Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Econometrics 2: Statistic Analysis of Econometric Time Series (StatØ2)

Practical information
Study year 2016/2017
Block 1
Programme level Full Degree Master
Course responsibles
  • Mogens Steffensen (6-72746c6a7378457266796d33707a336970)
  • Olivier Wintenberger (12-7b6d727869726669766b6976447165786c326f7932686f)
  • Department of Mathematical Sciences
Course number: NMAA05025U

Course content


The course introduces and analyzes models and statistical procedures for multivariate observations that are dependent over time. Examples of such data are interest rates and stock prices. The focus is on the autoregressive (AR) model and its multivariate version (VAR), including unit root inference and cointegration analysis. A brief introdution to related non-linear models (e.g. the ARCH-model) is also given. The probability theory and other mathematics necessary to analyze the models and estimation and test procedures is presented. The topics from probability theory include martingales, Markov chains, asymptotic stability, stationarity, mixing, and laws of large number and central limit theorems for time dependt processes. By means of the methods presented in the course, the students will solve theoretical econometric problems and use statistical software to analyse economic time series.


Learning outcome

Knowledge: The course covers the following topics. Dependence and correlation, stationary and mixing stochastic processes, laws of large numbers for dependent sequences, martingales, central limit theorems for martingales, Markov processes, asymptotic stability, linear processes, uni- and multivariate autoregressive processes, estimation and asymptotic statistical theory for time series models, exogeneity, tests for misspecification of time series models, non-linear time series models, autoregressive processes with unit roots, cointegration.

Skills: After the course, the students are expected to be able to apply the key time series models typically used for analysis of macro econometric data, to use statistical software for time series analysis, apply key concepts and methods from the theory of stochastic processes (including martingales, laws of large numbers and central limit theorems) to analyse statistical methods for time series, to formulate and apply likelihood based tests for linear hypotheses and specification tests for time series models, and to determine whether or not a stochastic process is exogenous.

Competences: After the course, the students are expected to be able to analyse macro economic time series statistically at an advanced level and to make predictions of future values of the series, and to be able to theoretically analyse uni- and multivariate time series models and to develop statistical methodology for such models.

Recommended prerequisites

Statistik 2 (Stat2) or equivalent.

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MSc Programme in Mathematics-Economics
MsC Programme in Statistics


Study Board of Mathematics and Computer Science

Course type

Single subject courses (day)


1 block


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Teaching and learning methods

5 hours of lectures and 3 hours of exercises per week for 7 weeks.


No limit




Category Hours
Lectures 35
Theory exercises 21
Project work 25
Preparation 90
Exam 35
English 206


Type of assessment

Written examination, 3 hours under invigilation


All aids allowed

NB: If the exam is held at the ITX, the ITX will provide you a computer. Private computer, tablet or mobile phone CANNOT be brought along to the exam. Books and notes should be brought on paper or saved on a USB key.

Marking scale

7-point grading scale

Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome.

Censorship form

No external censorship
One internal examiner


30 minutes oral exam with several internal examiners, no preparation time and no aids.

Compulsory written assignments from the course that are approved and valid do not need to be repeated. Compulsory assignments that have not been approved or are invalid must be handed in no later than one week before the start of the re-exam period.

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