### Table 6: Testing for a single change-point in the volatility of daily Stock Market Indices (SMI) over the period 1989-2001 Change-point Statistics

"... In PAGE 17: ... The empirical analysis commences with investigating the hypothesis of a single break in the four international stock market indices. The results in Table6 provide evidence that neither the K amp;L nor the I amp;T tests support the null hypothesis of homogeneity in the absolute or squared returns of the stock market indices over the sample 1989-2001. These results hold for two alternative nonparametric estimators of (rt)2 and |rt| used for standardizing the max UT (k) statistic defined in section (1.... In PAGE 17: ... It is interesting to note that the extension of the I amp;T statistic by Kim et al. (2000) (also reported in Table6 as BT (C)) does not detect any change-points. One possible explanation can be the poor power performance of the test in the presence of highly persistent GARCH processes as documented in Kim et al.... In PAGE 18: ...in Table6 refer to the Asian crisis period. However the single change point hypothesis can mask the existence of multiple breaks which implies that in dating change-points it is advisable to follow a multiple breaks procedure.... In PAGE 33: ...591(1), -1.559(0) 1 14/10/97 Notes: For brief data description refer to note 1, Table6 .... ..."

### Table 2. Change point detection tool performance in the presence of correlation

### Table 1: Performance summary for the change-point detection approach [15]. The energy column gives the energy consumed relative to no frequency/voltage scaling.

2002

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### Table 1: Performance summary for the change-point detection approach [15]. The energy column gives the energy consumed relative to no frequency/voltage scaling.

### Table 1: Nominal Size and Power of the Kokoszka and Leipus (2000) test for a single change-point in the volatility based on a GARCH process.

"... In PAGE 13: ...2 Simulation Results The simulation results commence with the evaluation of the K amp;L test when the underlying process is a Normal-GARCH(1,1). Table1 reports only minor size distortions for GARCH models with low persistence (e.g.... In PAGE 14: ... The power of the K amp;L test is evaluated by a number of alternative hypotheses as defined in the previous section. The results in Table1 suggest that the tests have good power in detecting breaks under the following alternative hypotheses: Break in the constant (HB 1 )or dynamics (HA 1 ) of volatility. The power of the test is demonstrated even for small changes (e.... In PAGE 28: ...odification by Liu et al. (1997) denoted as LWZ are used. The simulations focus on DGP1, DGP2, T u003d 1000 for 500 trials. For comparison purposes the alternative hypotheses of change points are similar to the K amp;L simulations ( Table1 ) and extended to larger breaks. Reported is the frequency distributionn of the breaks detected.... In PAGE 29: ....00 1.00 0.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 0.00 0.00 0.00 1.00 0.00 Notes: The K amp;L test (see notes in Table1 ) is applied following a sequential sample segmentation approach and the frequency distribution of the change-points is reported. The highlighted numbers refer to the true number of breaks in the simulated process.... In PAGE 36: ...Table1 0: Estimating volatility dynamics in subsamples prior and post the change-points of stock market returns indices. SMI Process Subsamples ku2217 Normal GARCH(1,1) Estimates (observations) Date u03c9u03b1u03b2 FTSE ue0a2rtue0a32 1-3338 0.... ..."

### Table 7: Testing for multiple change-points in the volatility of daily Stock Market Indices (SMI) over the period 1989-2001

"... In PAGE 18: ... In the Lavielle and Moulines test we adopt two penalty function criteria, the first is the Bayesian Information Set (BIC) and the second is a modified BIC as proposed in Liu et al. (1996) (denoted by LWZ in Table7 ) and we set the number of segments tk equal to 3 and 5. The empirical findings show that irrespective of the choice of tk the L amp;M test consistently detects the same number of breaks.... In PAGE 36: ...883[42.41] Note: The Moulines and Lavielle (2000) multiple breaks results in Table7 for the absolute and squared returns processes are used to create various subsamples of each stock market return index. The estimated Normal GARCH(1,1) coefficients as well as the Power-ARCH coefficients are reported for the total sample (Tu003d1-3338) as the various subsamples determined by the estimated break points.... ..."

### Table 9: Change-point Test Results of Daily YM/US$ on DM/US$ Standardized Returns based on 30 minute Intra-daySamplingFrequency

"... In PAGE 26: ...discussed in section 3. The K amp;L change-point test results for the conditional covariance between the DM/US$ and YN/US$ are reported in Table9 . The results show that the univariate normalized returns (using any volatility filter transformation) appear to be time-homogeneous processes.... In PAGE 26: ... Note that an application of the parametric CUSUM does not detect any change-points. These results are complemented by testing for multiple breaks using the L amp;M regression method and the two information criteria, BIC and LWZ, also reported in Table9 . Given the empirical results in the previous section which support a static regression framework for the two FX normalized returns, we apply the L amp;M test in the context of equation (3.... In PAGE 26: ...10). The number and timing of breaks detected (reported in Table9 ) not only vary depending on the information criterion but also on the specification of normalized returns. The general result is that the tests choose between zero, one and two change-points and the break dates are relatively more consistent for X(H)QV,t using both criteria.... ..."

### Table 6: Possible outcomes of the m statistical tests.

2007

"... In PAGE 13: ... We will use direct control of the false discoveries using the commonly applied FDR crite- rion. The FDR, based on the outcomes of m statistical tests ( Table6 ), is defined as the expected proportion of false positives among the rejected hypotheses, i.e.... ..."

### Table 4: Size, Power and Frequency Distribution of the number of change-points obtained with the Lavielle and Moulines (2000) test when there is a single break in a M-GARCH with dynamic conditional covariance. Samples, T u003d 1000 and change point, u03c0 u003d 0.5 Normalized returns regression Xue0a2u03c3i,t k ue0a3 u003d a u002b bX u03c3j,t k

"... In PAGE 21: ...hen those are small in size (e.g. a 0.1 parameter change). The results regarding the remaining alternative hypotheses (HA 1 and HB 1 ) show that the L amp;M test also detects breaks in the bivariate relationship of normalized returns when the source of these change-points rests in the univariate GARCH dynamics as well as breaks in the co-movements (HC 1 ). The above results also hold if the simulated process is an M-GARCH-VDC shown in Table4 , except that the size of the change-point needs to be even larger in either the conditional variance or covariance dynamics for the test to exhibit power. It is also interesting to note that in comparing the normalizing volatility filters we find that the regression involving XRM,t yields more power in detecting change-points in the conditional covariance of the M-GARCH-VDC whereas for the M-GARCH- CCC both XRM,t and XRV 26,t yield similar power properties.... ..."

### Table 3: Previous point and interval estimates of the change-point. Method ^ Left limit Right limit

"... In PAGE 8: ... Both data sets are given in terms of time between successive disasters, so prior approaches have involved using an exponential distribution to model the data. Previous estimates and con dence limits for the change-point are presented in Table3 . It should be noted that the estimate of Worsley (1986) was based on the original data of Maguire et al.... In PAGE 10: ... This is some- what surprising, considering the amount of information that is being \thrown away quot; for the larger bin sizes. Perhaps the most striking feature of the estimates given in Table 4 is their close correspondence to the previous estimates in Table3 . Due to the binning of data, one might expect much lower precision in the interval estimates.... ..."