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Syllabus for

Academic year
TMS086 - Financial time series
Syllabus adopted 2012-02-22 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Five, Four, Three, Not passed
Education cycle: Second-cycle
Major subject: Mathematics

Teaching language: English
Open for exchange students
Block schedule: X

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0101 Project 7,5c Grading: TH   7,5c    

In programs

TKIEK INDUSTRIAL ENGINEERING AND MANAGEMENT - Financial mathematics, Year 3 (elective)


Professor  Holger Rootzén

Course evaluation:

  Go to Course Homepage


For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.

Course specific prerequisites

Good knowledge of calculus and linear algebra, knowledge of basic probability and statistics. Some knowledge of stochastic processes is highly desirable.


Students will gain an understanding of the classical time-series theory and practice with an emphasis on the modeling of financial time series. They will develop an appreciation of the issues, goals and approaches of this theory through being exposed to basic probabilistic models, tools, and statistical estimation methods specific to this field. In the frame of the general time-series set-up they will develop an appreciation of the specific issues related to the analysis and forecasting of financial returns.

Learning outcomes (after completion of the course the student should be able to)

- compute and interpret a sample autocorrelation function
- derive the properties of ARIMA and GARCH models
- choose an appropriate ARIMA/GARCH model for a given set of data and fit the model using an appropriate package
- compute` forecasts for a variety of linear and non-linear methods and models.


This course introduces time-series techniques and their application to the analysis and forecasting of financial time-series. Emphasis is given to nonlinear methods applied to high-frequency financial data. Topics covered include:

Modeling of the marginal distribution of returns
- Modeling the tails (basic Extreme Value Theory)
- Modeling the center

ARIMA models - probabilistic properties and estimation
- Stationary processes
- The autocovariance and the autocorrelation functions
- Basic properties of ARMA processes
- Linear process representation
- Estimation of ARMA processes

ARCH and GARCH processes - theory and practice of volatility modeling
- The ARCH family, definition and relation with ARMA processes
- The tails of Garch processes
- Gaussian quasi-maximum likelihood
- Long memory in volatility, non-stationarities and GARCH
- Multivariate modeling of financial returns.


The theoretical discourse is supplemented by hands-on data analysis.
Familiarity with a statistical software analysis tool (like Matlab, Splus, R) is assumed.


Introduction to Time Series and Forecasting, second edition (2002) P.J. Brockwell and R.A. Davis, Springer-Verlag, New York.
The book is supplemented by hand-outs distributed in class.


Two projects (data analysis), one towards the middle of the period and one at the end (to be done in pairs) together with home assignments (theoretical questions). The home assignments are ABSOLUTELY INDIVIDUAL. No collaboration allowed. Time permitting the course will end with a presentation of the results of the project by each group.

Published: Mon 28 Nov 2016.