General Linear Processes: Understanding Stationarity and Invertibility

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Time Series: Structural Modelling and Kalman Filter

Covers structural modelling, Kalman Filter, stationarity, estimation methods, forecasting, and ARCH models in time series.

Vector Autoregression: Modeling Vector-Valued Time Series

Explores Vector Autoregression for modeling vector-valued time series, covering stability, reverse characteristic polynomials, Yule-Walker equations, and autocorrelations.

Linear Algebra: Inverse Matrix and Systems Resolution

Covers the concept of inverse matrices and systems resolution, including the conditions for matrix invertibility and the Gauss-Jordan algorithm.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

QR Factorization: Least Squares System Resolution

Covers the QR factorization method applied to solving a system of linear equations in the least squares sense.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Diagonalization of Matrices: Theory and Examples

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

Homogeneous Solutions: Linear Independence

Explores finding particular solutions for homogeneous differential equations, emphasizing linear independence and variation of constants.

Forecasting & Long Memory: Time Series

Explores forecasting methods and long memory in time series analysis.