Time Series Analysis

• 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

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.

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

Lectures and excercises.

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.