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題名 從假設檢定的觀點探討ARMA模型的參數配適
ARMA Model Selection from Hypothesis Point of View作者 林芸生
Lin, Yun Sheng貢獻者 黃子銘
Huang, Tzee Ming
林芸生
Lin, Yun Sheng關鍵詞 假設檢定
ARMA
Model selection
AIC
BIC
Hypothesis testing日期 2009 上傳時間 5-Sep-2013 15:11:08 (UTC+8) 摘要 本篇論文著重於探討ARMA模型的選模準則，過去較為著名的AIC、BIC等選模準則中，若總參數個數相同，模型選擇便簡化為比較各模型的概似函數在MLE下的值，故本研究將假設檢定定義為檢定總參數個數；截至目前為止，選模準則在使用上以AIC及BIC較為普遍，此兩種選模準則從本研究所定義的假設檢定的觀點來看，AIC犯型一誤差機率高，同時檢定力也高；BIC犯型一誤差的機率極低，同時檢定力也相對不高，本研究從此觀點提出一個選模準則方法，嘗試將上述兩種方法折衷，將型一誤差控制在5%，且檢定力略高於BIC。模擬的結果在理想的情形下皆符合預期，但在真實情形本研究方法涉及第一階段的模型選取，本研究提供兩種第一階段的模型選取方法，模擬的結果顯示，方法一型一誤差略為膨脹，檢定力增幅顯著；方法二型一誤差控制精準，但檢定力表現較差。本研究所提出的方法計算時間較為冗長，但若想將 AIC 及 BIC 方法折衷，可考慮嘗試本研究方法。
This thesis focuses on model selection criteria for ARMA models. For information-based criteria such as AIC and BIC, the task of model selection is reduced to the comparison among likelihood values at maximum likelihood estimates if the numbers of parameters in candidate models are all the same. Thus the key step in model selection is the determination of the total number of parameters. The determination of number of parameters can be addressed using a hypothesis testing approach, where the null hypothesis is that the total number of model parameters is equal to a given number k and the alternative hypothesis is that the total number of parameters is equal to k+1. In this thesis, an information-based model selection method is proposed, where the number of parameters is determined using a two-stage testing procedure, which is constructed with the attempt to control the average type I error probability to be 5%. When using BIC in the above testing problem, simulation results indicate that the average type I error probability for BIC is lower than 0.05, so it is expected the proposed test is more powerful than BIC.The first stage of the proposed test involves selecting the most likely models under the null and the alternative hypothesis respectively. Two methods are considered for the first-stage selection. For the first method, the type I error probability can be larger than 0.05, but the power is significantly larger than BIC. For the second method, the type I error probability is under control, but its power increment is comparatively low. The computing time for the proposed test is rather long. However, for those who need an eclectic method between AIC and BIC, the proposed test can serve as a reasonable choice.參考文獻 Akike, H. (1973), “Information theory and an extension of the maximum likelihood principle”, Budapest, Hungary, 267-281Akike, H. (1978), “A Bayesian analysis of the minimum AIC procedure”, Annals of the Institute of Statistical mathematics, 30(1), 9-14Brockwell, P.J. and Davis, R.A. (2009), “Time series: theory and methods”, Springer VerlagCasella, G. and Berger, R.L. and Berger, R.L. (2002), “Statistical inference”, Duxbury Pacific Grove, CAClarke, B. (2001), “Combining model selection procedures for online prediction”, Sankhy: The Indian Journal of Statistics, Series A, 229--249Hurvich, C.M. and Tsai, C.L. (1989), “Regression and time series model selection in small samples”, Biometrika, 76(2), 297Kullback, S. and Leibler, RA (1951), “On information and sufficiency”, The Annals of Mathematical Statistics, 79-86Reschenhofer , Erhard (2005), “Selecting Selection Methods”, InterStat: Statistics on the Internet, 7(3), 1-17Wagenmakers, E.J. and Grunwald, P. and Steyvers, M. (2006), “Accumulative prediction error and the selection of time series models”, Journal of Mathematical Psychology, 50(2), 149-166Yang, Y. (2005), “Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation”, Biometrika, 92(4), 937溫志宏, 無線通道模型概論, 國立中正大學葉欣甯(2002), 時間序列的選模分析：Cross Validation之應用, 國立清華大學碩士論文 描述 碩士
國立政治大學
統計研究所
97354017
