**Course program for 2016:**Can be found

**HERE**. The lectures at DTU will be in building 303b room 026, while the lectures in Sweden will be in MH:362d expect for the last lecture in Sweden that will be held in MH:228.

Exercises and computer exercises can be found HERE. The computer exercises are held in MH:230 between 13-17 (note: attendance is not compulsary!)

## Latest new, 2016

- The slides from lecture 4 can be found here, as well as matlab code, MainFilter.m and StochApproxMain.m
- The slides from lecture 3 can be found here. I also handed out some extra material on SDEs and filtering (please drop by my office for a copy!), as well as distributed some matlab code by email to all course participants.
- 28/9 Henriks slides:
- 21/9 Slides for the second lecture at DTU
- 19/9 Please sign up for the second lecture at DTU
- 7/9 The lectures in Lund will be in MH:362d (previously MH:227) due to the number of students on the course this year. Slides used by Henrik
- Non parametric regression slides
- Smoothing slides
- Time varying coefficients slides
- Identification of functional relation slides
- Lag dependent functions slides
- Polyspectra slides
- Lag Dependent functions: A generalization of some classical time series tools
- Semiparametric Lag Dependent Functions

- 31/8 Here are the slides and presentation used by Erik
- 30/8 The course starts tomorrow! The cars will leave from the parking lot south of the mathematics building (MH in the map) at 08:30 (sharp!). Please be there no later than 08.15.

Please remember to bring passport or national id (such as drivers licence)!
- 15/8 Please sign up for the first lecture at DTU using the doodle.

**COURSE DESCRIPTION**

**Department:** Division of Mathematical Statistics at the Centre for Mathematical Sciences, Lund Institute of Technology together with Informatics and Mathematical Modelling (IMM), Technical University of Denmark, Lyngby.

**Credits:** 7.5 ECTS credits.

**Lecturers:** Erik Lindström, phone: +46 46 222 45 78, email: erikl@maths.lth.se

Henrik Madsen, phone: +45 45 253408, email: hm@imm.dtu.dk

**Prerequisites:** Mathematical Statistics, basic course. Furthermore, it
is recommendable to have taken a course on Stationary Processes, and
necessary to have taken a basic course in Time Series Analysis, e.g. FMS051
Time Series Analysis / Tidsserieanalys in Lund or 02417 Time Series Analysis in Lyngby.

**Course program: ** Can be found **HERE**.

## A short description of the contents of the course:

The graduate course in Advanced Time Series Analysis has its target audience amongst students with technical or natural science background and with adequate basic knowledge in mathematical statistics. The primary goal to give a thorough knowledge on modeling dynamic systems. A special attention is paid to non-linear and non-stationary systems, and the use of stochastic differential equations for modeling physical systems. In more detail:

- Non-linear time series models; Generalized transfer functions
- Kernel estimators and time series analysis
- Non-parametric models and modeling techniques
- Identification of non-linear models, cumulants and polyspectra
- Parameter estimation in non-linear models, Case study
- State space models and state filtering
- Stochastic differential equations (SDEs), Ito calculus, Exact and approximate filters
- Estimation of linear and (some) non-linear SDEs
- Modelling using SDEs
- Methods for tracking parameters in non-stationary time series.
- Experimental design for dynamic system identification.
- Prediction in non-linear models

### Literature:

H. Madsen, J. Holst & E. Lindstrom (2010):*Modelling Non-Linear and Non-Stationary Time Series*This is being distributed during the first lecture in Denmark.

**Exercises during the lectures:**In the afternoon during the lecture days, one hour will be used for you working with small exercises to be solved without computer. These exercises will be delivered during the lecture days.

**Computer exercises:**During the course the computer exercises will be delivered in connection with the lectures. They are also downloadable from the course homepage.

The computer exercises will in Lund be guided by Erik Lindström, phone: +46 46 2224578.