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Handbook of Exchange Rates by Lucio Sarno, Ian Marsh, Jessica James

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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 images 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 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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