Course syllabus

Matematisk statistik, tidsserieanalys
Mathematical Statistics, Time Series Analysis

FMSN45, 7,5 credits, A (Second Cycle)

Valid for: 2023/24
Faculty: Faculty of Engineering, LTH
Decided by: PLED I
Date of Decision: 2023-04-14

General Information

Elective for: BME4-sbh, C4, D4-ssr, E4-ss, F4, F4-bg, F4-bm, F4-fm, F4-r, F4-ss, F4-mai, I4-fir, Pi4-fm, Pi4-ssr, Pi4-biek, Pi4-bam, MMSR2, R4
Language of instruction: The course will be given in English


Practical and theoretical knowledge in modelling, estimation, validation, prediction, and interpolation of time discrete dynamical stochastic systems, mainly linear systems. The course also gives a basis for further studies of time series systems, e.g. Financial statistics and Non-linear systems.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must


Time series analysis concerns the mathematical modelling of time varying phenomena, e.g., ocean waves, water levels in lakes and rivers, demand for electrical power, radar signals, muscular reactions, ECG-signals, or option prices at the stock market. The structure of the model is chosen both with regard to the physical knowledge of the process, as well as using observed data. Central problems are the properties of different models and their prediction ability, estimation of the model parameters, and the model's ability to accurately describe the data. Consideration must be given to both the need for fast calculations and to the presence of measurement errors. The course gives a comprehensive presentation of stochastic models and methods in time series analysis. Time series problems appear in many subjects and knowledge from the course is used in, i.a., automatic control, signal processing, and econometrics.

Further studies of ARMA-processes. Non-stationary models, slowly decreasing dependence. Transformations. Optimal prediction and reconstruction of processes. State representation, principle of orthogonality, and Kalman filtering. Parameter estimation: Least squares and Maximum likelihood methods as well as recursive and adaptive variants. Non-parametric methods,covariance estimation, spectral estimation. An orientation on robust methods and detection of outliers.

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written and oral project presentation, and compulsory computer exercises. The final grade is based on the project with bonus assignments for higher grade.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Code: 0120. Name: Computer Work 1.
Credits: 0,5. Grading scale: UG. Assessment: Computer exercise 1
Code: 0220. Name: Computer Work 2.
Credits: 0,5. Grading scale: UG. Assessment: Computer exercise 2 och 3
Code: 0320. Name: Project Work and Home Exam.
Credits: 6,5. Grading scale: TH. Assessment: Written and oral project report for passing grade; written take-home exam for higher grades.


Admission requirements:

Assumed prior knowledge: FMSF10 Stationary Stochastic Processes.
The number of participants is limited to: No
The course overlaps following course/s: FMS051, MASM17

Reading list

Contact and other information

Director of studies: Johan Lindström,
Course administrator: Susann Nordqvist,
Course homepage:
Further information: The course is also given at the faculty of science with the code MASM17.