Course syllabus

# Olinjära tidsserier Non-Linear Time Series Analysis

## FMS110, 7,5 credits, A (Second Cycle)

Valid for: 2012/13
Decided by: Education Board 1
Date of Decision: 2012-03-27

## General Information

Elective for: D5, F5, F5-ssr, F5-bm, Pi5
Language of instruction: The course will be given in English on demand

## Aim

The course builds on the acknowledgement that a large part of the technical and non-technical systems one encounters as a Master of Engineering contains non-linearities or non-stationary events, that reflects fundamental properties in the studied system. When describing such a system and then using the description for, e.g. prediction or adjustment, it is therefore necessary that the model also describes the non-linear and non-stationary parts of the system. Hence, the course aim is to give fundamental knowledge in modelling of non-linear and non-stationary dynamic, stochastic systems, as well as in the use of stochastic differential equations for modelling physical systems.

## Learning outcomes

Knowledge and understanding
For a passing grade the student must

• be able to explain qualitative differences between linear and non-linear models,
• be able to distinguish between the properties of parametric and non-parametric models,
• understand stochastic filtering of latent processes using Kalman filters and particle filters,
• be able to apply methods useful when data is non-stationary.

Competences and skills
For a passing grade the student must

• be able to determine whether data needs to be modelled using a non-linear model,
• be able to fit a suitable model to data using different methods,
• be able to solve all the parts of a modelling problem using scientific, technical and statistical theory (from this course and other courses) where the solution includes model specification, inference and model choice,
• present the solution in a technical report.

Judgement and approach
For a passing grade the student must

• be able to utilise scientific articles within the field and related fields.

## Contents

Different types of non-linear time series models. Non-parametric estimates of non-linearities, i.a. using kernel estimates. Identification of model structure using parametric and non-parametric methods, parameter estimation. State models for non-linear systems, filtering. Prediction in non-linear systems. Modelling using non-linear stochastic differential equations. Recursive methods for parameter estimation in non-stationary time series. Design of experiments for identification of dynamic systems.

## Examination details

Assessment: Written and oral project presentation and compulsory presence at the computer exercises. The course grade is based on the project grade. The project can be presented at one of two presentation seminars.

• FMS045 Stationary Stochastic Processes or FMSF10 Stationary Stochastic Processes
• 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 FMSF01 Mathematical Statistics

Required prior knowledge: FMS051 Time Series Analysis.
The number of participants is limited to: No
The course might be cancelled: If the number of applicants is less than 16.
The course overlaps following course/s: MAS222, MASM12