Advanced✓ Mathematical
◆ The PatternMultiple series forecasting each other
Vector Autoregression (VAR) generalises AR to multiple interrelated series. Each variable is modeled as a linear function of all variables’ lags. Granger causality tests whether one series helps predict another. Impulse response functions show how shocks propagate.
Yt = c + A1Yt−1 + A2Yt−2 + … + ApYt−p + εt
Y is a vector of all variables. Each A is a coefficient matrix capturing cross-series dependencies at that lag.
// Interactive — VAR impulse response
# Python — VAR from statsmodels.tsa.api import VAR model = VAR(df[['gdp', 'inflation', 'unemployment']]) results = model.fit(maxlags=4, ic='aic') # Granger causality test results.test_causality('gdp', ['inflation'], kind='f') # Impulse response irf = results.irf(20) irf.plot()
Pattern bridge: VAR captures how variables influence each other — the same idea as correlation matrices but with temporal structure. In markets, cross-asset correlations and intermarket analysis are VAR in practice.