參考Engle and Rangel(2008)提出的spline-GARCH，本篇文章提出了新的長期波動度的模型建立與預測方式。我們使用Empirical Mode Decomposition(EMD)方法拆解GDP與CPI的季資料得到數個不同頻率且互相獨立的數列。EMD方法有著簡單且適用於任何非線性、非穩態的好處。此外，我們可以觀察到拆解出的GDP成分與景氣循環間的相關性。於是本篇文章將利用這些成分建立隨總體環境變動而演變的財務市場長期波動度，使得短期波動度能在長期下自然的進行結構轉變。進一步，我們利用此架構預測2008與2009年的99%風險值，結果顯示在加入總體資訊的考量之下，長期風險管理的表現將會因此得到改進。

Generalizing the component GARCH by Engle and Rangel (2008), this paper proposes a new modeling and forecasting strategy for systemic risk both in the short term and long run. By utilizing the orthogonally decomposed stationary regularity series from real quarterly GDP and CPI by EMD (Empirical Mode Decomposition), an empirical adaptive decomposition method that entertains nonlinear and nonstationary time series, we demonstrate the close coupling relationship between long run stock market volatility and the business cycle fluctuations. As these component series preserve the most primary information in the macroeconomic state variables sampled at lower frequencies, the long run component volatility is capable of generating regime shift behaviors in daily volatility without resorting to Markov switching or other regime switching mechanisms. Moreover, prediction of future volatility at various horizons is easy within the framework by taking advantage of the stable cyclical pattern of these orthogonalized macro series. Our empirical applications in hedging and evaluating VaR reveals that incorporating information from lower frequency macroeconomic fundamentals did provide incremental value toward the modeling of long run risks.

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