motivated
by applications to financial engineering, but the methods and tools are applicable
to many other fields. Important topics include exploratory data analysis, empirical
distributions, the bootstrap, time series models, GARCH models and Bayesian methods
(including MCMC). As motivation for these methods, time will be devoted to studying
financial market design and financial market microstructure data. This material will
be good preparation for quantitative work in finance as well as other jobs that
require rigorous use of statistics. It will also be good preparation for graduate
coursework with a quantitative emphasis. As a 5-unit course, the non-lab portion of
the course should consist of approximately 15 hours of work per week, divided among
lectures, reading, assignments and exams.
Programming
We will use the R programming language
to work with data and to solve problems related to methodology taught in lecture. R
is a free software environment used by academic and professional researchers in statistics.
Many students prefer to use RStudio as
an R programming environment. While I recommend installing R on your own machine, I will
make a server-based version of RStudio available that you can access remotely from any web
browser using your UCSC login credentials. Learning R will be a major benefit to you if
you pursue a career or graduate work in a quantitative discipline that requires
state-of-the-art data analysis.
Laboratory
This course is paired with a mandatory lab component. The objective of the lab sessions is
to teach the fundamentals of R programming in support of the programming objectives outlined
above. The first lab sessions will focus on coding primitives (data structures, control
flow, etc.) and subsequent sessions will teach the necessary tools to implement the methods
taught in lecture. The weekly outline below lists the schedule of lab topics, paired with
the schedule of Econ 114 lecture topics. Students will receive a separate grade for the lab,
which will be entirely determined by attendance. As a 2-unit course, the lab portion of
the course should consist of approximately 6 hours of work per week, divided among
lectures and practice problems.
Course Materials
The textbook for the course is Statistics
and Data Analysis for Financial Engineering, which is freely downloadable from
the previous link, provided you access that website with a campus IP address. I will
also make my lecture notes available on
this website.
Assignments
There will be four assignments, due every second Tuesday (with an extra week
to account for the midterm): 22 January, 5 February, 26 February and 12 March. Late
assignments will not be accepted and extensions will not be granted.
Exams
There will be two exams:
- Midterm: Thursday, 7 February 2019, in class.
- Final: Monday, 18 March 2019, 8:00 - 11:00 A.M.
Grading
Assignments: 25%; Mid-Term Exam: 35%; Final Exam: 40%. I will curve grades
only at the end of the semester if the distribution is low enough and/or
spread out enough. It is important for me to emphasize that curving will
never hurt your grade - it will only work to your advantage.
Course Outline
| Week | Lecture | Lab | Reading |
| 1 | Foundations of Probability | Fundamentals of R programming | Rupert Appendix A |
| 2 | Exploratory Data Analysis | Fundamentals of R programming | Rupert Chapter 4 |
| 3 | Modeling Univariate Distributions: Moments/Heavy-tailed Distributions | Sampling and simulating from distributions | Rupert Chapter 5 |
| 4 | Modeling Univariate Distributions: Maximum Likelihood Estimation | Coding MLE in R | Rupert Chapter 5 |
| 5 | Review/Midterm | Review/Midterm | N/A |
| 6 | Resampling | Bootstrapping in R | Rupert Chapter 6 |
| 7 | Time Series Models: Stationarity/AR and MA Processes | Simulating and estimating AR and MA processes in R | Rupert Chapter 9 |
| 8 | Time Series Models: ARMA processes/GARCH Models | Simulating and estimating ARMA and GARCH models in R | Rupert Chapters 9 and 18 |
| 9 | Bayesian Data Analysis: Bayes Theorem/Prior and Posterior Distributions | Bayesian Estimation in R | Rupert Chapter 20 |
| 10 | Markov Chain Monte Carlo | MCMC in R | Rupert Chapter 20 |