### Table 8: Equality of Covariance and Correlation Matrices Covariance Correlation

"... In PAGE 26: ... 5. Inter-temporal stability of credit spread co-movements A comparison of the stability results using the Box, Jennrich test and the Bootstrap procedure is presented in Table8 . We report the results for the weekly data (5 days) and each correlation or covariance matrix thus is estimated based on 69 observations.... In PAGE 27: ... p-values of the standard statistics are given between parentheses, the bootstrapped p-values are placed between squared brackets. Table8 reports the test results on the stability of the covariances and correlations of the credit spread changes based on the standard (i.e.... In PAGE 28: ... For only two of the sub-samples, the bootstrapped tests reject the equality of correlation matrices at the 5% significance level. Finally, it is clear from the rating buckets in Table8 that the asymptotic statistical inference can lead to false conclusions. Taking these results into account, we can induce that the... ..."

### Table 8: Eigenvalues of Residual Covariance Matrix from Vector Autoregressive

in Market Design and Price Behavior in Restructured Electricity Markets: An International Comparison

1999

"... In PAGE 45: ... Table8 repeats this calculation for the (24x1) covariance matrix of the white noise process driving the Nordpool spot prices. This table is very different from the one for the E amp;W prices.... ..."

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### Table 8: Eigenvalues of Residual Covariance Matrix from Vector Autoregressive

"... In PAGE 46: ... Table8 repeats this calculation for the (24x1) covariance matrix of the white noise process driving the Nordpool spot prices. This table is very different from the one for the E amp;W prices.... ..."

### Table 6. Estimates of coefficient matrices and resulting covariance functions and their eigenvalues for genetic and permanent environmental effects (KA and KR for A and R with lAi and lRi, respectively), fitting a cubic regression (k=4) on orthogonal polynomials of age transformed to logarithmic scale, and forcing covariance functions to have rank m=2a

"... In PAGE 18: ... Together with seven measurement error variances, that resulted in 23 and 21 parameters to be estimated for HEF and WOK, respectively. Estimates of coefficient matrices of covariances and resulting genetic and permanent environmental covariances functions together with estimates of fixed regression coefficients to model the population trajectory are summarized in Table6 . Corresponding estimates of measurement error variances are given in Table 7.... In PAGE 22: ... (1990), eigenvalues and eigenfunctions of genetic CFs provide an insight into the way selection affects the character under consideration. Estimates of the first two eigenvalues of A are given in Table6 and the corresponding eigenfunctions are shown in Figure 14. The third, significant eigenvalue for A in HEF was 64.... ..."

### Table 2: Covariance matrices.

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### Table 8 repeats this calculation for the (24x1) covariance matrix of the white noise process

in Market Design and Price Behavior in Restructured Electricity Markets: An International Comparison

1999

"... In PAGE 58: ... Table8 : Eigenvalues of Residual Covariance Matrix from Vector Autoregressive Model used to Forecast Vector of Daily Spot Prices in Nord Pool Principal Component Eigenvalue Percent of Total Variation Principal Component Eigenvalue Percent of Total Variation 1 18.089 0.... ..."

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### Table 8 repeats this calculation for the (24x1) covariance matrix of the white noise process

"... In PAGE 59: ... Table8 : Eigenvalues of Residual Covariance Matrix from Vector Autoregressive Model used to Forecast Vector of Daily Spot Prices in Nord Pool Principal Component Eigenvalue Percent of Total Variation Principal Component Eigenvalue Percent of Total Variation 1 18.089 0.... ..."

### Table 4. Eigenvalues and relative proportions (in brackets) for the genetic and permanent environmental random regression coefficient matrices with different Legendre polynomial orders of fit m [LEG(m)]. Model

1999

"... In PAGE 6: ....20 to 0.46. Overall, model LEG(3) and higher resem- bled the bivariate estimates well, although the absolute level was slightly higher, which was probably caused by averaging of the covariances between DIM for the bivariates, and better correction for the correlations among DIM within the RRM. Eigenvalues of Covariance Matrices Eigenvalues ( Table4 ) for the genetic and permanent environmental matrices of random regression coeffi- cients did not vary much for the different orders, except the first eigenvalue (zero-th order) for permanent envi- ronment decreased with the order of fit of the model. For the genetic part, the first three eigenvalues ex- plained over 98% of the variation, but for the permanent environmental part, four eigenvalues were needed to explain over 98%; five were needed to explain over 99%.... In PAGE 7: ...2646 LEG(4) is also needed for the genetic effects (although Table4 suggests that it might be modeled by a lower- order Legendre polynomial). DISCUSSION For the implementation of a RRM in the genetic eval- uation of dairy cattle, it is important that breeding Figure 4.... In PAGE 9: ... Com- pared to LEG(3) and LEG(4), which modeled similar shapes as observed for the bivariate genetic covari- ances, the shape fitted by model LEG(1) was structur- ally different. 4) Eigenvalues for the genetic and permanent en- vironmental covariance function matrices ( Table4 ). A sufficiently large proportion of the variances observed for test-day records in the data was explained by LEG(3) and LEG(4) based on the eigenvalues.... ..."

### Table 1: Different eigenvaluestructures for n n matrices used in the simulation study.

1996

"... In PAGE 4: ... Then we compare the performance of the different parameterizations in computing the maximum likelihood estimate of the variance- covariance matrix in a linear mixed effects model (Laird and Ware, 1982). To investigate the effect of the eigenstructure of on the computational efficiency of the parameterizations, six different eigenvalue structures, described in Table1 , were considered in... In PAGE 4: ... Obtain = U UT . To evaluate the average time needed to calculate L, we gener- ated, for each of the eigenvalue structures in Table1 , 25 random n n matrices according to the above algorithm, with n vary- ing from 6 to 100. For each we obtained and recorded the average time to calculate L.... ..."

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