Advanced Financial and Macro Econometrics (F)
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.
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.
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.
Changes to teaching methods due to a pandemic crisis:
The teaching in this course might be changed to either fully or partly online due to a pandemic crisis. If changes are implemented please read the study messages at KUnet or the announcements in the virtual course room on Absalon (for enrolled students).
The course is based on selected journal articles and lecture notes.
- 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
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).
You can find the similar information in English at
-Select Department: “2200-Økonomisk Institut” (and wait for respond)
-Select Module:: “2200-F23; [Name of course]”
-Select Report Type: “List – Weekdays”
-Select Period: “Forår/Spring”
Press: “ View Timetable”
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.
- 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.
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)
- Class Instruction
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- 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)
- For teaching: Go to 'Remarks'.
- For exam and re-sits: Go to 'Exam'.
- Department of Economics, Study Council
- Department of Economics
- Faculty of Social Sciences
- Heino Bohn Nielsen (18-7774787d7e3d717e777d3d7d78747b82747d4f74727e7d3d7a843d737a)
- Anders Rahbek (13-6b786e6f7c7d387c6b726c6f754a6f6d797838757f386e75)
Lectures: See "Course Coordinators"
Teacher at the exercise class:
Ex. class 1:
Please read "Remarks" regarding the schedule of the teaching.
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Courseinformation of students