Dynamic conditional correlation (DCC) is a multivariate GARCH model that estimates time-varying correlations in two steps: univariate GARCH volatilities first, then a correlation process. Engle set it out in Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models (2002). Engle (2002) simulated 200 replications of 1000 daily observations for each of 6 correlation processes and compared eight estimators. The mean reverting DCC model had the smallest mean absolute error in four of the six cases.
What the Study Found
Summed over all six simulated processes, the mean reverting DCC (DCC LL MR) had the lowest mean absolute error. Integrated DCC by log likelihood and scalar BEKK finished a very close second and third. On the test for remaining autocorrelation in the squared second standardized residual, DCC LL MR was best in three out of six cases. For an equal weighted portfolio, integrated DCC produced the fewest Value at Risk test rejections in five out of six cases. In a long-short portfolio, Diagonal BEKK was best for 3 out of 6 processes and DCC LL MR for two.
"The comparison of DCC with simple multivariate GARCH and several other estimators shows that the DCC is often the most accurate."
Engle (2002), Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models, Section VIII.
Methodology
Each of 6 correlation processes was simulated 200 times for 1000 observations from a bivariate Gaussian GARCH process, approximately 4 years of daily data. Estimators were ranked by mean absolute error and by an F test on 5 lags of squared standardized residuals. A Dynamic Quantile Test with 5 lags checked Value at Risk accuracy. Empirical data sets of 1400 to 2600 daily observations covered the Dow Jones, NASDAQ, 30-year bond yields and European currencies.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| DCC model | H_t = D_t R_t D_t | D_t holds univariate GARCH volatilities; R_t is the time-varying correlation matrix |
| Mean reverting DCC | Q_t = (1 − α − β)S + α(ε_{t−1}ε′{t−1}) + βQ{t−1} | S is the unconditional correlation matrix; mean reverting when α + β < 1 |
| NASDAQ–Dow Jones DCC parameters | α = 0.039029, β = 0.941958 | Mean reverting model, Appendix 1 |
| Dow Jones–NASDAQ correlation | Between .6 and .9 | Most of the decade ending March 2000; dropped below .4 in 1993 and in March 2000 |
| Stock–bond correlation | Generally positive, in the range of .4 | Highly negative in summer 1998; about zero at the end of the sample |
| Empirical rejections at 5% level | 10 to 21 per model | Out of 28 possibilities; MA100 worst on every test and data set |
DCC LL MR vs Scalar BEKK
Mean absolute error and test rejection rates from the same 200-replication Monte Carlo experiments.
| Measure | DCC LL MR | Scalar BEKK |
|---|---|---|
| MAE, sine correlation | 0.1381 | 0.1422 |
| MAE, step correlation | 0.0709 | 0.0859 |
| MAE, constant correlation | 0.0070 | 0.0273 |
| Second-residual ARCH rejection rate, constant correlation | 0.0788 | 0.9800 |
| Second-residual ARCH rejection rate, sine correlation | 0.1400 | 0.5930 |
Why This Matters
Conventional multivariate GARCH needs more parameters with every asset added, which is why few earlier applications went beyond a handful of series. DCC keeps the correlation step's parameter count fixed regardless of how many assets enter. Risk desks can therefore reuse the univariate volatility forecasts they already run. Hedge ratios, portfolio VaR and asset allocation all depend on correlations that change over time, so a tractable dynamic estimator feeds directly into them.