### TABLE 4 Distributions of One-Day-Ahead Probability Integral Transforms Density Forecasts From Long-Memory Lognormal-Normal Mixture Model

### Table 7: Power of the Test

"... In PAGE 14: ... If we interpret T n as a measure of risk, the above nding means that the existing nite-variance models have di culties to explore the high risk that the actual stock markets have. Finally, Table7 provides the evidence that in nite samples our test has very good power. From Table6andFigure 1, we note that in terms of the size of the test, it works quite well for the normal distribution, the Student t distribution, the mixture of normal distribution, the compound log-normal and normal model, and the Weibull distribution.... ..."

### Table 6: Finite Sample Distribution of T

"... In PAGE 13: ... In Table 5 we present the nite sample means and sample variances of T n under H 0 for all three samples. We report the 95% critical value in Table6 and the power of the test in Table 7. We also perform a Monte Carlo study to obtain the real sizes of the test in nite samples and compare them with the nominal sizes.... In PAGE 13: ... A detailed examination of Table 3 and Table 5 reveals that the asymptotic distri- bution of T n is very close to the nite sample distribution of T n across all three samples and all nite-variance distributions. Not surprisingly, therefore, we end up the same conclusions from Table 4 and Table6 . Table 4 indicates that, for all three samples,... In PAGE 14: ... Finally, Table 7 provides the evidence that in nite samples our test has very good power. From Table6 andFigure 1, we note that in terms of the size of the test, it works quite well for the normal distribution, the Student t distribution, the mixture of normal distribution, the compound log-normal and normal model, and the Weibull distribution. Although the size distortions are larger for the mixed di usion jump model, the biases suggest under-rejection of the model and hence support our nding of rejection of all nite-variance distributions in the above empirical study.... ..."

### Table 7. We also perform a Monte Carlo study to obtain the real sizes of the test

"... In PAGE 14: ... If we interpret T n as a measure of risk, the above nding means that the existing nite-variance models have di culties to explore the high risk that the actual stock markets have. Finally, Table7 provides the evidence that in nite samples our test has very good power. From Table6andFigure 1, we note that in terms of the size of the test, it works quite well for the normal distribution, the Student t distribution, the mixture of normal distribution, the compound log-normal and normal model, and the Weibull distribution.... In PAGE 26: ...Table7 : Power of the Test Sample 1: 76-85 Sample 2: 88-97 Sample 3: 76-97 Normal 1 1 1 Student 1 Not Applicable Not Applicable MN 1 1 1 LN 1 1 1 MDJ 1 1 1 Weibull 1 1 1 Table 8: Size of the Test Nominal size 0.001 0.... ..."

### TABLE 6 Distribution of the forecasting errors

"... In PAGE 14: ... TABLE 5 Parameter estimation (after diagnostic checks) and root mean square error for the two STARMA models. TABLE6 Distribution of the forecasting errors LIST OF FIGURES FIGURE 1 Loop detectors at the Athens road network. The ones used in this study are highlighted with different color and a label.... ..."

### Table 3: 95% Con dence Intervals for lower upper parameter bound bound

"... In PAGE 25: ... The constraint is rejected in every year. The 95% con dence intervals shown in Table3 support the same conclusions.20 Regarding the other necessary conditions, 95% con dence intervals computed as in Table 3 show q (1.... In PAGE 25: ... The 95% con dence intervals shown in Table 3 support the same conclusions.20 Regarding the other necessary conditions, 95% con dence intervals computed as in Table3 show q (1.... In PAGE 36: ...hoice actually made is .57 (by year, .54, .56, .58, .59, .56, .59). 19. The 95% con dence interval for cEC;90, computed as in Table3 , is (?:001; :558). 20.... In PAGE 37: ... 22. The upper bounds of the 95% con dence intervals for , in Table3 , are smaller than the lower bounds of the 95% con dence intervals Mebane (2000, Table 4) reports for D or R for the winning presidential candidate ( D;76, R;80, R;84, R;88, D;92, D;96), for all years except 1984. The interval for R;84, (.... In PAGE 37: ...34, .79), is virtually the same as the interval for 86 in Table3 , suggesting that voters believed that Reagan apos;s in uence on policy remained about the same throughout his second term. 23.... ..."

### Table 3: 95#25 Con#0Cdence Intervals for #0B

"... In PAGE 28: ... The constraint is rejected in every year. The 95#25 con- #0Cdence intervals shown in Table3 support the same conclusions. 19 Regarding the other necessary conditions, 95#25 con#0Cdence intervals computed as in Table 3 show q #281.... In PAGE 28: ...0B = 1, imposed separately for eachyear. The constraint is rejected in every year. The 95#25 con- #0Cdence intervals shown in Table 3 support the same conclusions. 19 Regarding the other necessary conditions, 95#25 con#0Cdence intervals computed as in Table3 show q #281.28, 1.... In PAGE 38: ...verage probability of the pair of choices actually made is .57 #28byyear, .54, .56, .58, .59, .56, .59#29. 18. The 95#25 con#0Cdence interval for c EC;90 , computed as in Table3 , is #28,:001;:558#29. 19.... ..."

### Table 1: True mixture distribution for Example 1.

2004

Cited by 30

### Table 3: True mixture distribution for Example 3.

2004

Cited by 30

### Table 1: Prior distribution on number of components of mixture

"... In PAGE 8: ..., 1987) : Pn(K = k) = Z Pn(K = kj )p( ) d (8) I X i=1 Pn(K = kjti)wi; (9) where ti are the I nodes at which to evaluate Pn(K = kjti) and the wi are weights. Table1 shows the prior distribution on the number of components for a sample size of 200 and a Gamma(3,10) prior distribution on . The model above was run for a burn-in of 5000 cycles and then for a further 10,000 cycles to generate samples from the posterior distribution.... ..."