Course syllabus

Matematisk statistik, tidsserieanalys
Mathematical Statistics, Time Series Analysis

FMS051, 7,5 credits, A (Second Cycle)

Valid for: 2016/17
Decided by: Education Board B
Date of Decision: 2016-03-28

General Information

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

Aim

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

• be able to construct a model based on data for a concrete practical time series problem,
• be able to perform simple transformations of a non-stationary time series into a stationary time series,
• be able to predict and interpolate in linear time series models,
• be able to estimate parameters in linear time series models and validate a resulting model,
• be able to construct a Kalman-filter based on a linear state model,
• be able to estimate in time varying stochastic systems using recursive and adaptive techniques.

Competences and skills
For a passing grade the student must

• be able to present the analysis of a practical problem in a written report and present it orally.

Contents

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
Assessment: Written and oral project presentation with home exam, and compulsory computer exercises. The final grade is based on the project and the take-home exam.

Parts
Code: 0115. Name: Examination.
Credits: 2. Grading scale: UG. Assessment: Written take-home examination
Code: 0215. Name: Project Work.
Credits: 4,5. Grading scale: UG. Assessment: Written and oral project report
Code: 0315. Name: Computer Work 1.
Credits: 0,5. Grading scale: UG. Assessment: Computer exercise 1
Code: 0415. Name: Computer Work 2.
Credits: 0,5. Grading scale: UG. Assessment: Computer exercise 2 och 3

Admission

Admission requirements:

• FMS012 Mathematical Statistics, Basic Course or FMS032 Mathematical Statistics, Basic Course or FMS035 Mathematical Statistics, Basic Course or FMS086 Mathematical Statistics or FMS140 Mathematical Statistics, Basic Course or FMSF10 Stationary Stochastic Processes or FMSF20 Mathematical Statistics, Basic Course

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

Reading list

• Andreas Jakobsson: An Introduction to Time Series Modeling. Studentlitteratur, 2013, ISBN: 9789144083742.

Contact and other information

Director of studies: Studierektor Anna Lindgren, studierektor@matstat.lu.se
Course homepage: http://www.maths.lth.se/matstat/kurser/fms051/
Further information: The course is also given at the faculty of science with the code MASM17.