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Anticipating correlations : a new paradigm for risk by Robert Engle

By Robert Engle

Monetary markets reply to details almost right away. every one new piece of knowledge impacts the costs of resources and their correlations with one another, and because the process swiftly alterations, so too do correlation forecasts. This fast-evolving surroundings offers econometricians with the problem of forecasting dynamic correlations, that are crucial inputs to threat size, portfolio allocation, Read more...

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Anticipating correlations : a new paradigm for risk management

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For example, asymmetric volatility models such as TARCH, EGARCH, and PARCH can be used when the data warrant. Nonstationary models such as the Spline GARCH of Engle and Rangel (2008) or the filtering methods of Nelson and Foster (1994) can be used. The model can also include predetermined regressors in either the mean or the variance. 2. Estimating the Quasi-Correlations 45 Chou (2005), Engle (2002b), and Fernandes et al. (2005), who use the daily range to estimate the volatilities in this framework.

21) s=1 k=1 which is clearly positive definite if Ω is positive definite. The matrices of coefficients here can be full, symmetric, reduced rank, diagonal, or can even be scalars times the identity. None of this will affect the positive definiteness or symmetry of the matrix H. 5. 5. For any three conformable matrices A, B and C, vec(ABC) = A ⊗ C vec(B), where the symbol “⊗” refers to a tensor product. 4. 13). The big coefficient matrices in the vec model have n2 coefficients rather than roughly 14 n4 . These models correspond to nondiagonal versions of the vec model that are positive definite.

2 Vector GARCH A wide range of multivariate GARCH models have been proposed and used. These have been surveyed by several authors—including Bollerslev et al. (1994) and, more recently, Bauwens et al. (2006) and Silvennoinen and Terasvirta (2008)—and will not be discussed in great detail here. It is sufficient here to outline how they are typically formulated. The models can be described by an equation for each element of the covariance matrix. The most popular class, called diagonal multivariate GARCH or diagonal vector GARCH, formulates the i, j element of the covariance matrix in terms of only the product of the prior i and j returns.

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