We model the dynamics of volatilities and correlations of exchange rate returns using a set of specifications based on the DCC model (Engle, 2002). The DCC model offers an attractive multivariate framework for the study of correlation timing because it has the following advantages: (i) it is tractable and parsimonious with a low dimension of parameters; (ii) it is flexible and can be generalized to account for asymmetric correlations while ensuring that correlations are in the range; (iii) it provides for a positive-definite covariance matrix; and (iv) it is straightforward to implement even when the number of assets is large.
In order to assess the economic value of volatility and correlation timing, we estimate a set of multivariate models for dynamic correlations (such as the DCC model), each under a set of univariate specifications for dynamic volatility (such as the GARCH model). In the following discussion, we describe the complete set of models we estimate.
Let yt = (y1, t, … , yN, t)′ denote the N × 1 vector of nominal log-exchange rate returns at time t:
where μ = (μ1, … , μN)′ is the N × 1 vector of unconditional means, Σt is the N × N conditional covariance matrix, and ε t = ( ...