### Table 1: Implementation results for chaotic time-series prediction

1998

"... In PAGE 4: ...Matlab neural network toolbox and trained using conventional backpropagation algorithms. A summary of the implementation results obtained are presented in Table1 . Two different simulation approaches were used for the chaotic time series prediction problem.... In PAGE 4: ...ifference between the predicted and actual results, in terms of the prediction error is illustrated in Fig. 5. This compares favourably with a conventional fuzzy approach which employed an even finer-grained partitioning strategy ranging from 15 to 29 fuzzy sets to achieve a similar accuracy [Wang92]. For further comparison, the results using a conventional neural network approach which contains 40 nodes in the hidden layer are also included in Table1 . Previous work demonstrated that this size of network resulted in a similar degree of accuracy as a conventional fuzzy reasoning approach employing seven fuzzy sets on each input domain [Wang92].... In PAGE 4: ... Previous work demonstrated that this size of network resulted in a similar degree of accuracy as a conventional fuzzy reasoning approach employing seven fuzzy sets on each input domain [Wang92]. Table1 illustrates that the FNN approach provides a more accurate prediction of the time-series as compared to the conventional neural network approach. However, these results do not highlight that the training time of the conventional neural network was more than a factor of two slower than the largest FNN employed.... ..."

Cited by 2

### Table 1 Time-Series Regression Tests of Causal Direction between the Variables in the Analysis (N = 18 years)

"... In PAGE 15: ...8 or lower) indicates that the errors are homoscedastic. Table1 summarizes the results of this analysis for the three possible paths of media effects on binge-drinking behavior that are suggested by Hypotheses 1 through 3. Hypothesis 1 proposes a direct positive influence of binge-drinking-related media coverage on the perceived harmfulness of this behavior that in turn is associated with a reduction in the prevalence of this behavior.... In PAGE 15: ... Finally, Hypothesis 3 pertains to the plausi- bility of either a direct or indirect impact of news coverage on perceived peer disapproval of binge-drinking behavior, which is expected to be associated with a reduction in this behavior. Table1 also demonstrates that, overall, tests of serial correlation, multicollinearity, and heteroscedasticity did not detect any significant violation of OLS regression assumptions. The findings in Table 1 only partially support the Hypothesis 1 expecta- tion of a direct effect from media coverage to binge-drinking behavior.... In PAGE 15: ... Table 1 also demonstrates that, overall, tests of serial correlation, multicollinearity, and heteroscedasticity did not detect any significant violation of OLS regression assumptions. The findings in Table1 only partially support the Hypothesis 1 expecta- tion of a direct effect from media coverage to binge-drinking behavior. Although,as expected,the perceived harmfulness of binge-drinking behavior had a significant negative contribution to the trend in the percentage of high school seniors who performed this behavior over the research period (Step 2), there was no evidence of an independent contribution of binge-drinking- related news coverage on the perceived harmfulness of this behavior (Step 1).... In PAGE 15: ...armfulness of this behavior (Johnston et al., 1998). This possibility, as well as the possibility of a nonlinear association between media coverage and per- ceived harmfulness, will be explored here later on. The findings in Table1 also seem to partially support the prediction of Hypothesis 2 with regard to the indirect flow of influence from media cover- age to perceived harmfulness. As hypothesized, media coverage of binge- drinking behavior had a significant positive contribution to the trend in binge-drinking-related congressional bills over and above the secular trend in this behavior (Step 1).... In PAGE 17: ... Before we move to test Hypothesis 4,two additional points need to be men- tioned in relation to the analysis reported above. The first is that while all tests of causality in Table1 are in the direction prescribed by the research hypotheses, tests of a reversed causal direction were also conducted for each step in the analysis but were omitted from Table 1 because none has shown evi- dence of an independent effect. Second, the proposed model of media effects 224... In PAGE 17: ... Before we move to test Hypothesis 4,two additional points need to be men- tioned in relation to the analysis reported above. The first is that while all tests of causality in Table 1 are in the direction prescribed by the research hypotheses, tests of a reversed causal direction were also conducted for each step in the analysis but were omitted from Table1 because none has shown evi- dence of an independent effect. Second, the proposed model of media effects 224... In PAGE 20: ... The first is that the association between binge-drinking-related news coverage and the perceived harmfulness of this behavior (as proposed by Hypothesis 1) is essentially nonlinear. Thus, although the results of the time-series regres- sion indicate no contribution of media coverage to the trend in this variable (see Table1 ), they may simply be an artifact of forcing the association to be linear. The second additional proposition tested in Table 2 is that media coverage of drunk driving (and not that of binge drinking) contributed to the increase over time in the perceived harmfulness and peer disapproval of this behavior.... In PAGE 20: ...about 67%) were also related to binge-drinking behavior (i.e.,aimed at limit- ing alcohol availability to youth and reducing the minimum legal drinking age). Repeating the analysis for Hypotheses 1 through 3 in Table1 while replacing binge-drinking-related news coverage and congressional bills with drunk-driving-related news coverage and legislation, revealed that (a) news coverage of drunk driving had a statistically significant contribution to the perceived harmfulness of binge drinking while controlling for the previous values of this series (B = .03, SE = .... In PAGE 21: ...e., the direct path of media effects in Table1 ) was not simply an artifact of focusing on lin- ear associations. 228 COMMUNICATION RESEARCH April 2001 Table 2 A Comparison of Linear and Nonlinear Predictions of Perceived Harmfulness and Peer Disapproval of Binge Drinking Among High School Seniors From a Diffusion Process and Both Binge-Drinking-Related and Drunk-Driving-Related Media Cover- age, United States, 1978-1996 (N = 18 years) Independent Series Predicted Series Goodness-of-fit (R2) Time Harmfulness .... ..."

