結合小波分解和小波神經網路於非定性財務時間序列之預測

Abstract

傳統時間序列的分析，通常都植基於機率與統計學，並假設資料的性質是定性（stationary）和線性（linear）的。但是當系統動態呈現高度非線性並伴隨著非定性（non-stationary）時，這些傳統模型的適用性及準確性可能無法滿足研究的需求。因此本研究提出了『小波神經網路多尺度解析混合預測模型』，可適用於非定性時間序列之分析與預測。利用小波分解具有處理混沌訊號的能力，將原始時間序列分解成多個解析尺度之子序列，再結合具有廣域函數逼近能力之小波神經網路架構，建構出時間序列混合預測模型。期望能在處理非定性時間序列分析時，不受限於傳統模型之假設條件，且能準確地預測。研究中並以台灣證券交易所發行量加權股價指數為實例，應用於一日及五日之收盤價與價格變化率預測，且與傳統自回歸模型以及未經小波分解步驟之小波神經網路模型之預測結果做比較。研究的結果顯示，『小波神經網路多尺度解析混合預測模型』可準確地預測非定性時間序列，其預測結果較前兩者比較模型準確，並具有參考價值可提供制訂決策之參考。

Traditional time series analysis methodologies are based on probability and statistics with the assumption of stationary and linear properties. However, the system dynamic of time series usually arise with highly nonlinear and non-stationary properties, these conventional time series forecasting models cannot satisfy the feasibility and accuracy of which research desires. Consequently, the “multi-resolution wavelet neural network hybrid forecasting model,” capable of adaptive forecasting non-stationary time series, is proposed in this research. The original time series is decomposed into subsequences in different resolution scale using the wavelet decomposition, which is efficient in processing chaotic signals. Furthermore, combined with the wavelet neural network architecture, which is referred to an universal function approximator, to establish the time series forecasting model, and expect this model to predict accurately and conquer the restriction of the traditional models when encounter non-stationary time series. The TAIEX of Taiwan stock market index is used for one and five day ahead forecasting of close price and price change to demonstrate the proposed model. Two other forecast results, one is obtained from traditional autoregressive model, and the other is without using the wavelet decomposition, were also used to compare with the proposed model. The experimental results indicate that the multi-resolution wavelet neural network hybrid forecasting model can accurately predict non-stationary financial time series and provide a valuable reference for making investing decision.