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題名 時間數列模式之拔靴模擬法研究
作者 郭玉麟
貢獻者 鄭天澤
郭玉麟
關鍵詞 拔靴法
非常態ARMA(p,q)
最小平方法
bootstrap
non-normal ARMA(p,q)
least-square
日期 1998
上傳時間 21-Apr-2016 09:55:15 (UTC+8)
摘要 本篇文章之主要目的是將Efron於1979年所提出之拔靴法(Bootstrap method)應用在非常態ARMA(p,q)模式上。我們考慮的結構包括AR(1)，AR(2)，MA(1)，MA(2)，ARMA(1,1)，而考慮的非常態干擾分配則包括對數常態分配，均勻分配，迦瑪分配以及指數分配，對每一個模式，所設定之參數值組合涵蓋了使模式平穩及/或可逆之參數組合中的重要區域。我們比較傳統的最小平方法與利用500個拔靴重複子(Bootstrap repetitions)的拔靴法在參數估計上的差異。進一步我們也以MAE及MAPE等準則比較了這兩種估計模式在預測上的優劣。模擬結果顯示，在參數估計方面，當所設定的參數範圍接近非平穩或非可逆條件時，拔靴法所獲得的參數估計值表現會較佳。然而在預測效益方面，利用往前一期預測法，並配合拔靴法重新改造的數列，在具有非常態干擾項AR(1)，AR(2)以及ARMA(1,1)模式的預測效益上的確有較佳的效果。
In this thesis, the Bootstrap technique proposed by Efron in 1979 is applied to parameter estimation and forecasting of non-normal ARMA(p,q) time series models. A simulation study is conducted where artificial time series are generated from various ARMA structures with different non-normal noise distributions. The ARMA structures considered in the simulation are AR(1), AR(2), MA(1), MA(2) and ARMA(1,1), while the non-normal noise distributions include Log-normal, Uniform, Gamma, and Exponential distributions. For each structure, the parameter values used cover important regions of the stationary and/or invertible parameter space . The conventional least-square estimators of the parameters are compared with the corresponding non-parametric Bootstrap estimator, obtained by using 500 Bootstrap repetitions for each series. Furthermore, forecasts based on these estimated model are also compared by using such criteria as MAE and MAPE .
參考文獻 1. Aczel, A. D. and Josephy, N. H. (1992), "Using the bootstrap for Improved ARIMA Model Identification," Journal of Forecasting, 11, 71-80.
2. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C., (1994), Time Series Analysis: Forecasting and Control, U. S. A.: Prentice Hall,
Inc.
3. Chatterjee, S. (1986), "Bootstrap ARMA models: Some Simulations,"IEEE Transactions. on Systems, Man and Cybernetics; U.
SMC 16, 2, 294-297.
4. Efron, B. (1979), "Bootstrap Methods: Another Look at the Jacknife," Annals of Statistics, 7, 1-26.
5. Efron, B. (1982), The Jacknife, the Bootstrap and Other Resampling Plans, SIAM Monograph, No. 38.
6. Efron, B. and Tibshirani, R. J. (1986) "Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy," Statistical Science, 1, 54-77.
7. Efron, B. and Tibshirani, R. J. (1993), An Introduction to the Bootstrap, New York.: Chapman&Hall.
8. Freedman, D. A.,(1981) "Bootstraping regression model", The Annals of Statistics, 9, 1218-28.
9. Freedman, D. A. and Peters, S. C.,(1984)"Bootstraping a regression equation: some empirical results", Journal of the American Statistical Association , 79, 97-106.
10. Holbert, D. and Son, M. S. (1986), "Bootstraping a Time Series Model: Some Empirical Results," Communication in Statistics Theory and Methods, 15(12), 3669-3691.
11.Jeremy Berkowitz and Lutz Kilian(1996), "Recent Developments in Bootstrapping Time Series" .
12. Masarotto, G.(1990), "Bootstrap Prediction Intervals for Autoregressions," International Journal of Forcasting, 6, 229-239.
13. Souza, R. C. and Neto, A. C. (1996), "A Bootstrap Simulation Study in ARMA(p,q) Structure," Journal of Forecasting, 15, 343-53.
14. Stine, R. A. (1987), "Estimating Properties of Autoregressive Forecasts," Journal of the American Statistical Association, 82, 1072-1078.
