Are Correlations Constant? Empirical and Theoretical Results on Popular Correlation Models in Finance

Multivariate GARCH models have been designed as an extension of their univariate counterparts. Such a view is appealing from a modeling perspective but imposes correlation dynamics that are similar to time-varying volatility. In this paper, we argue that correlations are quite different in nature. We demonstrate that the highly unstable and erratic behavior that is typically observed for the correlation among financial assets is to a large extent a statistical artefact. We provide evidence that spurious correlation dynamics occur in response to financial events that are sufficiently large to cause a structural break in the time-series of correlations. A measure for the autocovariance structure of conditional correlations allows us to formally demonstrate that the volatility and the persistence of daily correlations are not primarily driven by financial news but by the level of the underlying true correlation. Our results indicate that a rolling-window sample correlation is often a better choice for empirical applications in finance.