How does VECM handle cointegrated time series?

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AcadiFi · Accepted Answer

A Vector Error Correction Model (VECM) is a restricted VAR designed for cointegrated non-stationary series. Cointegration means a linear combination of I(1) series is stationary, implying a long-run equilibrium. VECM represents short-run dynamics around this equilibrium by including an error correction term. Two-variable example: Δyt = α(yt-1 - β xt-1) + Σγi Δyt-i + Σδi Δxt-i + et. The term (yt-1 - β xt-1) is the cointegration residual—deviation from long-run equilibrium. Coefficient α measures adjustment speed: negative α means yt corrects toward equilibrium. If α = -0.3, yt closes 30% of last period's disequilibrium each period. ```mermaid flowchart TB A[Two I1 Series] --> B[Johansen Test
cointegration rank] B --> C[Estimate VECM] C --> D[Short-run Dynamics] C --> E[Error Correction
long-run pull] ``` Johansen's trace and maximum eigenvalue tests determine the number of cointegrating vectors r. With k variables, r can be 0 to k-1. Interpretation varies: r = 0 means no cointegration (use VAR in differences); r = k-1 means near-stationary system. Financial applications include PPP tests for exchange rates, spread trading on cointegrated stock pairs, and term-structure models where short and long rates share common stochastic trends. VECM forecasts incorporate both short-run correlations and the gravitational pull of long-run equilibrium, typically outperforming pure difference VARs for cointegrated systems.

How does VECM handle cointegrated time series?

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