A desk forecasting rates, equity returns, and inflation separately can miss the delayed links between them. A vector autoregression (VAR) extends the ARMA representation to a system: every variable has an equation, and every equation uses the lagged history of every variable. The price of this flexibility is a rapidly expanding parameter count. This note builds the reduced-form VAR, explains why separate OLS is valid, and selects a common lag length before the next lesson asks what the fitted system says about predictive content and shocks.
Learning objectives. By the end of this note you should be able to:
- write a reduced-form VAR() in scalar and matrix form;
- explain why all equations can be estimated separately by OLS;
- count the parameters that a VAR introduces and recognise the resulting degrees-of-freedom risk;
- select a common VAR lag order using multivariate AIC, BIC, or HQIC;
- distinguish a stationary VAR in levels from a VAR fitted to transformations selected after unit-root analysis.
In this lesson
- The reduced-form system
- Why equation-by-equation OLS works
- Lag length is a portfolio of parameters
Before you start
- AR, MA, and ARMA Models: Representation and the Wold Decomposition
- Box–Jenkins Methodology: Identification, Estimation, and Diagnostic Checking
The full lesson, with worked examples and exercise solutions, is for members.
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