Advanced Financial and Macro Econometrics (F)

Course content

The course introduces selected topics from research in multivariate time series econometrics with applications to finance and macroeconomics. For each topic, the econometric theories are discussed and illustrated by empirical applications.

Topics include theory and application of:

  • Co-integration in vector autoregressive (VAR) models with application to e.g. term-structure models with non-stationary driving trends and portfolio strategies based on pairs-trading.
  • Multivariate models with autoregressive conditional heteroscedasticity (ARCH) with applications to portfolio selection and risk assessments.
  • Static and dynamic models for asses pricing. This includes the capital asset pricing model (CAPM), the asset pricing theory (APT) model, as well as extensions allowing time-varying conditional betas.
  • Bootstrap based testing in the financial and macro-econometric contexts above.

MSc programme in Economics – elective course
MSc programme in mathematics-economics


The PhD Programme in Economics at the Department of Economics - elective course with research module. PhD students must contact the study administration and the lecturer in order to register for the research module.


The course is a part of the admission requirements for the 5+3 PhD Programme in Economics. Please consult the 5+3 PhD admission requirements.


7 Nov.: Name changed from "Multivariate Financial and Macro Econometrics"  to "Advanced Financial and Macro Econometrics".

Learning outcome

After completing the course the student is expected to be able to:



  • Account for the theory for co-integrated VAR models, including the role of deterministic terms in the model, interpretation of the driving stochastic trends, and hypothesis testing and identification in the model.
  • Account for the application of the co-integrated VAR model to macroeconomics and finance and the interpretation of the results.
  • Account for the theory for multivariate ARCH models, including necessary restrictions for positive definiteness of the time varying covariance, and  discuss advantages and drawbacks of different model formulations.
  • Account for the application of multivariate ARCH models within the area of portfolio selection and risk assessment.
  • Account for the theory for factor models and applications within asset pricing. This includes a detailed discussion of the underlying assumptions, and the restrictions implied by the assumption of no-arbitrage.
  • Account for bootstrap-based inference.



  • Construct co-integrated VAR models and test assumptions for valid inference.
  • Perform inference withint the co-integrated VAR model, including determination of the co-integration rank, hypotheses testing on the structure of the model, and identification the co-integration relationships.
  • Construct and estimate multivariate ARCH models based on a suitable parametrization.
  • Apply the time varying conditional covariance matrix for portfolio optimization and risk assessments.
  • Use factor models for empirical asset pricing, and test restrictions implied by no-arbitrage.
  • Implement simple bootstrap algorithms.
  • Critically evaluate research papers containing econometric time series analyses.
  • Identify and analyze the characteristic properties of economic time series data



  • Apply the acquired knowledge and skills independently in later employment in either public or private institutions.
  • Master and implement relevant statistical models and solutions in new and complex contexts.

Lectures and exercise classes.

The course is based on selected journal articles and lecture notes.

Supplementary reading:

  • Francq, C. and J. M. Zakoian, GARCH Models: Structure, Statistical Inference and Financial Application, 2nd edition, Wiley, 2019.
  • Taylor, S.J., Asset Price Dynamics, Volatility and Prediction, Princeton University Press, 2005.
  • Tsay, R., Analysis of Financial Time Series, Wiley, 2005.

The course requires knowledge of time series econometrics equivalent to that achieved in Econometrics II. In addition, knowledge of theory in financial econometrics equivalent to that achieved in Financial Econometrics A is recommended.

2 hours lectures one to two times a week from week 6 to 20 (except holidays).
2 hours exercise classes from week 6 or 7 to 20 (except holidays).

The overall schema can be seen at KUnet:
MSc in Economics => "courses and teaching" => "Planning and overview" => "Your timetable"
KA i Økonomi => "Kurser og undervisning" => "Planlægning og overblik" => "Dit skema"

Timetable and venue:
To see the time and location of lectures and exercise classes please press the link under "Se skema" (See schedule) at the right side of this page (F means Spring).

You can find the similar information in English at
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-F20; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Forår/Spring – Week 5-30”
Press: “ View Timetable”

Please be aware regarding exercise classes:
- The schedule of the exercise classe can be changed until just before the teaching begins without the participants accept. If this happens it will be informed at the links in the right side, in the app myUCPH and at your personal schema at KUnet.
- If too many students have wished a specific class, students will be registered randomly at another class.
- It is not possible to change class after the second registration period has expired.
- The student is not allowed to participate in an exercise class not registered, because the room has only seats for the amount of registered student.
- That the study administration allocates the students to the exercise classes according to the principles stated in the KUnet.



  • The students receive oral collective feedback from quizzes on the content of the lectures.
  • Each student receive written feedback on the mandatory assignments from the teaching assistants
  • The teaching assistant gives oral collective feedback on the written assignment.
7,5 ECTS
Type of assessment
Written assignment, 12 hours
individual take-home exam. It is not allowed to collaborate on the assignment with anyone.
The exam assignment is in English and must be answered in English.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
for the written exam. The exam may be chosen for external censorship by random check.
Criteria for exam assessment

Students are assessed on the extent to which they master the learning outcome for the course.


To receive the top grade, the student must with no or only a few minor weaknesses be able to demonstrate an excellent performance displaying a high level of command of all aspects of the relevant material and can make use of the knowledge, skills and competencies listed in the learning outcomes.

Single subject courses (day)

  • Category
  • Hours
  • Exam
  • 12
  • Preparation
  • 124
  • Lectures
  • 42
  • Class Exercises
  • 28
  • English
  • 206