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We proposed some nonlinear versions of the AR-ARCH model, which is often used for financial computing but is based on the linear regression. Our nonlinear AR-ARCH model can temporally change its model parameters following the local structure hidden in the observed financial data. To confirm the validity of our model, we performed some statistical significance tests. First, as one of the learning process, we performed the surrogate data test to the learning data, but we could not aggressively suggest that the original financial data have nonlinearity. However, from the viewpoint of predictive performance of the test data, our nonlinear models, especially the NAR-NARCH model, can improve the prediction accuracy of both of the return rate and the volatility. This improvement can be verified by the Wilcoxon signed-rank test. 


Financial computing, AR-ARCH model, nonlinear prediction model, surrogate data test

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