98資料來源 http://thesis.lib.nccu.edu.tw/record/#G0097354017 資料類型 thesis dc.contributor.advisor 黃子銘 zh_TW dc.contributor.advisor Huang, Tzee Ming en_US dc.contributor.author (Authors) 林芸生 zh_TW dc.contributor.author (Authors) Lin, Yun Sheng en_US dc.creator (作者) 林芸生 zh_TW dc.creator (作者) Lin, Yun Sheng en_US dc.date (日期) 2009 en_US dc.date.accessioned 5-Sep-2013 15:11:08 (UTC+8) - dc.date.available 5-Sep-2013 15:11:08 (UTC+8) - dc.date.issued (上傳時間) 5-Sep-2013 15:11:08 (UTC+8) - dc.identifier (Other Identifiers) G0097354017 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/60434 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 97354017 zh_TW dc.description (描述) 98 zh_TW dc.description.abstract (摘要) 本篇論文著重於探討ARMA模型的選模準則，過去較為著名的AIC、BIC等選模準則中，若總參數個數相同，模型選擇便簡化為比較各模型的概似函數在MLE下的值，故本研究將假設檢定定義為檢定總參數個數；截至目前為止，選模準則在使用上以AIC及BIC較為普遍，此兩種選模準則從本研究所定義的假設檢定的觀點來看，AIC犯型一誤差機率高，同時檢定力也高；BIC犯型一誤差的機率極低，同時檢定力也相對不高，本研究從此觀點提出一個選模準則方法，嘗試將上述兩種方法折衷，將型一誤差控制在5%，且檢定力略高於BIC。模擬的結果在理想的情形下皆符合預期，但在真實情形本研究方法涉及第一階段的模型選取，本研究提供兩種第一階段的模型選取方法，模擬的結果顯示，方法一型一誤差略為膨脹，檢定力增幅顯著；方法二型一誤差控制精準，但檢定力表現較差。本研究所提出的方法計算時間較為冗長，但若想將 AIC 及 BIC 方法折衷，可考慮嘗試本研究方法。 zh_TW dc.description.abstract (摘要) This thesis focuses on model selection criteria for ARMA models. For information-based criteria such as AIC and BIC, the task of model selection is reduced to the comparison among likelihood values at maximum likelihood estimates if the numbers of parameters in candidate models are all the same. Thus the key step in model selection is the determination of the total number of parameters. The determination of number of parameters can be addressed using a hypothesis testing approach, where the null hypothesis is that the total number of model parameters is equal to a given number k and the alternative hypothesis is that the total number of parameters is equal to k+1. In this thesis, an information-based model selection method is proposed, where the number of parameters is determined using a two-stage testing procedure, which is constructed with the attempt to control the average type I error probability to be 5%. When using BIC in the above testing problem, simulation results indicate that the average type I error probability for BIC is lower than 0.05, so it is expected the proposed test is more powerful than BIC.The first stage of the proposed test involves selecting the most likely models under the null and the alternative hypothesis respectively. Two methods are considered for the first-stage selection. For the first method, the type I error probability can be larger than 0.05, but the power is significantly larger than BIC. For the second method, the type I error probability is under control, but its power increment is comparatively low. The computing time for the proposed test is rather long. However, for those who need an eclectic method between AIC and BIC, the proposed test can serve as a reasonable choice. en_US dc.description.tableofcontents 第一章 緒論、研究動機 1第二章 文獻回顧 3第一節 假設檢定 3第二節 AIC 3第三節 BIC 4第四節 Kullback-Leiber Distance 4第五節 Selecting Selection Method 5第三章 研究方法 7第四章 模擬結果、分析與討論 12第一節 總參數個數p+q+1=2 12第一小節 Power 13第二小節 Type I error 15第三小節 p+q+1=2 模擬結果 15第二節 總參數個數p+q+1=3 16第一小節 p+q+1=3 模擬結果 17第三節一般情形下本研究方法的型一誤差及檢定力分析 18第一小節 Type I error 19第二小節 Power 22第五章 實際資料分析 26第六章 結論 39參考文獻 41 zh_TW dc.format.extent 860794 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0097354017 en_US dc.subject (關鍵詞) 假設檢定 zh_TW dc.subject (關鍵詞) ARMA en_US dc.subject (關鍵詞) Model selection en_US dc.subject (關鍵詞) AIC en_US dc.subject (關鍵詞) BIC en_US dc.subject (關鍵詞) Hypothesis testing en_US dc.title (題名) 從假設檢定的觀點探討ARMA模型的參數配適 zh_TW dc.title (題名) ARMA Model Selection from Hypothesis Point of View en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) Akike, H. (1973), “Information theory and an extension of the maximum likelihood principle”, Budapest, Hungary, 267-281Akike, H. (1978), “A Bayesian analysis of the minimum AIC procedure”, Annals of the Institute of Statistical mathematics, 30(1), 9-14Brockwell, P.J. and Davis, R.A. (2009), “Time series: theory and methods”, Springer VerlagCasella, G. and Berger, R.L. and Berger, R.L. (2002), “Statistical inference”, Duxbury Pacific Grove, CAClarke, B. (2001), “Combining model selection procedures for online prediction”, Sankhy: The Indian Journal of Statistics, Series A, 229--249Hurvich, C.M. and Tsai, C.L. (1989), “Regression and time series model selection in small samples”, Biometrika, 76(2), 297Kullback, S. and Leibler, RA (1951), “On information and sufficiency”, The Annals of Mathematical Statistics, 79-86Reschenhofer , Erhard (2005), “Selecting Selection Methods”, InterStat: Statistics on the Internet, 7(3), 1-17Wagenmakers, E.J. and Grunwald, P. and Steyvers, M. (2006), “Accumulative prediction error and the selection of time series models”, Journal of Mathematical Psychology, 50(2), 149-166Yang, Y. (2005), “Can the strengths of AIC and BIC be shared? A conflict between model indentification and regression estimation”, Biometrika, 92(4), 937溫志宏, 無線通道模型概論, 國立中正大學葉欣甯(2002), 時間序列的選模分析：Cross Validation之應用, 國立清華大學碩士論文 zh_TW
