
Proxy for the conditional covariance/correlation matrix



Estimate of the conditional covariance/correlation matrix.


Compute the Euclidean distance between the matrices S and H. See, Laurent et al. (2012) and Amendola et al. (2015).

Euclidean distance

Statistical Performance Measure

Statistical performance measures used in the econometric literature to evaluate conditional covariance/correlation matrix estimates (MSE, MAE, Euclidean distance, Frobenius distance, Stein distance, asymmetric loss function, eigenvalue loss function and the loss function defined in Eq. (4.6) of Engle et al. (2016) <doi:10.2139/ssrn.2814555>). Additionally, compute Eq. (3.1) and (4.2) of Li et al. (2016) <doi:10.1080/07350015.2015.1092975> to compare the factor loading matrix. The statistical performance measures implemented have been previously used in, for instance, Laurent et al. (2012) <doi:10.1002/jae.1248>,  Amendola et al. (2015) <doi:10.1002/for.2322> and  Becker et al. (2015) <doi:10.1016/j.ijforecast.2013.11.007>.

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Examples