Overview — Multivariate Time Series: VAR and Structural Analysis

A portfolio manager rarely needs a forecast for one series in isolation. The relevant question is whether an inflation surprise, curve move, credit-spread change, or equity return propagates through the rest of a book. A vector autoregression (VAR) makes every included series depend on the joint history of the system, then turns the fitted dynamics into forecasts, predictive-content tests, and shock traces. This topic moves from the reduced-form VAR, through Granger tests and impulse responses, to the restrictions required before an innovation can be read as an economic shock.

By the end of this note you should be able to:

• specify a stable reduced-form VAR and choose its lag order without ignoring parameter proliferation;
• distinguish Granger predictability from economic or structural causation;
• read an impulse response and a forecast-error variance decomposition while treating the innovation ordering as an identifying assumption;
• explain why a cointegrated system is represented by a vector error-correction model (VECM), rather than a VAR in unrestricted differences;
• distinguish a reduced-form VAR, an SVAR, and a VECM by the question each is designed to answer.

1. Contents
2. The big picture