Prediction Of Chaotic Time Series Based On Adaptive Function-coefifcient Autoregressive Models

In the first part, we explained what was chaotic and introduced the development ofchaos all over the world. As far as we knew, the research of chaos has push social sciencesand natural science further. Chaos was the hotpot in today’s society. In the second part, weconstrue the basic idea and algorithm of the adaptive functional-coefficient autoregressivemodels, and then we use it to forecast the chaotic time series. The chaos was produced byHenon, Mackey-Glass function and Lorenz function. We compare it with the results of BP,LS-SVM, RBF. We found the result was better to use adaptive function-coefficientautoregressive models than BP, LS-SVM and RBF when the chaos was not interfered bywhite noise. The accuracy of the adaptive functional-coefficient autoregressive modelswere1.2696e-004.324e-004,0.0098. but the results were not better enough when weadd the white noise into the chaos time series. In order to prove the accuracy and calculatefurther, we simple the models. We use polynomial as the functional-coefficient toapproximate the adaptive function-coefficient autoregressive models in the third part. Weuse two methods to fix the order and estimate the parameters. We used this reducedmodels to predicted the chaos, and compared the results with TLLP and NLLP’s. Theconclusion demonstrate the accuracy and stability had improved. The adaptivefunction-coefficient autoregressive models and its reduced models were worth predictingchaotic time series.