Mathematical Statistics, Time Series Analysis
Matematisk statistik, tidsserieanalys

FMSN45F, 7.5 högskolepoäng

Gäller från och med: Autumn 2020
Beslutad av: Professor Thomas Johansson
Datum för fastställande: 2020-05-19

Allmänna uppgifter

Avdelning: Mathematical Statistics
Kurstyp: Gemensam kurs, avancerad nivå och forskarnivå
Kursen ges även på avancerad nivå med kurskod: FMSN45
Undervisningsspråk: English

Syfte

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.

Mål

Kunskap och förståelse

För godkänd kurs skall doktoranden

• 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.

Färdighet och förmåga

För godkänd kurs skall doktoranden be able to present the analysis of a practical problem in a written report and present it orally.

Kursinnehåll

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.

Kurslitteratur

Jakobsson, A.: An Introduction to Time Series Modeling. Studentlitteratur, 2019.

Kursens undervisningsformer

Undervisningsformer: Föreläsningar, laborationer, övningar

Kursens examination

Examinationsformer: Skriftlig tentamen, skriftlig rapport, seminarieföredrag av deltagarna
Betygsskala: Underkänd, godkänd
Examinator:

Antagningsuppgifter

Förutsatta förkunskaper: FMSF10 Stationary Stochastic Processes.

Kurstillfällesinformation

Kontaktinformation och övrigt

Kursansvarig: Andreas Jakobsson <andreas.jakobsson@matstat.lu.se>
Hemsida: www.maths.lth.se/matstat/kurser/fmsn45/