FA541 Applied Statistics with Applications in Finance
Course Catalog Description
Introduction
Campus  Fall  Spring  Summer 

On Campus  X  X  
Web Campus  X  X 
Instructors
Professor  Office  

Zhenyu Cui

zcui6@stevens.edu  Babbio 545 
More Information
Course Description
Prerequisites
Students require sound understanding of probability gathered through an undergraduate class such as MA222 or equivalent. Also students must have the ability to program in R. Please consider taking FE515 if you are not familiar with R.
Attendance
Attendance is mandatory, and there may be short pop quizzes every week, starting from the second week.
Course Outcome
This course will allow the students to:
 Understand and summarize complex data sets through graphs and numerical measures.
 Calculate estimates of parameters using fundamental statistical methods.
 Measure the “goodness” of an estimator by computing confidence intervals.
 Apply statistical tests to experimental observations.
 Estimate and calibrate parameters of mathematical models using real data.
 Study relationships between two or more random variables.
 Be prepared for more advanced applied statistical courses.
Course Resources
Textbook
The only required textbook is Moore, McCabe, and Craig (2017).
 Moore et al. (2017) will be our main textbook. Earlier editions (say back to the sixth edition) should be OK.
 Greene (2012) (or other editions) will be useful for classes on Inference.
 Dalgaard (2004) is a useful basic reference concentrating on the use of R in statistics.
 Florescu and Tudor (2013) is useful for Probability and Estimation Methods.
 James et al. (2013) will be useful for its chapter on Variable Selection. It is available free online from its authors: http://wwwbcf.usc.edu/~gareth/ISL/.
Additional References
Peter Dalgaard. Introductory Statistics with R. Springer, 2004.
Ionut Florescu and Ciprian Tudor. Handbook of Probability. Wiley, 2013.
William H. Greene. Econometric Analysis. Prentice Hall, Seventh edition, 2012.
Gareth James, Daniela Witten, Trevor Hastie, and Robert Tibshirani. An Introduction to Statistical Learning with Applications in R. Springer Verlag, 2013.
David Moore, George P. McCabe, and Bruce A. Craig. Introduction to the Practice of Statistics. W. H. Freeman and Co., Ninth edition, 2017.
Grading
Grading Policies
You will be required to submit four homework assignments.
All homework assignments must be submitted in R markdown (.Rmd) format, with all answers written as functions. For your information, the main markdown page is here: https://rmarkdown.rstudio.com/. A nice summary of the use of R markdown appears here: http://www.stat.cmu.edu/~cshalizi/rmarkdown/. You may wish to include mathematical expressions in your markdown code. If so, it is useful to use L A TEX, which is taught in FE505. If you wish, you may optionally submit a .pdf version of your assignment, but no other formats will be accepted.
To emphasize: submission in R markdown format is mandatory. When I grade your homework, I will automatically parse your markdown code to extract your functions. I will run your functions with test data to confirm that they work and provide the correct results.
Late assignments will not be accepted unless you inform me of your circumstances before the assignment is due, and I grant you an extension. I will only grant extensions for serious medical or compassionate reasons. You will not receive an extension just because your computer fails or the network goes down at an inconvenient time.
There will be an inclass, closedbook, handwritten, midterm examination. This will test your understanding of the basic concepts. There will also be a takehome final project that will test your ability to put theory into practice.
For the project, you will work in groups of three to propose, design, and analyze a research topic that contains a significant data component and is applicable to your primary field of study. The project must use statistical methods that are taught in this course. Before you spend more than a few hours of work on your project, you must get my formal approval of your topic.
Your final grade will be determined by your performance in the homework, midterm examination, project, and spot quizzes, as weighted below. However, I reserve the right to “curve” the grades; i.e., to adjust the grades such that they follow the usual distribution at Stevens.
 30% Homework
 30% Midterm
 20% Project Part 1 (proposal) and Part 2 (implementation
 20% Project Report and Presentation:
 Each team of size 34 students will a) identify a research topic, b) apply statistical methods, c) interpret the results, and d) report the research findings.
 Each team will write a management report and make a brief presentation describing the research question and hypotheses, methods, results, and implications.
Lecture Outline
Topic  Reading  

Week 1  General statistical methods  Moore et al. (2017): Ch. 1 Moore et al. (2017): Ch. 2 
Week 2  Looking at Data. Descriptive graphical measures. Numerical measures. Sampling distributions.  Moore et al. (2017): Ch. 5 
Week 3  Maximum likelihood, Method of moments, Bayesian estimators. Applications to financial models.  Moore et al. (2017): Ch. 6 
Week 4  One variable statistical inference Confidence intervals and Testing Hypotheses on Population Means and Proportions  Moore et al. (2017): Ch. 7 
Week 5  Two Population tests for Means and Proportions  Moore et al. (2017): Ch. 8 
Week 6  Tests of Population Variance, Two Populations Review  Greene (2012): Ch. 12 Greene (2012): Ch. 13 Greene (2012): Ch. 14 Greene (2012): Ch. 16 
Week 7  Midterm Examination  
Week 8  Categorical Data Analysis. One and Two Way Tables. Goodness of Fit test. Independence Test.  Moore et al. (2017): Ch. 9 
Week 9  Regression Analysis. Least Squares Fitting. Analysis and Testing. Prediction. Multiple Regression. Confidence intervals ANOVA table, multiple R2, residuals  Moore et al. (2017): Ch. 10 
Week 10  Selection of variables. Correlation analysis, Variance inflation factors. Nonlinear regression. Generalized Additive Models.  Moore et al. (2017): Ch. 11 
Week 11  Analysis of variance (ANOVA) models. Applications. Expansion to mixture models Analysis of Covariance  James et al. (2013): Ch. 6 
Week 12  Logistic regression.  Moore et al. (2017): Ch. 12 Moore et al. (2017): Ch. 13 
Week 13  Intro to Risk measures: VaR, CVaR and CoVar Bootstrap Method and Permutation tests. Crossvalidation methods.  Moore et al. (2017): Ch. 14 
Week 14  Applications. Review and catching up  Moore et al. (2017): Ch. 16 