Quantile VAR (QVAR)

Definition

Quantile VAR is an extension of the standard VAR model that allows dynamic interactions among variables to vary across quantiles of the distribution. Chavleishvili and Manganelli (2019) proposed factorising the joint quantile distribution into a recursive structure, making it possible to compute multivariate quantile forecasts. QVAR is particularly relevant for stress testing and growth-at-risk exercises, where the tail behaviour of the economy under large shocks is of primary concern.

Why It Matters

Standard VAR models estimate conditional mean relationships, which capture average dynamics but miss how variable interactions change under extreme conditions. During financial crises, correlations and spillovers intensify at the tails of the distribution. QVAR addresses this limitation by modelling the full conditional distribution, providing a more complete picture of systemic risk, tail dependence, and the asymmetric effects of shocks.

Example

A QVAR estimated on Turkish financial data shows that a shock to the US interest rate at the 10th quantile of the distribution has a much larger negative effect on the Turkish lira than the same shock at the median. This asymmetry, invisible to a standard VAR, is crucial for stress-testing scenarios where the central bank evaluates downside risks to the currency under adverse global conditions.

Related Terms

• Vector Autoregression (VAR)
• Cross-Quantilogram
• GARCH
• Connectedness

Software Notes

• SPSS: Not available; requires custom programming or R integration.
• R: No standard package; implement using quantile regression with quantreg::rq() in a recursive structure, or use the QVAR package if available on GitHub.
• Stata: No built-in QVAR; implement using qreg in a recursive system or use R integration. The sqreg command estimates simultaneous quantile regressions.