經驗解構法與台灣經濟成長之預測

本文應用Huang et al.（1998）針對非線性及非定態時間序列的經驗解構法（empirical mode decomposition, EMD），對台灣實質國內生產毛額序列解構並進行預測。我們發現經驗解構法能成功地將台灣實質國內生產毛額序列分解成數個正交、定態循環的實證基底數列，以及潛在可能存在非線型的局部時間趨勢（local trend）。特別的是，EMD所解構出來的本質模態函數（intrinsic mode functions, IMF），可以在總體經濟研究中被廣為使用的HP濾波法（Hodrick-Prescott filter）特定的參數下找到相對應的分身。不僅如此，由於所得的基底數列遵循一定的定態循環走勢，利用定態時間序列對基底函數建模，可以容易地對該原始非定態數列進行預測。因此，本文的方法與一般先差分再對差分數列（成長或報酬率）配適模型、預測的常規有本質上的不同：因為經驗解構，我們得以考慮、納入原始數列解構後所有成份數列所反映的動態性質與資訊內涵於預測，而避免因為對資料差分造成對預測有攸關性的資訊漏損，從而影響預測績效。在實證上，我們以國內實質生產毛額為對象，直接將預測表現與近來文獻上不同的經濟預測方法做比較。我們的初步結果顯示，應用EMD解構台灣經濟成長進行相關的預測，不僅簡單而且有不錯的預測表現。

關鍵字

經濟成長； HP濾波法；預測方法；經驗解構

並列摘要

We use the empirical mode decomposition (EMD), specifically designed for decomposing nonstationary and nonlinear series by Huang et al. (1998), to disentangle and forecast Taiwan's real GDP growth. We find that the real GDP could be decomposed into six stationary and near-orthogonal intrinsic mode functions (IMFs), along with a nonlinear trend. Specifically, some IMFs have cyclical patterns similar to the Hodrick-Prescott filtered real GDP series under certain smoothing parameters. Based on the empirical stationarity and near-orthogonality of the IMFs, we can estimate and forecast these component series easily through simple time series models. In particular, our approach differs from the typical difference-first-then-fit recipes in that it retains all information and dynamic content of the original series instead of discarding partial information, which can be relevant for anticipating futures, due to differencing. By comparing with the other popular methodologies, linear or nonlinear, in predicting Taiwan's real GDP quarterly growth, our empirical results confirm the superior yet simple forecasting performance of the new approach.