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題名 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
Modeling the U.S. Yield Curves with Different Maturities by The EEMD and the UPEMD
作者 姜林宗叡
Tsung-Jui, Chiang Lin
貢獻者 蔡尚岳<br>曾正男
Tsai,Shang-Yueh<br>Tzeng, Jengnan
姜林宗叡
Tsung-Jui, Chiang Lin
關鍵詞 總體經驗模態分解法
均勻相位經驗模態分解法
美國債券殖利率曲線
非線性現象
非定態現象
nonlinearity
the ensemble empirical decomposition (EEMD)
the uniform phase empirical decomposition (UPEMD)
the U.S. bond yield curves
nonstationarity
日期 2020
上傳時間 2-Sep-2020 12:16:37 (UTC+8)
摘要 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。

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.
We 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.
In 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.
參考文獻 Reference

Abhyankar, A., Copeland, L. S., and Wong, W. (1995). Nonlinear dynamics in real-time equity market indices: Evidence from the United Kingdom. The Economic Journal, 105(431), 864-880.

Abhyankar, A., Copeland, L. S., and Wong, W. (1997). Uncovering nonlinear structure in real-time stock-market indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100. Journal of Business & Economic Statistics, 15(1), 1-14.

Box, G. E., Jenkins, G. M., Reinsel, G. C., and Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control. John Wiley & Sons.

Cheng, C. H. and Wei, L. Y. (2014). A novel time-series model based on empirical mode decomposition for forecasting TAIEX. Economic Modelling, 36, 136-141.

Diebold, F. X., Rudebusch, G. D., and Aruoba, B. S. (2006). The macroeconomy and the yield curve: A dynamic latent factor approach. Journal of Econometrics 127 (1–2), 309–338.

Fama, E. F. (1991). Efficient capital markets: II. The journal of finance, 46(5), 1575-1617.



Huang, N. E., Shen, Z., Long, S. R., Wu, M. L., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C., and Liu, H. H. (1998), The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. Roy. Soc. London A, 454, pp. 903–995.


Lake, D. E., Richman, J. S., Griffin, M. P., and Moorman, J. R. (2002). Sample entropy analysis of neonatal heart rate variability. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 283(3), R789-R797.

Li, G., Yang, Z., and Yang, H. (2018). Noise reduction method of underwater acoustic signals based on uniform phase empirical mode decomposition, amplitude-aware permutation entropy, and Pearson correlation coefficient. Entropy, 20(12), 918.

Mönch, E. (2008). Forecasting the yield curve in a data-rich environment: A no-arbitrage factor-augmented VAR approach. Journal of Econometrics, 146(1), 26-43.

Nelson, C. R. and Siegel, A. F. (1987). Parsimonious modeling of yield curves. Journal of Business, 473-489.


Pincus, S. (1995). Approximate entropy (ApEn) as a complexity measure. Chaos: An Interdisciplinary Journal of Nonlinear Science, 5(1), 110-117.



Wang, Y. H., Hu, K., and Lo, M. T. (2018). Uniform phase empirical mode decomposition: An optimal hybridization of masking signal and ensemble approaches. IEEE Access, 6, 34819-34833.



Wang, Y. H., Yeh, C. H., Young, H. W. V., Hu, K., and Lo, M. T. (2014), On the computational complexity of the empirical mode decomposition algorithm. Physica A: Statistical Mechanics and Its Applications, 400(15), pp. 159-167.


Wu, Z. and Huang, N. E. (2009), Ensemble empirical mode decomposition: A noise-assisted data analysis method. Advances in Adaptive Data Analysis, 1, pp. 1-41.

Yeh, J. R., Shieh, J. S., and Huang, N. E. (2010), Complementary ensemble empirical mode decomposition: A novel noise enhanced data analysis method. Advances in Adaptive Data Analysis, 2(2), pp. 135–156.

Zhang, C., & Pan, H. (2015, December). A novel hybrid model based on EMD-BPNN for forecasting US and UK stock indices. In 2015 IEEE International Conference on Progress in Informatics and Computing (PIC) (pp. 113-117). IEEE.

