經驗解構法與台灣經濟成長之預測

Empirical Decomposition and Economic Growth Forecasting

10.29628/AEP.201212.0004

葉錦徽(Jin-Huei Yeh)；程英賓(Nick Y. P. Cheng)；王景南(Jying-Nan Wang)

經濟成長 ； HP濾波法 ； 預測方法 ； 經驗解構 ； Economic growth ； H-P filter ； Forecasting ； Empirical decomposition

經濟論文

40卷4期（2012 / 12 / 01）

559 - 598

繁體中文

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。

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.

1. 徐士勛、管中閔、羅雅惠(2005)。以擴散指標為基礎之總體經濟預測。台灣經濟預測與政策，36，1-28。
   連結：
2. 陳宜廷、徐士勛、劉瑞文、莊額嘉(2011)。經濟成長率預測之評估與更新。經濟論文叢刊，39，1-44。
   連結：
3. 黃裕烈、徐之強(2004)。行政院經濟建設委員會研究計畫行政院經濟建設委員會研究計畫,未出版
   連結：
4. Burns, A. and W. Mitchell (1946), Measuring Business Cycle Turning Points, New York: National Bureau of Economic Research.
5. Bai, J.(2003).Inferential Theory for Factor Models of Large Dimensions.Econometrica,71,135-171.
6. Bai, J.,Ng, S.(2002).Determining the Number of Factor in Approximate Factor Models.Econometrica,70,191-221.
7. Bai, J.,Ng, S.(2008).Forecasting Economic Time Series Using Targeted Predictors.Journal of Econometrics,146,304-317.
8. Baxter, M.,King, R. G.(1999).Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series.Review of Economics and Statistics,81,575-593.
9. Clark, T. E.,McCracken, M. W.(2006).The Predictive Content of the Output Gap for Inflation: Resolving In-Sample and Out-of-Sample Evidence.Journal of Money Credit and Banking,38,1127-1148.
10. Diebold, F. X.,Mariano, R. S.(1995).Comparing Predictive Accuracy.Journal of Business and Economic Statistics,13,253-263.
11. Diebold, F. X.,Rudebusch, G. D.(1996).Measuring Business Cycles: A Modern Perspective.Review of Economics and Statistics,78,67-77.
12. Durland, J. M.,McCurdy, T. H.(1994).Duration-Dependent Transitions in a Markov Model of U.S. GNP Growth.Journal of Business and Economic Statistics,12,279-288.
13. Filardo, A. J.,Gordon, S. F.(1998).Business Cycle Durations.Journal of Econometrics,85,99-123.
14. Forni, M.,Hallin, M.,Lippi, M.,Reichlin, L.(2000).The Generalized Dynamic-Factor Model: Identification and Estimation.The Review of Economics and Statistics,82,540-554.
15. Geweke, J.(1977).The Dynamic Factor Analysis of Economic Time Series Models.Latent Variables in Socioeconomic Models,Amsterdam:
16. Hamilton, J. D.(1989).A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle.Econometrica,57,357-384.
17. Hansen, B. E.(1992).The Likelihood Ratio Test under Nonstandard Conditions: Test the Markov Switching Model of GNP.Journal of Applied Econometrics,7,61-82.
18. Harvey, D.,Leybourne, S.,Newbold, P.(1997).Testing the Equality of Prediction Mean Squared Error.International Journal of Forecasting,13,281-291.
19. Hodrick, R. J.,Prescott, E. C.(1997).Postwar U.S. Business Cycles: An Empirical Investigation.Journal of Money, Credit, and Banking,29,1-16.
20. Hornik, K.,Stinchocombe, M.,White, H.(1989).Multilayer Feed Forward Networks Are Universal Approximators.Neural Networks,2,359-366.
21. Huang, N. E.,Shen, Z.,Long, S. R.,Wu, M. C.,Shih, H. H.,Zheng, Q.,Yen, N. C.,Tung, C. C.,Liu, H. H.(1998).The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis.Proc. R. Soc. London,A454,903-993.
