Robust Forecasting For Nonlinear Time Series

由於時間序列在不同範疇的廣泛應用，許多實證結果已明白指出時間序列資料普遍地存在非線性(nonlinearity)，使得非線型方法在最近幾年受到極大的重視。然而，對於某些特定的非線型模式，縱然現在已有學者提出模式選取之檢定方法，但是它們的模式階數確認問題至今卻仍無法有效率地解決，更遑論得到最佳的模式配適與預測結果了。所以，我們試圖利用一已於其他科學領域成功應用之新技術──神經網路，來解決非線型時間序列之預測問題，而我們之所以利用神經網路的原因是其多層前輸網路是泛函數的近似器(functional approximator)，對任意函數均有極佳之逼近能力，使我們免除對時間序列資料之屬性(線性或非線性)作事先檢定或假設的必要。在本篇論文中，我們首先建構15組雙線型時間序列資料，然後對於這些數據分別以神經網路與自我迴歸整合移動平均(ARIMA) 模式配適。藉著比較兩者間的配適與預測結果，我們發現神經網路對於預測非線型時間序列是較具有穩健性。最後，我們以台幣對美元之即期匯率作為我們的實證資料，結果亦證實了神經網路對於預測一般經濟時間序列亦較具穩健性。With rapid development at the study of time series, thenonlinear approaches have attracted great attention in recentyears. However, there are no efficient processes for theproblem of identification to many specifically nonlinear models. Even if many testing methods have been proposed, we stillcan not find the best fitted model and obtain the best forecastperformance. Hence, we try to solve the forecast problemsby a new technique -- neurocomputing, which has beensuccessfully applied in many scientific fields. The reason whywe apply the neural networks is that the multilayer feedforwardnetworks are functional approximators for the unknown function.In this paper, we will first construct several sets of bilineartime series and then fit these series by neural networks andARIMA models. In this simulation study, we have found that theneural networks perform the robust forecast for some nonlineartime series. Finally, forecasting performance with favorablemodels will also be compared through the empirical realizationof Taiwan