**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 |

**Required Reading **

*Econometric Models and Economic Forecasts-*Robert S. Pindyck and Daniel L. Rubinfeld 4^{th} Edition 1998