22. Huang, N. E.,Wu, M. C.,Long, S. R.,Shen, S. S. P.,Qu, W.,Glosersen, P.,Fan, K. L.(2003).A Confidence Limit for Empirical Mode Decomposition and Hilbert Spectral Analysis.Proc. R. Soc. London,A459,2317-2345.
23. Kim, C.-J.,Nelson, C. R.(1999).State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications.Cambridge, MA:MIT Press.
24. Mark, N.(1995).Exchange Rates and Fundamentals: Evidence on Long-Horizon Predictability.American Economic Review,85,201-218.
25. Nelson, C. R.,Plosser, C. R.(1982).Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications.Journal of Monetary Economics,10,139-162.
26. Newey, W. K.,West, K. D.(1987).Hypothesis Testing with Efficient Method of Moments Estimation.International Economic Review,28,777-787.
27. Sargent, T. J.,Sims, C. A.(1977).Business Cycle Modeling without Pretending to Have Too Much a Priori Theory.New Methods in Business Cycle Research: Proceedings from a Conference,Minneapolis, MN:
28. Stock, J. H.(ed.),Watson, M. W.(ed.)(1993).Business Cycles, Indicators and Forecasting.Chicago, IL:University of Chicago Press.
29. Stock, J. H.,Watson, M. W.(1999).Forecasting Inflation.Journal of Monetary Economics,44,293-335.
30. Stock, J. H.,Watson, M. W.(2002).Macroeconomic Forecasting Using Diffusion Indexes.Journal of Business and Economic Statistics,20,147-162.
31. Stock, J. H.,Watson, M. W.(1998).NBER Working PaperNBER Working Paper,未出版
32. Stock, J. H.,Watson, M. W.(2002).Forecasting Using Principal Components from a Large Number of Predictors.Journal of the American Statistical Association,97,1167-1179.
33. Stock, J. H.,Watson, M. W.(2005).NBER Working PaperNBER Working Paper,未出版
34. Stock, J. H.,Watson, M. W.(1991).A Probability Model of the Coincident Economic Indicators.Leading Economic Indicators: New Approaches and Forecasting Records,Cambridge, MA:
35. Stock, J. H.,Watson, M. W.(1989).New Indexes of Coincident and Leading Economic Indicators.NBER Macroeconomics Annual,Cambridge, MA:
36. Wang, X.,Ma, J. J.,Wang, S.,Bi, D. W.(2007).Time Series Forecasting Energy-Efficient Organization of Wireless Sensor Networks.Sensors,7,1766-1792.
37. White, H.(1990).Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can Learn Arbitrary Mappings.Neural Networks,3,535-549.
38. White, H.(1980).A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroscedasticity.Econometrica,48,817-838.
39. Wu, Z.,Huang, N. E.(2004).A Study of the Characteristics of White Noise Using the Empirical Mode Decomposition Method.Proc. R. Soc. London,A460,1597-1611.
40. Xu, X.,Wang, S. Y.,Lai, K. K.(2010).Forecasting Demand of Commodities after Natural Disasters.Expert System with Applications,37,4313-4317.
41. Yogo, M.(2008).Measuring Business Cycles: A Wavelet Analysis of Economic Time Series.Economics Letters,100,208-212.
42. Yu, L.,Wang, S. Y.,Lai, K. K.(2008).Forecasting Crude Oil Price with an EMD-Based Neural Network Ensemble Learning Paradigm.Energy Economics,30,2623-2635.
43. 林向愷、黃裕烈、管中閔(1998)。景氣循環轉折點認定與經濟成長率預測。經濟論文叢刊，26，431-457。
44. 徐士勛、管中閔(2001)。九零年代台灣的景氣循環—馬可夫轉換模型與紀卜斯抽樣法的應用。人文及社會科學集刊，13，515-540。