Lecture 9 summary · March 12, 2027
Multivariate dynamics and regional networks
Complete chapter · Laboratory ch09 · Practice · All summaries
The economic question
Several outcomes evolve together through a matrix recursion. Stability belongs to the system, and predictive cross-lags do not themselves identify transmission.
Central relation
Individual problem
A has rows 0.5, 0.1 and 0.2, 0.4. With zero intercept and current vector eight, three, find the forecast. Innovation variances are four and one with covariance one; find variance of their sum.
Worked reasoning
The forecast is 4.3 and 2.8. The sum has variance four plus one plus twice one, or seven. Covariance is part of system forecast risk.
A consequential failure
Only diagonal coefficients are checked for stability, or an estimated predictive matrix is presented as a physical network.
Repair
Check spectral radius and covariance propagation. Distinguish a declared teaching graph from estimated reduced-form dependence.