使用總體經驗模態分解法與均勻相位經驗模態分解法對美國債券殖利率建模

Abstract

在過去的研究當中，我們發現財金的時間序列相關的資料，存在著非線性與非定態的現象。我們認為不同到期期間的美國債券殖利率曲線也存在著非線性與非定態。傳統上，財金領域的學者對於時間序列相關資料的研究，大多使用時間序列的分析模型進行建模，不過使用時間序列分析模型的限制是所欲分析的標的必須是定態的資料。如果原始資料為非定態，一般會使用差分使其轉換成定態的資料。不過此種處理模式會使得原始資料損失一些重要資訊，比方說資料序列中低頻率部分的資訊。經驗模態分解法被認為可以針對非線性與非定態的時間序列資列進行拆解與分析，並有良好的結果。總體經驗模態分解法更進一步修正了經驗模態分解法的一些缺點，而均勻相位經驗模態分解法解決了總體經驗模態分解法模式分割的問題。\n\n在本研究中，我們使用了總體經驗模態分解法與均勻相位經驗模態分解法拆解不同到期期間的美國債券殖利率曲線，並建立預測模型。此外，我們發現邊界條件對於總體經驗模態分解法有很嚴重的影響，因此我們建立了三種型態的模型，其中包含了有修正邊界條件的模型與未修正邊界條件的模型。在我們以總體經驗模態分解法與均勻相位經驗模態分解法拆解完原始資料後，經由本研究所設計的程序，篩選出實用的本徵模函數，再利用立方曲線配適法進行預測。經由預測誤差的比較，本研究發現使用均勻相位經驗模組拆解法篩選出的實用本徵模函數有最好的預測結果。

The existence of nonstationarity and nonlinearity in the financial series is common and difficult to handle. Traditionally, financial researchers apply statistical time series models. However, the series must be stationary in order to apply time series models. If a series is not stationary, it is usually detrend by taking difference although losing certain information such as the low frequency part of the data.\nWe try to model the time series of the U.S. bond yield curves with different maturities, which show the nonstationarity and nonlinearity as well. Other than the statistical models, the empirical decomposition (EMD) is recognized as the suitable mothed to analyze the nonstationarity and nonlinearity time series data among a wide range of scientific disciplines, and is promising for financial data. Nevertheless, there exists the mode-mixing problem in the EMD, hence some approaches are proposed to solve it including the ensemble empirical decomposition (EEMD). The uniform phase empirical decomposition (UPEMD) further improve the EEMD by reducing the mode-splitting and residual noise effects.\nIn the study, we implement the EEMD and the UPEMD to the U.S. bond yield curves with different maturities. The boundary effect of the original data may occur, so that we also consider some methods for boundary effect reduction during the decomposition. After the decomposition, we obtain the useful IMF and predict future values by cubic curve fitting. From our investigation, the UPEMD with boundary condition modification produces the accurate predictions.