### Table 5: Finite Sample Distribution of T

"... In PAGE 13: ... The sizes are reported on Table 8 and plotted in Figure 1. A detailed examination of Table 3 and Table5 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 Table 6.... ..."

### 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 1: Finite Sample Sizes

2000

"... In PAGE 18: ... For each statistics, we report the minimum, mean, median and maximum of the rejection probabilities under the null and the alternative hypothesis. As can be seen from Table1 ,thefinite sample sizes of the test SN are quite close to the corresponding nominal sizes. The sizes are calculated using the critical values from the standard normal distribution, and therefore the simulation results corroborate the asymptotic normal theory for SN.... ..."

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### Table2:FiniteSamplePowers

2000

"... In PAGE 17: ... In such cases, one might use a little larger value of K to correct the upward size distortion. 9 Table2 in Im, Pesaran and Shin (1997) tabulates the values of E(ti)andvar(ti)forT = 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 100 and for pi = 1,.... ..."

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### Table 3: Size-adjusted Finite Sample Powers

2000

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### TABLE 2. Key vectors and matrices for likelihoc with finite sample and parameter spac

1993

### Table 1. Finite-Sample Critical Values for the LR and LR Statistics uc cc

"... In PAGE 9: ... With respect to size, the finite sample distribution of LR for the specified parameters may be sufficiently different uc from a G33 (1) distribution that the asymptotic critical values may be inappropriate. Table1 , Panel 2 A presents the finite-sample critical values as determined via simulation, and meaningful differences between the two distributions are present and must be accounted for when drawing statistical inference. As for the power of this test, Kupiec (1995) describes how this test has a limited ability to distinguish among alternative hypotheses and thus has low power in samples of size 250.... In PAGE 10: ... The relevant test statistic is which is distributed G33 (2). The finite sample critical values for the regulatory parameter values are shown 2 in Table1 , Panel B. The LR statistic is the likelihood ratio statistic for the null hypothesis of serial ind independence against the alternative of first-order Markov dependence.... ..."

### Table 1 Finite-Sample Performance of Tests for Conditional Goodness-of-Fit Restrictions

1997

"... In PAGE 16: ... The number of Monte Carlo replications is set to 1000. Table1 shows the rejection frequencies #28#25#29. The size here is a pointwise one #28for #0Cxed #16 and #1B 2 #29 and thus is di#0Berent from the size in the sense of Lehmann #281986#29: the supremum of the type I error probabilities over all possible DGP under the null #28for all possible values of #16 and #1B 2 #29.... ..."

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