Zhan, L., & Li, C. (2017). A comparative study of empirical mode decomposition-based filtering for impact signal. Entropy, 19(1), 13.
描述 碩士
國立政治大學
應用物理研究所
106755001
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0106755001
資料類型 thesis
dc.contributor.advisor 蔡尚岳<br>曾正男zh_TW
dc.contributor.advisor Tsai,Shang-Yueh<br>Tzeng, Jengnanen_US
dc.contributor.author (Authors) 姜林宗叡zh_TW
dc.contributor.author (Authors) Tsung-Jui, Chiang Linen_US
dc.creator (作者) 姜林宗叡zh_TW
dc.creator (作者) Tsung-Jui, Chiang Linen_US
dc.date (日期) 2020en_US
dc.date.accessioned 2-Sep-2020 12:16:37 (UTC+8)-
dc.date.available 2-Sep-2020 12:16:37 (UTC+8)-
dc.date.issued (上傳時間) 2-Sep-2020 12:16:37 (UTC+8)-
dc.identifier (Other Identifiers) G0106755001en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/131637-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用物理研究所zh_TW
dc.description (描述) 106755001zh_TW
dc.description.abstract (摘要) 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。

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。		zh_TW
dc.description.abstract (摘要) 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.
We 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.
In 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.		en_US
dc.description.tableofcontents TABLE　OF　CONTENTS
English abstract i
Chinese abstract ii
Table of contents iii
List of tables v
List of figures vi

1. Introduction------------------------------------------------------------------------- 1
1.1 Background--------------------------------------------------------------------1
1.2 Motivation---------------------------------------------------------------------2
2. Literature review---------------------------------------------------------------------4
3. Methodology-------------------------------------------------------------------------6
3.1 Basic mathematical process---------------------------------------------------6
3.1.1 Empirical mode decomposition (EMD)---------------------------------6
3.1.2 Ensemble empirical mode decomposition (EEMD)--------------------7
3.1.3 Uniform phase empirical mode decomposition (UPEMD)------------9
3.1.4 Sample entropy (SampEn)-------------------------------------------------10
3.1.5 Augmented Dickey–Fuller test (ADF test) ------------------------------10
3.1.6 Poincaré plot-----------------------------------------------------------------11
3.1.7 Curve fitting-----------------------------------------------------------------12
3.2 Statistical measures-------------------------------------------------------------12
3.2.1 Power percentage-----------------------------------------------------------12
3.2.2 Computed period------------------------------------------------------------13
3.2.3 Pearson correlation---------------------------------------------------------13
3.2.4 The measures of error------------------------------------------------------13
4. Empirical Study-----------------------------------------------------------------------14
4.1 Data description------------------------------------------------------------------14
4.2 Descriptive statistics and the stationarity--------------------------------------15
4.3 The result of the Poincaré graph-----------------------------------------------17
4.4 Model specification-------------------------------------------------------------19
4.5 The procedure of data analysis-------------------------------------------------20
4.6 Results-----------------------------------------------------------------------------23
4.6.1 The IMFs----------------------------------------------------------------------23
4.6.2 The power percentage and the sample entropy---------------------------34
4.6.3 The calculated period and correlation coefficient-----------------------------41
4.6.4 The prediction---------------------------------------------------------------------45
5. Conclusion--------------------------------------------------------------------------------50

Appendix----------------------------------------------------------------------------------52
A1. Statistical measures of Model 1----------------------------------------------------52
A2. Statistical measures of Model 2----------------------------------------------------56
A3. Statistical measures of Model 3----------------------------------------------------60
Reference----------------------------------------------------------------------------------64






LIST OF TABLES

Table 1 Means and standard deviations of the bond yield curves----------16
Table 2 ADF test for the bond yield curves-----------------------------------16
Table 3 The sample entropy for each replicate of the synthetic data------23
Table 4 MO3 EEMD with boundary modified (mirror method)-----------42
Table 5 Yr5 EEMD with boundary modified (mirror method)-------------42
Table 6 Yr30 EEMD with boundary modified (mirror method)-----------42
Table 7 MO3 (EEMD with no boundary modified)-------------------------43
Table 8 Yr5 (EEMD with no boundary modified)---------------------------43
Table 9 Yr30 (EEMD with no boundary modified)-------------------------43
Table 10 MO3 (UPEMD)---------------------------------------------------------44
Table 11 Yr5 (UPEMD)----------------------------------------------------------44
Table 12 Yr30 (UPEMD)--------------------------------------------------------44
Table 13 The average RMSE and MAE of all models for different maturities ---------------------------------------------------------------49









