### Table 1: Di erences between the short-range dependent processes and the long-range dependent processes

1996

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### TABLE I IMPACT OF LONG-RANGE DEPENDENCE ON PERFORMANCE GAIN OF AFEC-MT VS. AFEC.

2000

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### Table 1: Results of Canonical Correlation Analysis for Common Long-range Dependent Component plus White Noise

1997

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### Table 2: Results of Canonical Correlation Analysis for Common Long-range Dependent Component plus MA Noise

1997

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### Table 3: Results of Canonical Correlation Analysis for Common Long-range Dependent Component plus AR and MA Noise

1997

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### Table 2: Estimated Long-range Dependence Parameter for Daily Volatilities of 100 Ran- domly Selected S amp;P 500 Companies

2000

"... In PAGE 4: ... Any company having fewer than 3000 daily returns was replaced by another random draw within the same decile. The selected companies are given in Table2 , identified by their tick symbols. We test for long-range dependence in daily stock volatilities by estimating the fractional integrating parameter d for the logarithm of squared returns of selected companies.... In PAGE 6: ...he standard deviation of the GPH estimates, 0.0538 compared to 0.0913. We use these two methods to estimate d for the volatilities of S amp;P 500 companies. The second column of Table2 shows the estimates of d for the 100 selected companies using the spectral regression method. The mean and median of dGPH are 0.... In PAGE 7: ...Table2 shows the estimates of d for the 100 selected companies using QMLE. The QMLE estimates are consistent with those obtained using GPH, again in- dicating strong evidence of significant long-range dependence in the majority of sampled companies.... ..."

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### Table 9: Estimated Long-range Dependence Parameter for Daily Volatilities of S amp;P 500 Companies within Different Sectors

2000

"... In PAGE 15: ... We identified 20 utilities, 20 banks or financial institutions, and 11 oil companies having over 3000 daily returns as of December 29, 1995. The estimated d values for log of modified squared returns from each of these companies are given in Table9 , along with the size decile of the company. A two-way ANOVA indicated no significant differences between estimated d values for companies in different sectors or companies in different deciles, and no sig- nificant interaction between sector and decile.... In PAGE 16: ... Many groups of banks and financial institutions have three, or even four, linear combinations that are short-range dependent. Some reasons that daily stock returns of banks and financial institutions might be driven by fewer long-range dependent components in volatility include (a) the 20 companies used are more homogeneous in market capitalizations than the S amp;P 500 companies as a whole; see the decile classification in Table9 , (b) bank stocks are sensitive to key interest rates that depend on the U.S.... ..."

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### Table 2 Summary or the long-range dependence analysis (n.a.=statistical results non reliable due to insufficient sample size)

### Table 3: Summary Statistics and One-Way Analysis of Variance Table for Size Effect on the Long-Range Dependent Parameter: Estimates obtained using Spectral Regression Method

2000

"... In PAGE 6: ... In fact, the results of our simulation study imply that the amount of persistence in volatility may be even higher than that reflected by the GPH estimates, depending on the SNR of the particular series. Some additional summary statistics for dGPH are given in Table3 (a). It is interesting to note that the mean and median of dGPH are close to the values 0.... In PAGE 7: ...3 Size effects on d To look for size effects on the strength of long memory in individual stock volatilities, we conduct a one-way analysis of variance (ANOVA) on the estimates of d by decile. The results are shown in Table3 (b) for the GPH estimates and Table 4(b) for the QMLE esti- mates. In our application, the sample sizes are relatively large, so that the variances of d obtained using a particular method are approximately equal.... ..."

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### Table 3: Comparison on tra c models. A good performance of the model has been obtained through extensive tests on three video sources and one Ethernet data trace using both the auto-correlation and the bu er loss rate as performance measures. The bu er loss rate of the wavelet model has shown analytically to be similar to that of the FGN process for a FGN workload, and thereby demonstrates the capability and the performance of the independent wavelet models. Since the self-similar structure of wavelets naturally matches the statistical self-similarity in network tra c, the resulting wavelet models are parsimonious and have much fewer parameters than FARIMA models. The computational complexity for developing such a wavelet model and for synthesizing a large volume of tra c has shown to be O(N), which is the lowest attained. In our future work, we will further investigate the capability of independent wavelet models, and extend the analysis to non-Gaussian tra c in order to make up for insu cient the network data at low loss rate. We will also investigate other performance measures to account for e ects of long-range dependence on loss patterns.

1997

"... In PAGE 24: ... When used to model the FGN process with a zero mean, the variance of dj is given in [42][13] as V ar(dj) = 2?j(1?2H)(22(1?H) ? 1) 2(1 ? O(2?2(1?H)K)): (15) aj(s) is a weighting factor which depends on the aggregation length s, where aj(s) = ( rs j; for either rs j = rs j?1 or j = 1, 2j?1 ? rs j?1; otherwise; (16) with rs j = s ? bs2?jc 2j, and b c represents the largest integer smaller than s. Examples of such aj(s) are given in Table3 . As can be seen from the table, aj(s) is periodic with a period 2j.... ..."

Cited by 1