To learn the basics of time series analysis and system identification theory.
Afterwards one is able to:
• Determine if a stochastic system is stable, invertible and/or wide-sense stationary.
• Determine covariance function and spectral density of such a system.
• Determine the maximum likelihood estimator and determine if an estimator is unbiased, efficient and/or consistent.
• Find the dynamics of the m-step ahead predictor.
• Calculate the expected value and the variance of independent stochastic variables and understand the multivariate normal distribution.
• Analyze the quality of estimates of AR(X), MA, ARMA(X) and of systems identified using the IV method.
• Do practical time series analysis, including choice of model, model order and analysis of residuals
• Do practical system identification including choice of input
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Time series analysis deals with the analysis of measured or observed data that evolve with time. For instance water heights, the Dow Jones index and population growth. Based on the data, a mathematical model is made of the underlying mechanisms. This model serves to explain the time series and may be used for prediction of the time series.
An application of TSA is system identification. In System Identification the aim is to find a model of a system on the basis of recorded input-output data. The course relies on techniques from stochastic processes, statistics and system theory.
The following items will be discussed in the course: stochastic processes, estimators, non-parametric time series analysis, estimation of ARMA models and system identification.
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