Course Code:               STAT 3000

Course Title:                 REGRESSION WITH TIME SERIES ANALYSIS

Course Type:                Core

Level:                            3

Semester:                      2

No. of Credits:                3

Pre-requisites:              MATH2275

Course Rationale

The aim of this course is to introduce students to the science of model building and their use. In model building students will use a set of quantitative parameters to construct and test mathematical models of the real world by using regression analysis and time series. Students develop problem solving and data analysis skills by using statistical software to analyze real data.

The course is constructed in such a way as to satisfy the requirements in Applied Statistics of SOA.

Course Description

This course biulds on the applied aspects of Statistics I. It is primarily concerned with the construction of regression and time series models relevant to econometric modelling.

Assessment is designed to encourage students to work continuously with the course materials. Active learning will be achieved through marked assignments supplemented by problem papers, allowing continuous feedback and guidance on problem solving techniques in tutorials and lectures. Assessment will be based on the marked assignments and in-course tests followed by a final examination based on the whole course. Software used in the actuarial field will be incorporated in the course so that students develop practical skills

Course Content

• Single and multiple regression models;
• Heteroscedasticity;
• Time series analysis;
• Stochastic processes;
• Forecasting and estimating times series models;

Learning Outcomes

On completion of these modules the student should be able to:

A. Review of Elementary Statistics

•  Review the concepts of the normal, chi-squared, t and F distributions

B. Single and Multiple Regression Models

• Define single and multiple regression models
• Construct single and multiple regression models
• Define the Guass-Markov theorem
• Apply the multiple regression model to relevant data
• Define and use dummy variables

C. Serial Correlation and Heteroscedasticity

• Define serial correlation and heteroscedasticity
• Calculate least squares estimates
• Construct and interpret tests for heteroscedasticity
• Define and interpret the Breusch-Pagan and White test

D. Instrumental Variables and Model Specification

• Calculate parameters for ordinary least square estimates
• Define instrumental variables

E. Smoothing and Extrapolation of Time Series

• Define smoothing
• Construct time series models with smoothing and extrapolation

F. Properties of Stochastic Models

• Define white noise
• Construct and interpret the Box-Pierce test
• Construct and interpret the Dickey-Fuller test

G. Linear Time Series Models

• Define and construct moving average processes
• Define and construct autoregressive processes

Cognitive skills, Core skills and Professional Awareness

• Awareness of the principal statistical methods and models used in assessing problems in actuarial work
• Possession of the knowledge required to work in the area of economics in the actuarial context
• Application of the appropriate and rigorous use of mathematical modeling to formulate workable solutions to important statistical problems

Assessment Criteria

Regression and Time Series Anlysis is assessed by combination of coursework (50%) and a single 2-hour written exam at the end of the semester (50%).

Assessment:                    In-course Tests                            40%

Assignments                                10%

Final Exam                                  50%

In-course Tests:Two 50-minute written papers (20% each) consisting of compulsory questions of varying length.

Assignments: Two papers to be handed. One paper on the first part of the course and the other on the second part of the course. Each assignment is worth 5%. Tutorial practice papers will be given every week to be handed in the next week. Tutorial papers are not graded as part of the course work.

Exam Format:One two-hour written paper with compulsory questions.

Teaching Methodology

Lectures:           Two lectures per week (50 minutes each).

Lab:                   One two-hour computer lab.

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Course Calendar

 Week Topic to be taught Assessment 1 Introduction to Course/Course Overview Review of elementary statistics Assignment #1 is given 2 Single and multiple regression models Assignment #2 is given and Assignment #1 is corrected 3 Serial correlation Assignment #3 is given and Assignment #2 is corrected 4 Heteroscedasticity Assignment #4 is given and Assignment #3 is corrected 5 Instrumental variables First coursework test is given 6 Model specification Assignment #5 is given and Assignment #4 is corrected 7 Smoothing of time series models Assignment #6 is given and Assignment #5 is corrected 8 Extrapolation of time series models Assignment #7 is given and Assignment #6 is corrected 9 Properties of stochastic models Assignment #8 is given and Assignment #7 is corrected 10 Linear time series models Second coursework test is given 11 Estimating and forecasting with time series models Assignment #9 is given and Assignment #8 is corrected 12 Practical applications Assignment #10 is given and Assignment #9 is corrected 13 Revision Revision