# NMAA05025U Econometrics 2: Statistical Analysis of Econometric Time Series (StatØ2)

Volume 2021/2022
Education

MSc Programme in Mathematics-Economics
MSc Programme in Statistics

Content

The course aims at introducing and analysing stochastic models and statistical procedures for time-dependent observations. Examples of such data are interest rates, stock prices and composite indices. Special attention will be given to the autoregressive (AR) and moving average (MA) models. A brief introdution to related non-linear models (e.g. the ARCH, GARCH) will be given. The probabilistic and mathematical tools for analysing the models, as well as estimation and test procedures will be presented. Topics from probability theory include martingales, Markov chains, asymptotic stability, stationarity, mixing, as well as the law of large number and central limit theorem for time-dependent processes. Using the methods presented in the course, the students will solve theoretical econometric problems and use statistical software to analyse econometric time series.

Learning Outcome

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

Skills: After the course, the student will be able to apply standard time series models used for the analysis of macro-econometric data, to use statistical software for time series, to apply key concepts and methods from the theory of stochastic processes (including martingales, law of large number and central limit theorem) to statistically analyse time series, and to formulate and apply likelihood-based tests for linear hypotheses and specification tests for time series models.

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

Lecture notes will be provided.

Statistik 2 (Stat2) or equivalent.

Academic qualifications equivalent to a BSc degree is recommended.
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
• Category
• Hours
• Lectures
• 35
• Preparation
• 90
• Theory exercises
• 21
• Project work
• 25
• Exam
• 35
• Total
• 206
Oral

Oral feedback will be given on students’ presentations in class.

Feedback by final exam (in addition to the grade): In connection with the written exam and the two tests.

Credit
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
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Exam registration requirements

Two mandatory written assignments (mid and final term tests) must be handed in and approved.

Aid
Only certain aids allowed

The exam is open book. The student is allowed to bring the lecture notes,  weekly assignments, and their solutions to the exam.

Marking scale
Censorship form
No external censorship
One internal examiner
Re-exam

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

The mandatory written assignments from the course that are approved and valid do not need to be repeated.

Mandatory assignment(s) that have not been approved or are invalid must be handed in no later than three weeks before the start of the re-exam period.

##### Criteria for exam assesment

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