Vector Autoregression

This lecture on Vector Autoregression covers the modeling of vector-valued time series using autoregressive processes. Starting from AR processes, the instructor explains the generalization to vector-valued processes and the concept of Vector Auto-Regression. The lecture delves into the stationarity of VAR models, including the conditions for stability. Examples of VAR(1) processes are provided to illustrate stability analysis. The lecture also discusses the Yule-Walker equations for VAR processes and the computation of auto-covariance matrices. Additionally, the lecture explores the recursive computation of auto-covariance matrices and the spectral representation of multivariate time series. The summary includes an overview of stationarity, linear processes, spectral decomposition, forecasting methods, financial time series models, and Kalman filtering.