DCC-GARCH Deep Dive

Dynamic Conditional Correlation captures time-varying co-movement between two assets. The correlation ρ₁₂(t) itself follows a GARCH-like updating rule driven by standardised residuals.

DCC stationary

Yes ✓

Mean ρ₁₂

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Min ρ₁₂

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Max ρ₁₂

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Dynamic Correlation ρ₁₂(t) — coloured by correlation level

Bivariate Return Scatter — coloured by |ρ₁₂|

Individual Conditional Volatilities

α₁ (ARCH asset 1)0.05

β₁ (GARCH asset 1)0.90

α₂ (ARCH asset 2)0.08

β₂ (GARCH asset 2)0.87

a (DCC ARCH)0.04

b (DCC GARCH)0.93

ρ̄ (long-run corr.)0.50

Observations1000

Seed7

Step 1: σ_{i, t}^{2} = ω_{i} + α_{i} ε_{i, t - 1}^{2} + β_{i} σ_{i, t - 1}^{2}; z_{i, t} = ε_{i, t} / σ_{i, t}

Step 2 (DCC): Q_{t} = (1 - a - b) \overset{ˉ}{Q} + a z_{t - 1} z_{t - 1}^{⊤} + b Q_{t - 1}

ρ_{12, t} = Q_{12, t} / Q_{11, t} Q_{22, t}

High a → correlation reacts quickly to joint shocks. High b → correlation is persistent. Reduce ρ̄ to model assets that are normally uncorrelated but occasionally spike together (contagion).

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