The dynamic conditional correlation (DCC) method is an example of a model-based multivariate volatility method that is popular in finance and recently introduced in neuroimaging. This method provides a way to estimate conditional correlations between time series.
Time-varying correlations are usually estimated with multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models that are linear in terms of the squares and cross products of the data. A new class of multivariate models, called dynamic conditional correlation models, has been proposed. They have the flexibility of univariate GARCH models combined with parsimonious parametric models for correlations. They are nonlinear but can be estimated very simply by univariate or two-step methods, usually based on a likelihood function. They have been shown to perform well in a variety of situations and provide reasonable empirical results.
Dynamic bivariate correlation, or dynamic correlation for short, is the correlation between a pair of time-varying time series. Assessing dynamic correlation is important in many areas of neuroscience. Estimating dynamic correlation is of interest in neuroimaging because many studies have identified dynamic changes in functional connectivity during functional magnetic resonance imaging testing, particularly at rest. Estimating dynamic correlation is also of interest in neurophysiology. For example, dynamic correlation between local field potential time series obtained from different brain regions can be used to explore how specific brain regions work together during certain specific behaviors. When identifying such changes, it is important to ensure that dynamic shifts in observed correlations are not due to spurious fluctuations specific to the estimation method used.
The two approaches currently available for dynamic correlation estimation in the neuroscience literature are the sliding window method and dynamic conditional correlation:
Although dynamic conditional correlation has many desirable properties compared to the sliding window method, it has certain limitations.
Time series measurements appearing in the neuroscience literature occasionally have a few outliers, as seen in local field potential time series data. Such values can be ignored if they are simply anomalies that are not compatible with the underlying scientific framework. The performance of the dynamic conditional correlation method appears to be not robust in the presence of outliers. Another limitation of this method concerns its practical application using numerical algorithms.
Today, besides the sliding window method and the dynamic conditional correlation method, there is a third method for estimating dynamic correlation, which is based on the weighted graph algorithm.
Essentially, correlation analysis is a statistical method that defines the relationship between variables and provides information about the direction and degree of this relationship. The correlation coefficient is a value that shows the strength of the relationship between the dependent variable and the independent variables. This value provides information about the direction of the variables and how the interactions are.
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