A test of non-constant correlation based on Engle and Sheppard (2001).

```
DCCtest(Data, garchOrder = c(1,1), n.lags = 1, solver = "solnp",
solver.control = list(), cluster = NULL, Z = NULL)
```

Data

A multivariate data matrix.

garchOrder

The first stage common GARCH order.

n.lags

The number of lags to test for the presence of non-constant correlation.

solver

Either “solnp” or “nlminb” .

solver.control

Control arguments list passed to optimizer.

cluster

A cluster object created by calling `makeCluster`

from
the parallel package. If it is not NULL, then this will be used for parallel
estimation (remember to stop the cluster on completion).

Z

(Optional) The standardized residuals from a constant correlation model. If supplied the model is not estimated since this is the only input the test requires.

A list with the proposed Null hypothesis (H0), the test statistic and its p-value.

The test effectively equates to estimating a multivariate dataset using the Constant Conditional Correlation (CCC) model of Bollerslev (1990) and after which the standardized residuals (standardized by the symmetric square root decomposition of the estimated constant correlation matrix) should be i.i.d. with covariance the identity matrix. Testing for this can be done using a series of artificial regressions on the outer and lagged product of these residuals and a constant. In the rmgarch package, the CCC model is calculated using a static GARCH copula (Normal) model.

Bollerslev, T. 1990, Modelling the coherence in short-run nominal exchange
rates: a multivariate generalized ARCH model, *The Review of Economics and
Statistics*, **72(3)**, 498--505.
Engle, R.F. and Sheppard, K. 2001, Theoretical and empirical properties of
dynamic conditional correlation multivariate GARCH, *NBER Working Paper*.