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# 15.2 Dynamic Models for Volatility and Correlation

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.

## 15.2.1 The Set of Multivariate Models

Let yt = (y1, t, … , yN, t) denote the N × 1 vector of nominal log-exchange rate returns at time t:

15.1 where μ = (μ1, … , μN) is the N × 1 vector of unconditional means, Σt is the N × N conditional covariance matrix, and ε t = ( ...

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