Syllabus academic year 2011/2012
(Created 2011-09-01.)
MATHEMATICAL STATISTICS, TIME SERIES ANALYSISFMS051
Credits: 7,5. Grading scale: TH. Cycle: A (Second Cycle). Main field: Technology. Language of instruction: The course might be given in English. FMS051 overlaps following cours/es: MAS216 and MASM17. Optional for: C4, C4ssr, D4, D4ssr, E4, E4pe, E4ssr, F4, F4bm, F4fm, F4ssr, I4, Pi4, Pi4bm, Pi4fm, Pi4mrk, Pi4ssr. Course coordinator: Director of studies, Anna Lindgren, studierektor@matstat.lu.se, Mathematical Statistics. Recommended prerequisits: FMS045/FMSF10 Stationary Stochastic Processes. The course might be cancelled if the number of applicants is less than 16. Assessment: Written and oral project presentation and home exam. Further information: The course is also given at the faculty of science with the code MASM17. Home page: http://www.maths.lth.se/matstat/kurser/fms051/.

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.

Knowledge and understanding
For a passing grade the student must

Skills and abilities
For a passing grade the student must

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.

Literature
Madsen, H.: Time Series Analysis. Chapman & Hall (CRC texts in Statistical Sciences Series) 2007. ISBN 987-1-4200-5967-0