LIST OF FIGURES

Figure 1 Bond yield with maturities ----------------------------------------14
Figure 2 The Poincaré plot of MO1 ----------------------------------------17
Figure 3 The Poincaré plot of MO6 ----------------------------------------18
Figure 4 The Poincaré plot of Yr5------------------------------------------18
Figure 5 The Poincaré plot of Yr30-----------------------------------------19
Figure 6 The research flow of data analysis--------------------------------20
Figure 7 The IMFs of MO3 of Model 1 in the first segment-------------25
Figure 8 The IMFs of Yr3 of Model 1 in the first segment---------------26
Figure 9 The IMFs of Yr30 of Model 1 in the first segment--------------27
Figure 10 The IMFs of MO3 of Model 2 in the first segment--------------28
Figure 11 The IMFs of Yr3 of Model 2 in the first segment----------------29
Figure 12 The IMFs of Yr30 of Model 2 in the first segment---------------30
Figure 13 The IMFs of MO3 of Model 3 in the first segment---------------31
Figure 14 The IMFs of Yr3 of Model 3 in the first segment-----------------32
Figure 15 The IMFs of Yr30 of Model 3 in the first segment---------------33
Figure 16 The power percentage of MO3 of Model 1------------------------35
Figure 17 The power percentage of Yr3 of Model 1-------------------------35
Figure 18 The power percentage of Yr30 of Model 1------------------------35
Figure 19 The power percentage of MO3 of Model 2------------------------36
Figure 20 The power percentage of Yr3 of Model 2--------------------------36
Figure 21 The power percentage of Yr30 of Model 2------------------------36
Figure 22 The power percentage of MO3 of Model 3------------------------37
Figure 23 The power percentage of Yr3 of Model 3--------------------------37
Figure 24 The power percentage of Yr30 of Model 3------------------------37
Figure 25 The sample entropy of MO3 of Model 1---------------------------38
Figure 26 The sample entropy of Yr3 of Model 1-----------------------------38
Figure 27 The sample entropy of Yr30 of Model 1---------------------------38
Figure 28 The sample entropy of MO3 of Model 2---------------------------39
Figure 29 The sample entropy of Yr3 of Model 2-----------------------------39
Figure 30 The sample entropy of Yr30 of Model 2---------------------------39
Figure 31 The sample entropy of MO3 of Model 3---------------------------40
Figure 32 The sample entropy of Yr3 of Model 3-----------------------------40
Figure 33 The sample entropy of Yr30 of Model 3---------------------------40
Figure 34 Predicted errors of all models for MO1---------------------------46
Figure 35 Predicted errors of all models for MO3---------------------------46
Figure 36 Predicted errors of all models for Yr1-----------------------------47
Figure 37 Predicted errors of all models for Yr2-----------------------------47
Figure 38 Predicted errors of all models for Yr3-----------------------------47
Figure 39 Predicted errors of all models for Yr7-----------------------------48
Figure 40 Predicted errors of all models for Yr10----------------------------48
Figure 41 Predicted errors of all models for Yr20----------------------------48
Figure 42 Predicted errors of all models for Yr30----------------------------49
Figure 43 Mean errors of all models for different maturities---------------50		zh_TW
dc.format.extent 6605293 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0106755001en_US
dc.subject (關鍵詞) 總體經驗模態分解法zh_TW
dc.subject (關鍵詞) 均勻相位經驗模態分解法zh_TW
dc.subject (關鍵詞) 美國債券殖利率曲線zh_TW
dc.subject (關鍵詞) 非線性現象zh_TW
dc.subject (關鍵詞) 非定態現象zh_TW
dc.subject (關鍵詞) nonlinearityen_US
dc.subject (關鍵詞) the ensemble empirical decomposition (EEMD)en_US
dc.subject (關鍵詞) the uniform phase empirical decomposition (UPEMD)en_US
dc.subject (關鍵詞) the U.S. bond yield curvesen_US
dc.subject (關鍵詞) nonstationarityen_US
dc.title (題名) 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zh_TW
dc.title (題名) Modeling the U.S. Yield Curves with Different Maturities by The EEMD and the UPEMDen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Reference

