### hfsl_course

- Fall On Campus
- Spring Online

Each section of the course will cover theory and test the student’s knowledge on developing models. The course is designed to familiarize students with statistical software needed for analysis of the data. Financial applications are emphasized but the course serves areas of science and engineering where statistical concepts are needed. The course objective is to equip students with fundamental statistical analytical techniques to have better success in the financial engineering curriculum whenever statistical analysis of data is involved and to provide students with a solid foundation of statistical problem solving empirical methods with the ability to summarize, and calibrate observed multivariate data.

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
- Give measures of how good the estimators are by providing confidence intervals or approximate 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 ready to go into a more advanced applied statistical course such as time series analysis.

- D. Moore, G. McCabe and B. Craig, Introduction to the practice of Statistics, 8th edition, W.H. Freeman and Co, 2014

- Michael Kutner, Christopher Nachtsheim, John Neter, William Li: Applied Linear Statistical Models, McGraw-Hill/Irwin, 2004

- Peter Daalgard, Introductory Statistics with R,Springer; 2002. Corr. 3d printing edition January 9, 2004.

- Ionut Florescu and Ciprian Tudor, Handbook of Probability, Wiley, 2013 (for reference)

- John C. Hull, Options, Futures and Other Derivatives, Prentice Hall, 2014, 9th edition,(for reference - you may get any of the older editions as the current edition is quite expensive. You should use whatever edition you used or plan to use in FE620).

The final grade will be determined upon the student's performance in the Homework and Exams. We will have several assignments (each weighted equally toward your final grade) during the course of the semester. Only use the .pdf format for submitting assignment files. You should be able to transform any document into a pdf file. You can use Adobe acrobat - should be free to Stevens students as far as I know (please call the students help desk), or a simple alternative is to use a pdf printer driver. I write all my documents in LATEX and that typesetting program produces pdf files. A simple alternative (using any typesetting program) would be to search on google for a driver that would print to a pdf file. Such drivers are generally free.

In this course the students will be required to design and work on a project which contains a data component and is applicable to their primary field of study. Any project topic needs to be approved by the instructor and is required to apply statistical methods learned in this course. This project (written report and the presentations) will count as the final exam in this course. As such it is an important component of the course that should not be taken lightly.

Late assignments will not be accepted under any circumstances without prior notice and permission of the instructor. If outside circumstances are affecting your ability to perform in the course, you must contact me before you fall behind.

Week |
Topic(s) |
References |

week 1, 2, 3 |
General Statistical methods Looking at Data. Descriptive graphical measures. Numerical measures. Sampling distributions. Intro to R. Distributions in R. Methods of finding estimators, Maximum likelihood, Method of moments, Bayesian estimators. Conditional Maximum likelihood estimators. Approximations. Applications to financial models. |
Notes, Ch 1, 2 in [4] Ch 1-6 in [1]
Ch. 8 in [2] Hwk 1 due Lecture notes Hwk 2 due |

Week 4, 5, 6 |
One variable statistical inference Confidence intervals and Testing Hypotheses on Population Means and Proportions Two Population tests for Means and Proportions Tests of Population Variance, Two Populations Review |
Ch 6, 7.1, 8.1 in [4] Project decision Ch 7.2, 8.2 in [4] Hwk 3 due
Ch 7.3 in [4] Hwk 4 due |

Week 7 | Midterm examination | |

Week 8, 9 |
Multivariate Statistics Categorical Data Analysis. One and Two Way Tables. Goodness of Fit test. Independence test. Regression Regression (cont) . Least Squares Fitting. Analysis and Testing. Prediction. Multiple Regression. Confidence intervals ANOVA table, multiple R2, residuals |
Ch 9 in [4] Part 1 in [3] Part 2 in [3] Project update Hwk 5 due |

Week 10, 11 |
Selection of variables. Correlation analysis, Variance inflation factors. Nonlinear regression. Generalized Additive Models. Analysis of variance (ANOVA) models. Applications. Expansion to mixture models Analysis of Covariance |
Part 2 in [3]
Part 4 in [3] Ch 12, 13 in [4] Ch 14 in [4] Hwk 6 due |

Week 12, 13, 14 |
Applications Logistic regression. Intro to Risk measures: VaR, CVaR and CoVar Bootstrap Method and Permutation tests. Cross-validation methods. Applications. Review and catching up |
Lecture notes
Ch 16 in [4] Hwk 7 due |