To learn the basics of time series analysis.
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) using the IV method.
- Do practical time series analysis, including choice of model, model order and analysis of residuals
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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.
The course relies on techniques from stochastic processes, and statistics.
The following items will be discussed in the course: stochastic processes, estimators, non-parametric time series analysis, estimation of ARMA models. In addition to classical topics in time series analysis, popular time series models that have been found to be effective at modeling non-linear behavior of time series data will be introduced.
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