Abhyankar, A., Copeland, L. S., and Wong, W. (1995). Nonlinear dynamics in real-time equity market indices: Evidence from the United Kingdom. The Economic Journal, 105(431), 864-880.

Abhyankar, A., Copeland, L. S., and Wong, W. (1997). Uncovering nonlinear structure in real-time stock-market indexes: The S&P 500, the DAX, the Nikkei 225, and the FTSE-100. Journal of Business & Economic Statistics, 15(1), 1-14.

Box, G. E., Jenkins, G. M., Reinsel, G. C., and Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control. John Wiley & Sons.

Cheng, C. H. and Wei, L. Y. (2014). A novel time-series model based on empirical mode decomposition for forecasting TAIEX. Economic Modelling, 36, 136-141.

Diebold, F. X., Rudebusch, G. D., and Aruoba, B. S. (2006). The macroeconomy and the yield curve: A dynamic latent factor approach. Journal of Econometrics 127 (1–2), 309–338.

Fama, E. F. (1991). Efficient capital markets: II. The journal of finance, 46(5), 1575-1617.



Huang, N. E., Shen, Z., Long, S. R., Wu, M. L., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C., and Liu, H. H. (1998), The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. Roy. Soc. London A, 454, pp. 903–995.


Lake, D. E., Richman, J. S., Griffin, M. P., and Moorman, J. R. (2002). Sample entropy analysis of neonatal heart rate variability. American Journal of Physiology-Regulatory, Integrative and Comparative Physiology, 283(3), R789-R797.

Li, G., Yang, Z., and Yang, H. (2018). Noise reduction method of underwater acoustic signals based on uniform phase empirical mode decomposition, amplitude-aware permutation entropy, and Pearson correlation coefficient. Entropy, 20(12), 918.

Mönch, E. (2008). Forecasting the yield curve in a data-rich environment: A no-arbitrage factor-augmented VAR approach. Journal of Econometrics, 146(1), 26-43.

Nelson, C. R. and Siegel, A. F. (1987). Parsimonious modeling of yield curves. Journal of Business, 473-489.


Pincus, S. (1995). Approximate entropy (ApEn) as a complexity measure. Chaos: An Interdisciplinary Journal of Nonlinear Science, 5(1), 110-117.



Wang, Y. H., Hu, K., and Lo, M. T. (2018). Uniform phase empirical mode decomposition: An optimal hybridization of masking signal and ensemble approaches. IEEE Access, 6, 34819-34833.



Wang, Y. H., Yeh, C. H., Young, H. W. V., Hu, K., and Lo, M. T. (2014), On the computational complexity of the empirical mode decomposition algorithm. Physica A: Statistical Mechanics and Its Applications, 400(15), pp. 159-167.


Wu, Z. and Huang, N. E. (2009), Ensemble empirical mode decomposition: A noise-assisted data analysis method. Advances in Adaptive Data Analysis, 1, pp. 1-41.

Yeh, J. R., Shieh, J. S., and Huang, N. E. (2010), Complementary ensemble empirical mode decomposition: A novel noise enhanced data analysis method. Advances in Adaptive Data Analysis, 2(2), pp. 135–156.

Zhang, C., & Pan, H. (2015, December). A novel hybrid model based on EMD-BPNN for forecasting US and UK stock indices. In 2015 IEEE International Conference on Progress in Informatics and Computing (PIC) (pp. 113-117). IEEE.

Zhan, L., & Li, C. (2017). A comparative study of empirical mode decomposition-based filtering for impact signal. Entropy, 19(1), 13.		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU202001401en_US