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

The PhD Programme in Economics at the Department of Economics:

  • The course is an elective course with research module. In order to register for the research module and to be able to write the research assignment, the PhD students must contact the study administration AND the lecturer.
  • The course is a part of the admission requirements for the 5+3 PhD Programme. Please consult the 5+3 PhD admission requirements.


The course is open to:

  • Exchange and Guest students from abroad
  • Credit students from Danish Universities
  • Open University students
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.

It is strongly recommended to have followed the course Econometrics II at the Study of Economics, University of Copenhagen, or equivalent prior taking ”Advanced Financial and Macro Econometrics”.

Knowledge of theory in financial econometrics equivalent to that achieved in "Financial Econometrics A" at the Study of Economics, University of Copenhagen, or equivalent is recommended.

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

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 "Timetable"/​"Se skema" at the right side of this page (F means Spring).

Please be aware:
- The study administration allocates the students to the exercise classes according to the principles stated in the 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.
- If there is not enough registered students or available teachers, the exercise classes may be jointed.
- The student is not allowed to participate in an exercise class not registered.
- The teacher of the exercise class cannot correct assignments from other students than the registered students in the exercise class except with group work across the classes.
- All exercise classes are taught in English and it is expected that the students ask questions in English, so foreign students are included in the dialog.
- The schedule of the lectures and the exercise classes can change without the participants´ acceptance. If this occure, you can see the new schedule in your personal timetable at KUnet, in the app myUCPH and through the links in the right side of this course description and the link above.
- It is the students´s own responsibility continuously throughout the study to stay informed about their study, their teaching, their schedule, their exams etc. through the curriculum of the study programme, the study pages at KUnet, student messages, the course description, the Digital Exam portal, Absalon, the personal schema at KUnet and myUCPH app etc.



  • 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
Type of assessment details
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.
Exam registration requirements

To qualify for the exam the student must no later than the given deadlines during the course:

  • Hand in and have approvede 3 out of 3 mandatory assignments.
  • The assignments must be handed in individually.
All aids allowed

for the written exam.

Information about allowed aids for the re-examination, please go to the section "Re-exam".

Marking scale
7-point grading scale
Censorship form
No external censorship
for the written exam.
An oral re-examination may be with external assessment.
Exam period


Exam information:

More information is available in Digital Exam from the middle of the semester. In special cases decided by the Department, the exam can change to another day and/or time than announced. 

More information about examination, rules, aids etc. at Master (UK) and Master (DK).


20 minutes oral examination with 20 minutes preparation time.

Written aids allowed during the preparation time.

No aids allowed during the examination.

External assessment. 


Reexam information:

More information in Digital Exam in August. In special cases decided by the Department, the re-sit can change to another day, and/or time than announced.

More information at Master UK) and Master DK).

Criteria for exam assessment

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


In order to obtain the top grade “12”, 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.


In order to obtain the passing grade “02”, the student must in a satisfactory way be able to demonstrate a minimal acceptable level of  the knowledge, skills and competencies listed in the learning outcomes.

Single subject courses (day)

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


Course number
7,5 ECTS
Programme level
Full Degree Master

1 semester

- Go to 'Signup' for information about registration and enrollment.

Information about admission and tuition fee: Master and Exchange Programme, credit students and guest students (Open University)

and venue:
- For teaching: Go to 'Remarks'.
- For exam and re-sits: Go to 'Exam'.
Department of Economics, Study Council
Contracting department
  • Department of Economics
Contracting faculty
  • Faculty of Social Sciences
Course Coordinators
  • Heino Bohn Nielsen   (18-7471757a7b3a6e7b747a3a7a7571787f717a4c716f7b7a3a77813a7077)
  • Anders Rahbek   (13-68756b6c797a3579686f696c72476c6a767535727c356b72)

Lectures: See "Course Coordinators"

Teacher at the exercise class:
Ex. class 1:

Please read "Remarks" regarding the schedule of the teaching.

Saved on the 16-05-2024

Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students