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Elsevier, Neural Networks In Finance 2005_6

Tham khảo tài liệu 'elsevier, neural networks in finance 2005_6', tài chính - ngân hàng, ngân hàng - tín dụng phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 5.2 Stochastic Chaos Model 119 FIGURE 5.2. Stochastic chaos process for different initial conditions TABLE 5.1. In-Sample Diagnostics Stochastic Chaos Model Structure 4 Lags 3 Neurons Diagnostic Linear Model Network Model Estimate R2 .29 .53 HQIF 1534 1349 L-B .251 M-L .0001 E-N .0000 J-B .55 L-W-G 1000 B-D-S .0000 marginal significance levels network model appearing in parentheses explains 53 . The Hannan-Quinn information criterion favors not surprisingly the network model. The significance test of the Q statistic shows that we cannot reject serial independence of the regression residuals. By all other criteria the linear 120 5. Estimating and Forecasting with Artificial Data FIGURE 5.3. In-sample errors stochastic chaos model specification suffers from serious specification error. There is evidence of serial correlation in squared errors as well as non-normality asymmetry and neglected nonlinearity in the residuals. Such indicators would suggest the use of nonlinear models as alternatives to the linear autoregressive structure. Figure 5.3 pictures the error paths predicted by the linear and network models. The linear model errors are given by the solid curve and the network errors by dotted paths. As expected we see that the dotted curves generally are closer to zero. 5.2.2 Out-of-Sample Performance The path of the out-of-sample prediction errors appears in Figure 5.4. The solid path represents the forecast error of the linear model while the dotted curves are for the network forecast errors. This shows the improved performance of the network relative to the linear model in the sense that its errors are usually closer to zero. Table 5.2 summarizes the out-of-sample statistics. These are the root mean squared error statistics RMSQ the Diebold-Mariano statistics for lags zero through four DM-0 to DM-4 the success ratio for percentage 5.2 Stochastic Chaos Model 121 FIGURE 5.4. Out-of-sample prediction errors stochastic chaos model TABLE 5.2. Forecast Tests .