Basics of linear algebra and matrix calculus .
Basic computer Programming
Stationary Processes and Time Series. Stationary Process, White Process, MA Process, AR Process, ARMA Process, Spectrum of a Stationary Process, Spectrum Process and Diagrams, Maximum Frequency in Discrete Time, White Noise Spectrum, Complex Spectrum, ARMA Model, Ruzicka Stability Criterion, Variance of an ARMA Process, Fundamental Theorem of Spectral Analysis, Spectrum Drawing, Representations of a Stationary Process .
Estimation of Process Characteristics. General Properties of the Covariance Function. Covariance Function of ARMA Processes. Estimation of the Mean. Estimation of the Covariance Function. Estimation of the Spectrum. Whiteness Test.
Prediction. A fake Predictor. Practical Determination of the Fake Predictor. Spectral Factorization. Whitening Filter. Optimal Predictor from Data. Prediction of an ARMA Process. ARMAX Process. Prediction of an ARMAX Process.
Model Identification. The Identification Problem. A General Identification Problem. Static and Dynamic Modeling . External Representation Models. Box and Jenkins Model. ARX and AR Models. ARMAX and ARMA Models. Multivariable Models. Internal Representation Models. The model Identification Process. The Predictive Approach. ARX and AR Model. ARMAX and ARMA models.
Identification of Input-Output Models. Estimating AR and ARX Models. The Least Squares Method. Identifiability. Estimating ARMA and ARMAX Models. Estimating the Uncertainty in Parameter Estimation. Recursive Identification . Recursive Least Squares . Extended Least Squares. Robustness of Identification Methods. Prediction Error and Model Error. Frequency Domain Interpretation.
Subjects | Text References | |
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1 | Stationary Processes and Time Series. | Model Identification and Data Analysis - Chapter 1 |
2 | Estimation of Process Characteristics | Model Identification and Data Analysis - Chapter 2 |
3 | Prediction | Model Identification and Data Analysis - Chapter 3 |
4 | Model Identification | Model Identification and Data Analysis - Chapter 4 |
5 | Heteroskedasticity: structure and identification of ARCH and GARCH models | Time series - Application to finance with R and S-Plus -Chapter 9 |
6 | Multivariate Time Series | Time series - Application to finance with R and S-Plus Chapter 10 |