### T able 1:On the left: NMSE of the predictions for time series A. On the right:

2000

"... In PAGE 5: ... We adopt for the series A an embedding model having the same dimension m = 16 proposed in [8] and for the series D an embedding model with m = 20 as reported in [10]. Table1 (left) compares the NMSE (Normalized Mean Squared Error) on the A test set of the local predictor based on the consistency criterion (CC) with the local method based on cross-v alidation(Press) proposed in [4] and with the performance statistics reported by Sauer [8] and Wan [9]. T able1 (righ t) compares the RMSE (Root Mean Squared Error) on the seriesD of the D-Facto public.... ..."

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### Table 14. Significance Tests for the Difference of Five Days Ahead Absolute Prediction Errors with the Merton and Constant Intensity Models in Time Series Design

2005

"... In PAGE 23: ... These results have mostly arisen from a very small mean difference, complemented with a very low standard error and large sample size. [Table 12 is presented here] [Table 13 is presented here] [ Table14 is presented here] [Table 15 is presented here] Nevertheless, these levels are still better than cross-sectional setup. The better fit of the time series analysis over cross-sectioning signifies that credit risk may not be priced the same in a given risk class.... ..."

### Table 2: Error (RMSE) of one-step and trajectory predictions for gaussian and polynomial kernels for the time series Laser. The regularizing values used for KDM are in subscript.

2003

"... In PAGE 6: ... The validation error (RMSE) is evaluated on the points in the range 101 to 200. Table2 reports the validation errors obtained for the two kinds of prediction. The most striking information provided by this table is the large error archieved by KDM with no regularizer when a gaussian kernel is used.... ..."

Cited by 8

### Table 2: Error (RMSE) of one-step and trajectory predictions for gaussian and polynomial kernels for the time series Laser. The regularizing values used for KDM are in subscript.

2003

"... In PAGE 6: ... The validation error (RMSE) is evaluated on the points in the range 101 to 200. Table2 reports the validation errors obtained for the two kinds of prediction. The most striking information provided by this table is the large error archieved by KDM with no regularizer when a gaussian kernel is used.... ..."

Cited by 8

### Table II. Model Parameters for Time-Series Prediction

2005

### Table 7: Aggregate time-series: 1973-1990

### Table 1. Correlation and Residual Variance Between Altimetric Velocities and SQG Velocities for the Data Centered on January 5, 2005 and the Mean Values for the Whole Time Seriesa

"... In PAGE 4: ... Therefore, there seems that the SQG method used in combination with microwave SST is able to estimate a velocity field that seems qualitatively consistent with the velocity field derived from the altimeter. Table1 shows a more quantitative comparison obtained by computing the linear correlations (R) for each component of the velocity field for the whole image and the quotient between the variance of the residual velocities and the altimetric veloc- ities (nu C17 var(usqg C0 ualtim)/var(ualtim)). If we focus on those regions exhibiting large thermal gradient, correlations are closer to one and residual variances are smaller.... ..."

### Table 2: Tests of the time-series properties of the dataa

"... In PAGE 7: ...ppendix 1. The data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Appendix 2. Table2 : Tests of the time-series properties of the data .... In PAGE 16: ... Both the ADF test and the modified Phillips-Perron test allow us to test formally the null hypothesis that a series is I(1) against the alternative that it is I(0). The results from the tests of the time-series properties of the data can be found in Table2 in Appendix 2. ADF critical values are generated to account for the finite-sample distribution of the series by performing Monte Carlo simulations with 5,000 replications for the level of inventories, the level of new orders, capacity utilization, the price of raw materials and the yield spread.... In PAGE 16: ... Evidence was found that capacity utilization contains a moving-average component, while the yield spread appears to follow an autoregressive moving- average process.9 Table2 (Appendix 2) indicates that both the ADF and the tests suggest that inventories, new orders, and raw material prices are non-stationary or I(1) processes in levels. The ADF test rejects the null hypothesis of a unit root in the level of the yield spread at conventional levels of significance and also provides evidence that capacity utilization is characterized as a stationary or I(0) process.... ..."