Time Series: Structural Modelling and Kalman Filter

This lecture covers structural modelling of time series, including trend, cyclical, seasonal, and irregular components, as well as the application of the Kalman Filter for estimation and prediction. It delves into local linear trend models, state space modelling, and the mathematical mechanisms behind these components. The lecture also explores the concepts of weak and strong stationarity, moving average and autoregressive processes, spectral density, and digital filters. Estimation methods such as least squares, Yule-Walker equations, and Box-Jenkins framework are discussed, along with forecasting techniques for AR, MA, and ARMA processes. The lecture concludes with the analysis of ARCH models and the implementation of the Kalman filter in state space models.