Single-Course English 5 ECTS

# Time Series Analysis

## Overall Course Objectives

To give a thorough introduction to time series analysis with a focus on applications relevant to engineering science and for modelling of physical systems. A special attention is put on methods for model formulation and estimation. A main goal is to form the theoretical background for applications within forecasting, automatic and adaptive control, image analysis, econometrics and technometrics.

Learning Objectives

• Apply methods for building stochastic dynamic models
• Understand the relation between dynamic systems and stochastic processes
• Knowlegde about linear stochastics process models (ARMA; ARX; Box-Jenkins; GLM; OE; ARIMA; Seasonal models; etc.)
• Apply and calculate correlation functions
• Apply time domain and frequency domain descriptions
• Predictions in time series
• Formulate state space descriptions
• Understand and implement the Kalman filter
• Apply regression based methods for time series
• Optimize prediction functions and model based control
• Document and present results in a written report
• Give constructive feedback to others reports

Course Content

Linear stochastic processes. Conditional expectations with applications. Characterisation of stochastic processes. Second order analysis. Description in time and frequency domain. Correlation functions and their applications. Model formulation. Non-stationary processes. Time series with periodic variations and trends. Identification, estimation and verification of models for stochastic processes. Box-Jenkins method. Spectral analysis. Bivariate and multivariate time series analysis. Transfer functions with stochastic models. State space formulation, prediction and reconstruction. Kalman filter. Time series with missing observations. Methods for recursive estimation. Adaption methods. Introduction to non-linear stochastic processes.
A number of examples of real life applications will be used for illustrating the methods. Likewise some of the assignments will be focused on application areas, e.g. development of medicine or modelling of sewage systems.

Recommended prerequisites

02402/02403/02631/02525, An elementary course in statistics and an introductory course in programming.

Teaching Method

Lectures and excercises.

Faculty

Remarks

The course provides a good background for a number of activities such as signal processing, modelling, forecasting, process control, dynamic simulation, optimal decision making, automatic control and system identification.

See course in the course database.

## Registration

Language English 13 weeks Compute DTU Lyngby Campus 02417 Candidate Week 5 Week 19 Fri 8-12
Price 7.500,00 DKK