描述 碩士
國立政治大學
統計學系
86354011
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002001567
資料類型 thesis
dc.contributor.advisor 鄭天澤zh_TW
dc.contributor.author (Authors) 郭玉麟zh_TW
dc.creator (作者) 郭玉麟zh_TW
dc.date (日期) 1998en_US
dc.date.accessioned 21-Apr-2016 09:55:15 (UTC+8)-
dc.date.available 21-Apr-2016 09:55:15 (UTC+8)-
dc.date.issued (上傳時間) 21-Apr-2016 09:55:15 (UTC+8)-
dc.identifier (Other Identifiers) B2002001567en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/85895-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 統計學系zh_TW
dc.description (描述) 86354011zh_TW
dc.description.abstract (摘要) 本篇文章之主要目的是將Efron於1979年所提出之拔靴法(Bootstrap method)應用在非常態ARMA(p,q)模式上。我們考慮的結構包括AR(1)，AR(2)，MA(1)，MA(2)，ARMA(1,1)，而考慮的非常態干擾分配則包括對數常態分配，均勻分配，迦瑪分配以及指數分配，對每一個模式，所設定之參數值組合涵蓋了使模式平穩及/或可逆之參數組合中的重要區域。我們比較傳統的最小平方法與利用500個拔靴重複子(Bootstrap repetitions)的拔靴法在參數估計上的差異。進一步我們也以MAE及MAPE等準則比較了這兩種估計模式在預測上的優劣。模擬結果顯示，在參數估計方面，當所設定的參數範圍接近非平穩或非可逆條件時，拔靴法所獲得的參數估計值表現會較佳。然而在預測效益方面，利用往前一期預測法，並配合拔靴法重新改造的數列，在具有非常態干擾項AR(1)，AR(2)以及ARMA(1,1)模式的預測效益上的確有較佳的效果。zh_TW
dc.description.abstract (摘要) In this thesis, the Bootstrap technique proposed by Efron in 1979 is applied to parameter estimation and forecasting of non-normal ARMA(p,q) time series models. A simulation study is conducted where artificial time series are generated from various ARMA structures with different non-normal noise distributions. The ARMA structures considered in the simulation are AR(1), AR(2), MA(1), MA(2) and ARMA(1,1), while the non-normal noise distributions include Log-normal, Uniform, Gamma, and Exponential distributions. For each structure, the parameter values used cover important regions of the stationary and/or invertible parameter space . The conventional least-square estimators of the parameters are compared with the corresponding non-parametric Bootstrap estimator, obtained by using 500 Bootstrap repetitions for each series. Furthermore, forecasts based on these estimated model are also compared by using such criteria as MAE and MAPE .en_US
dc.description.tableofcontents 附表索引 1
第一章 緒論 2
1.1研究動機與目的 2
1.2 文獻探討 3
第二章、ARMA(P,Q)模式之建立 7
2.1 ARMA(P,Q)模式參數估計 7
2.2 ARMA(P,Q)模式預測 9
第三章 模擬研究 11
3.1 ARMA(P,Q)模式參數估計 13
3.2 ARMA(P,Q)模式預測 15
第四章、模擬結果分析 16
4.1 ARMA(P,Q)模式參數估計 16
4.2 ARMA(P,Q)模式預測 18
第五章、結論 20
參考文獻 21		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002001567en_US
dc.subject (關鍵詞) 拔靴法zh_TW
dc.subject (關鍵詞) 非常態ARMA(p,q)zh_TW
dc.subject (關鍵詞) 最小平方法zh_TW
dc.subject (關鍵詞) bootstrapen_US
dc.subject (關鍵詞) non-normal ARMA(p,q)en_US
dc.subject (關鍵詞) least-squareen_US
dc.title (題名) 時間數列模式之拔靴模擬法研究zh_TW
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 1. Aczel, A. D. and Josephy, N. H. (1992), "Using the bootstrap for Improved ARIMA Model Identification," Journal of Forecasting, 11, 71-80.
2. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C., (1994), Time Series Analysis: Forecasting and Control, U. S. A.: Prentice Hall,
Inc.
3. Chatterjee, S. (1986), "Bootstrap ARMA models: Some Simulations,"IEEE Transactions. on Systems, Man and Cybernetics; U.
SMC 16, 2, 294-297.
4. Efron, B. (1979), "Bootstrap Methods: Another Look at the Jacknife," Annals of Statistics, 7, 1-26.
5. Efron, B. (1982), The Jacknife, the Bootstrap and Other Resampling Plans, SIAM Monograph, No. 38.
6. Efron, B. and Tibshirani, R. J. (1986) "Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy," Statistical Science, 1, 54-77.
7. Efron, B. and Tibshirani, R. J. (1993), An Introduction to the Bootstrap, New York.: Chapman&Hall.
8. Freedman, D. A.,(1981) "Bootstraping regression model", The Annals of Statistics, 9, 1218-28.
9. Freedman, D. A. and Peters, S. C.,(1984)"Bootstraping a regression equation: some empirical results", Journal of the American Statistical Association , 79, 97-106.
10. Holbert, D. and Son, M. S. (1986), "Bootstraping a Time Series Model: Some Empirical Results," Communication in Statistics Theory and Methods, 15(12), 3669-3691.
11.Jeremy Berkowitz and Lutz Kilian(1996), "Recent Developments in Bootstrapping Time Series" .
12. Masarotto, G.(1990), "Bootstrap Prediction Intervals for Autoregressions," International Journal of Forcasting, 6, 229-239.
13. Souza, R. C. and Neto, A. C. (1996), "A Bootstrap Simulation Study in ARMA(p,q) Structure," Journal of Forecasting, 15, 343-53.
14. Stine, R. A. (1987), "Estimating Properties of Autoregressive Forecasts," Journal of the American Statistical Association, 82, 1072-1078.		zh_TW