WEERACHART T. KILENTHONG

­­­­­Graduate School

University of the Thai Chamber of Commerce

SM512 StatisticalTheory

M.Sc. in Financial Engineering

First Semester of 2019

Course Syllabus

Instructor:                    Weerachart Kilenthong

Course Schedule:        Saturday at Room 5603

Email:                          [email protected]

Website:                       riped.utcc.ac.th/tee/teaching/sm512

Teaching Assistance: Sartja Duangchaiyoosook and Wasinee Junton 

Email: [email protected] and [email protected]ped.utcc.ac.th

1. Course Description

This course studies basic concepts of probability and statistical theory relevant to financial engineering. The topics include basic probability, conditional probability, random variables and their distributions, expectation and moments, special distributions, asymptotic theory and properties of large random samples, point estimation and maximum likelihood estimation, sampling distributions of estimators, hypothesis testing, linear statistical models, basic nonparametric methods. Advanced topics may include Markov chains both in discrete and continuous time models, basic Bayesian estimation methods and Kalman filtering.

2. Course Objective

The aim of this course is to give master-level students an introduction to principles, theories, and tools in advanced statistical theory. Students will also learn how to apply statistical models with real data using R software.

3. Required Textbooks:

1. DeGroot, Morris H. and Mark J. Schervish. 2012. Probability and Statistics. 4th edition: Preason. [DS]

2. Hogg, Robert V., Allen T. Craig and Joseph W. McKean. 2005. Introduction to Mathematical Statistics. 6th edition, Pearson. [HCM]

Optional Textbooks:

Lecture Note

Data Sources

We will provide relevant data through the course website: riped.utcc.ac.th/tee/teaching/sm512

Program Sources

Program R version 3.5.1+RStudio

4. Grades and Requirements

Grades will be based on the following weights:

30%         Assignment(s)

30%         Mid-Term Exam   

40%         Final Exam          

Tentative Grading Range:

85 – 100   A

80 – 84     B+

70 – 79     B

65 – 69     C+

55 – 64     C

50 – 54     D+

40 – 49     D

39 or less F

4.1 Assignment

Students will be assigned to complete 8-10 individual assignments during the semester. An assignment with the lowest score will be dropped when calculating the total score for each student. Note: Late submission of the assignments is not accepted; a score of zero will be recorded for that assignment.

4.2 Examination

There will be two examinations: a mid-term exam counting for 30% of the total points, and a final exam counting for 40% of the total points. If a student misses a regular examination without acceptable excuse, a score of zero will be recorded for the examination.

Problem Assignments

1. Problem Assignment 1 (Due on August 24 at the beginning of the class),

2. Problem Assignment 2 (Due on August 31 at the beginning of the class),

3. Problem Assignment 3 (Due on September 14 at the beginning of the class),

    data for Problem Assignment 3

4. Problem Assignment 4 (Due on September 14 at the beginning of the class),

5. Problem Assignment 5 (Due on September 21 at the beginning of the class),

    data for Problem Assignment 5

6. Problem Assignment 6 (Due on September 28 at the beginning of the class),

    data for Problem Assignment 6

7. Problem Assignment 7 (Due on October 26 at the beginning of the class),

    data for Problem Assignment 7

8. Problem Assignment 8 (Due on November 3 at the beginning of the class),

    data for Problem Assignment8

9. Problem Assignment 9 (Due on November 9 at the beginning of the class),

10. Problem Assignment 10 (Due on November 16 at the beginning of the class),

11. Problem Assignment 11 (Due on November 16 at the beginning of the class), 

      data for Problem Assignment11

12. Problem Assignment 12 (Due on December 7 at the beginning of the class), 

      data for Problem Assignment12

 

Course Schedule

The course will be carried out in 15 sessions, totalling 45 lecture hours. The structure of the course is subject to revision if necessary (e.g., to conform to the background, knowledge, and interests of the students). The tentative structure of the whole course is as follows:

Week

Topics

Reading Materials

1

Basic Probability Theory lecture 

Chp. 1-2 of DS and Lecture Note

2

Random Variables and Their Probability Distributions lecture

Chp. 3 of DS and Lecture Note

3

Conditional Probability and Bivariate Distributions                                        

Chp. 2-3 of DS and Lecture Note

4

Conditional Distributions and Function of Random Variables             

Chp. 3 of DS and Lecture Note

5

Expectation Covariance and Correlation of Radom Variable

Chp. 4 of DS and Lecture Note

6

Covariance, Correlation, and Moments

Chp. 4 of DS and Lecture Note

7

Conditional Expectation

Chp. 4 of DS and Lecture Note

8

conclusion_1

covering up to the 7th session

 

Midterm Examination

covering up to the 7th session

9

Normal Distribution

Chp. 5 of DS and Lecture Note

10

Popular Distributions

Chp. 5 of DS and Lecture Note

11

Large-Sample Theories

Chp. 6 of DS and Lecture Note

12

Bays Estimation        

Chp. 8 and Chp. 9 of DS and Lecture Note

13

Maximum Likelihood Estimation and Method of Moments

Chp. 10 of DS and Lecture Note

14

Hyperthesis_Testing

Chp. 11 of DS and Lecture Note

15

Hyperthesis_Testing: T-test and F-test

Chp. 11 of DS and Lecture Note

 

Final Exam

 

covering from the 7th session to the 15th session