Time Series Analysis, 7.5 credits

Contents

The main purpose of the course is that the student should be well aquainted with the basic notions, theory, models and methods for solutions, in time series analysis. The course covers models for time dependent data. Such data frequently occurs in financial (e.g. the price development of a merchandise) and scientific (e.g. metheorological observations, radar signales) applications.

The course consists of two parts.

Module 1 (4.5 hp) Theory.

The module consists of general theory of time series, stationary and non-stationary models, such as ARMA, ARIMA, SARIMA, and GARCH models including exogeneous variables, multivariate models, state-space models, parameter estimation and prediction.

Module 2 (3 hp) Lab Assignments. The module consists of analysis of time series using suitable software.

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• independently define the notions expectation, covariance function and spectral distribution for time series
• independently define parametric ARMA models
• thoroughly explain how ARMA-models can be expanded to ARIMA-, SARIMA-, ARCH- and GARCH-models
• describe state-space and multivariate models in general terms

Skills

• identify trends and seasonal variation in time series
• derive and estimate expectation, covariance function and spectral distribution for time series, analyse their connections, and derive the uncertainty of the estimates
• utilize parametric and extended ARMA models to real data and validate the results
• predict the future of observed time series of different lengths, and critically evaluate the results

Judgement and approach

• clearly present the results from time series analyses, and evaluate the results from a scientific perspective

Required Knowledge

The course requires 90 ECTS including one of the following options or equivalent knowledge

- minimum 12 ECTS in Mathematical Statistiscs or
- minimum 6 ECTS in Mathematical Statistics and a course in Transform Methods minimum 7,5 ECTS or
- minimum 75 ECTS in Statistics 

In all options we also require a course in Basic Caculus minimum 7,5 ECTS. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies.

Form of instruction

The teaching mainly consists of lectures and lessons.

Examination modes

Module 1 is examined  by a written exam. Module 2 is examined by written lab reports (U/G).
On module 1, one of the following judgements is assigned: Fail (U), Pass (G) or Pass with distinction (VG). On module 2, one of the following judgements is assigned: Fail (U) or Pass (G). For the whole course, one of the following grades is assigned: Fail (U), Pass (G) or Pass with distinction (VG). In order to receive a passing grade on the course, all parts must be completed with a passing judgement. The course grade is decided by the grade on Module 1, and is assigned only when all mandatory examination has been completed. A student who has received a passing grade on a test is not allowed to retake the test in order to receive a higher grade.

Deviations from the syllabus examination form can be made for a student who has a decision on pedagogical support due to disability. Individual adaptation of the examination form shall be considered based on the student's needs. The examination form is adapted within the framework of the expected learning outcomes of the course syllabus. At the request of the student, the course coordinator, in consultation with the examiner, must promptly decide on the adapted examination form. The decision shall then be communicated to the student.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Credit transfer
All students have the right to have their previous education or equivalent, and their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be addressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications.

Other regulations

This course can not be included in a degree together with another course with similar contents. When in doubt, the student should consult the director of study at the department of mathematics and mathematical statistics.

In the event that the syllabus ceases to apply or undergoes major changes, students are guaranteed at least three examinations (including the regular examination opportunity) according to the regulations in the syllabus that the student was originally registered on for a period of a maximum of two years from the time that the previous syllabus ceased to apply or that the course ended.