# ELE 3916 Introduction to Econometric Theory

## ELE 3916 Introduction to Econometric Theory

In mathematical disciplines, there is always an answer to “why is that so?”, yet due to time-constraints, many presentations of financial and econometric tools are based around black boxes, even when solid mathematical arguments and assumptions led to their development. In this course, we take our time and work through the reasoning and motivation for some well-known and elementary tools in finance and economics that are based on statistics. Examples include the market beta, the Sharpe ratio, confidence intervals and omitted variable bias. We will see why such tools and formulas are the way they are and will use simulation and programming in R to see how they behave outside the conditions they were originally developed under.

Using simple mathematical tools, such as sums, the normal distribution, and central programming techniques such as the for-loop, we aim at understanding these foundational tools in a rather complete manner. This enables the student to much easier understand complex tools used both in later courses at higher levels as well as being able to responsibly use such tools in an industry-setting.

After completing the course, the student should have gained knowledge in the following topics:

- The interpretation of the Pearson correlation, and when it serves as a useful summary of dependence.
- The interpretation of hypothesis tests and confidence intervals, an overview of some of the most important conceptual problems that surround these tools.
- The robustness of statistical tools, or lack thereof.
- Understanding of the problem of asymptotics: Most statistical tools apply only with large sets of data, but how large is large? Are there methods that work on paper but do not work in practice?
- Knowledge of the mathematical arguments leading to the development of some central financial tools.

After completing the course, the student should have gained skills in the following topics:

- Calculation rules with sums and averages.
- Calculation rules of variances and covariances, and the relation between these rules and the calculation rules for averages.
- Practice in mathematical problem solving, with a focus on problems relevant for econometrics and finance.
- Practice in the mathematical framework surrounding hypothesis testing and inference.
- Programming simulation experiments.
- How different types of time variation may influence statistical methodology.

Through solving projects with mathematical and programming problems, the student will reflect on the limitations of econometrics, the issue of subjectivity in reaching statistical conclusions, and the level of trust one may place in statistically based decisions. Further, simulation will be introduced as a tool to assess the validity of econometric techniques. The student will reflect on using large-sample techniques in finite samples, the assessment of econometric assumptions and the concept of robustness in econometrics.

- Sums, averages, variance and covariances, and Pearson correlation.
- Population and sample properties. Statistical inference, consistency, and bias.
- Topics in linear regression.

The course is based on a learning-by-doing approach: There will be just one hour of lectures each week, and the remaining course time is spent on classes helping you be able to solve problems, with a focus on understanding.

Examples of time series models will be used during the course, but we will not develop systematic theory on time series. Previous exposure to time series models is an advantage but not a prerequisite.

Previous programming experience in R is advantageous but not required, and the programming techniques we require (looping, vectorial operations, and random number generation) will be developed during the course. Some illustrations will use financial datasets.

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Higher Education Entrance Qualification

**Disclaimer**

Deviations in teaching and exams may occur if external conditions or unforeseen events call for this.

A basic course in statistics and mathematics.

Previous exposure to time series models is an advantage but not a prerequisite.

Previous programming experience in R is advantageous but not required.

Assessments |
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Exam category: Submission Form of assessment: Written submission Weight: 40 Grouping: Group (1 - 3) Duration: 1 Week(s) Comment: Home exam. An oral defence may be required. All exams must be passed to obtain a final grade in the course. Exam code: ELE 39161 Grading scale: ECTS Resit: Examination when next scheduled course |

Exam category: Submission Form of assessment: Written submission Invigilation Weight: 60 Grouping: Individual Support materials: - BI-approved exam calculator
- Simple calculator
- Bilingual dictionary
Duration: 3 Hour(s) Comment: All exams must be passed to obtain a final grade in the course. Exam code: ELE 39162 Grading scale: ECTS Resit: Examination when next scheduled course |

All exams must be passed to get a grade in this course.

Activity | Duration | Comment |
---|---|---|

Teaching | 36 Hour(s) | Lectures and blended learning with projects for students. |

Feedback activities and counselling | 9 Hour(s) | |

Student's own work with learning resources | 75 Hour(s) | |

Group work / Assignments | 62 Hour(s) | |

Examination | 15 Hour(s) | Work related to the home exam. |

Examination | 3 Hour(s) | Final exam |

A course of 1 ECTS credit corresponds to a workload of 26-30 hours. Therefore a course of 7,5 ECTS credit corresponds to a workload of at least 200 hours.