Quantitative Econometric Modeling in Macroeconomics

Quantitative Econometric Modeling

This research paper explores advanced time-series estimation models. The ordinary least-squares estimate, β̂, minimizes the sum of squared residuals. Here, X is the design matrix and Y is the vector of observed outcomes; the inverse exists only when XᵀX is nonsingular.

$\hat{\beta} = (X^T X)^{-1} X^T Y$ In words, the estimate projects the observed outcomes onto the column space of X.