**Course program for 2019:**can be found

**HERE**.

**Exercises and computer exercises**can be found HERE.

**All lectures in Lund can be found here.**

The course starts September 4th (full day of lectures) in Denmark. The department will rent a number of cars/minibuses for our transportation (we need drivers!). The cars will leave from Lund at around 8:30 (sharp), and be back around 17:30. The cars will leave from the parking lot south of the mathematics building (MH in the map).

## Latest new, 2019

- 2/12 Lecture at DTU
- The slides from lecture 4 can be found here.
- On Remarks on Iterated Filtering
- Paper on time varying parameters in finance
- Matlab code MainFilter.m, StochApproxMain.m and FilteringStateEstimation.m

- 25/11 Doodle for the lecture at DTU on Wednesday
- 13/11 Slides for the lecture in Lund
- Grey Box modelling
- SDE state dependent diffusions

- 6/11 Slides for the lecture at DTU.
- Introduction to Stochastic calculus
- Classic introduction to Sequential Monte Carlo from SMC in Practice, 2001
- More recent overview on SMC from Statistical Science, 2015

- 3/11 Doodle for the third lecture at DTU. Please make sure that you have responded before noon on Tuesday.
- 3/11 Slides from the lecture in Lund
- 27/9 Matlab code used for lecture 2 at DTU
- 24/9 Slides for the second lecture at DTU (updated to latest version) , Semiparametric Lag Dependent Functions
- 23/9 Doodle for the second lecture
- 23/9 Slides from the lecture in Lund: Lag Dependent functions: A generalization of some classical time series tools
- 10/9 The lecture in Lund on September 11th will be in MH:228 between 10-12 and MH:362A between 13-16
- 4/9 The slides from lecture 1 can be found here, presentation used by Erik
- 30/8 The doodle for the first lecture in Denmark is online, please sign up here. Please indicate if you can drive when signing up, as we may need two cars/minibusses to go to DTU.

**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 Lindstr�m, 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 Lindstr�m, phone: +46 46 2224578.