U.S.-U.K. 0.5 U.S.- Japan 37 90 92 95 97 00 U.S.-Germany     82 85 87 90 92 95 97 00 1 Japan-UK, 0.5 0 <iHy W\f#Hif   87 90 92 95 97 00 Japan-Germany 1 0.5 0 ' 85 S7 90 92 95 97 00 U_K.-Gerrnariy   82 85 87 90 92 95 97 00 82 85 87 90 92 95 97 00 FIGURE 1 6.2 Correlations: Comparison between Constant and Time-Varying Estimates want to construct an estimator that can capture as many empirical regularities as possible. On the other hand, we must keep in mind that most practitioners need to estimate covariance matrices of large dimensions, for hundreds or even thousands of assets. A model that is excessively parameterized may be impossible to estimate when applied to large sets of assets, and therefore its flexibility may become the cause of its practical irrelevance. TABLE 16.4 Test of Time Variation in Correlations     Observed Data         Constant   Standard Deviation of Monte Carlo Data           Standard     Volatility Observed Time Varying Average Deviation Maximum   Estimate aad Estimates aad of aad aad U.S .-Japan 0.1150 0.0965 0.0729 0.0788 0.0062 0.1033 U.S.-U.K. 0.3514 0.1201 0.0907 0.0703 0.0056 0.0883 U.S.-Germany 0.2654 0.1728 0.1080 0.0744 0.0057 0.0919 Japan-U.K. 0.2478 0.1184 0.0859 0.0753 0.0059 0.0956 Japan-Germany 0.2569 0.1196 0.0813 0.0747 0.0056 0.0986 U.K.-Germany 0.4684 0.1927 0.1221 0.0627 0.0048 0.0771