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題名 雙線性時間序列模式選取之研究
Model Selection of Bilinear Time Series
作者 劉瑞芝
Liou, Ruey Chih
貢獻者 鄭天澤
Jeng, Tian Tzer
劉瑞芝
Liou, Ruey Chih
關鍵詞 雙線性時間序列
模式選取
Bilinear time series
Model selection
日期 1993
上傳時間 29-四月-2016 16:44:14 (UTC+8)
摘要 時間序列在過去二十年當中，受到熱列地討論，而絕大多數的文獻都是研究線性時間序列模式。但在現實生活中，很多時間序列並不符合線性的假設，因此近十年來很多學者致力研究非線性時間序列模式。其中有一種雙線性模式，因其性質與線性模式類似，故引起了廣泛注意。在本篇文章中我們是採用Subba Rao 和Gabr(1984)提出的迭代等式以及高斯－賽德迭代法估計參數，再配合 Subba Rao(1981)提出的巢狀搜尋程序，來選取雙線性模式的階數。將其選模結果與AIC、BIC以及修正後的 PKK 選模法比較。
參考文獻 Bhaskara Rao, [vl., and Subba Rao, T ., and Walker, A.IVl.(1983), "On the
     Existence of some Bilinear Time Series Models," Journal of Time Series
     Analysis, 4,95-110.
     Brockett, R.W.(1976), "Volterra Series and Geometric Control Theory," A•uto`matica,
     12, 167-176.
     Granger, C.W.J.,and Andersen, A.P.(1978),An Introduction to Bilinear Time
     Series Analysis) Vandenhoeck and Ruprecht: Gottingen.
     Haggan, V. and Ozaki) T. (1981) , " rvIodelling Non-linear RanclOln Vi brations
     Using an Amplitude-dependent Autoregressive Tirne Series Model,"
     Biometrika, 68, 189-196.
     Koreisha, S., and Pukklia, T.(1990), "A Generalized Least -Squares Approach
     for Estimation of Autoregressive Moving-Average Models," J ournal
     of Time Series Analysis, 11, 139-151.
     Eumar, K. (1986), "On the Identification of some Bilinear Time Series rdodels,"
     Journal of Ti`me Series Analysis, 7, 117-122.
     Li, W.K. (1984), "On the Autocorrelation Strnct ure and Identification of
     some Bilinear T ime Series," Jo urnal of T i`me S eries Analysis, 5 172-
     181.
     Liu, J., and Brockwell, P,J.(1988), "On the General Bilinear Time Series
     Ivlodels," Journal of Applied Probability, 25, 553-564.
     
     Pham Dinh, T., and Tran, L.(1981), On the First Order Bilinear Time
     Series Moclels," Journal of Applied Probability, 18, 617-627
     Priestley, M.B.(1988),Non-Linear and Non-Stationary Time Series Analysis)
     Academic Press: London.
     Pukkila, T.M., and Koreisha, S., and Kallinen, A.(1990), :`The Identification
     of ARMA Models," Biornetrika, 77, 537-548.
     Pukkila, T,IvI., and Krishnaiah , P.R.(1988), "On the Use of Autorgressive
     Order Determination Criteria in Univariate "White~ oise Tests," IEEE
     Transaction, on Aco`lLstics) Speech, Signal Processing, 36, 764-774.
     Quinn, B. G. (1982), " Stationarity and Invertibility of Simple Bilinear Mod-els, Stochastic Processes and their Applications, 12,225-229.
     Subba Rao, T. (1981), "On the Theory of Bilinear Time Series Model," Jour-nal of The Royal Statistical Society Series B ; 43, 244-255.
     Subba Rao, T., and Eduarda A. da Silva, M.(1992), "Identification of Bilinear
     Time Series Models," Statistica Sinica, 2, 479-494.
     Subba Rao, T., and Gabr, M.M.(1980), `A Test for Linearity of Stationary
     Tinle Series ," Journal of Time Series Analysis, 1, 145-158.
     Subba Rao, T., and Gabr, }VLNI.(1984),An Introd`uction to Bispectral Analysis
     and Bilinear Time Series NIodels) Springer-Verlag: Berlin.
     Tong, H., and Lim, K.S.(1980), "Threshold Autoregression, Limit Cycles
     and Cyclical Data," Journal of The Royal Statistical Society Series
     B, 42,245-2 92.
     Tsay, R.S .(1986), "Nonlinearity Tests for Time Series," Biometrika, 73, 461-
     466.
描述 碩士
國立政治大學
統計學系
G80354019
資料來源 http://thesis.lib.nccu.edu.tw/record/#B2002004203
資料類型 thesis
dc.contributor.advisor 鄭天澤zh_TW
dc.contributor.advisor Jeng, Tian Tzeren_US
dc.contributor.author (作者) 劉瑞芝zh_TW
dc.contributor.author (作者) Liou, Ruey Chihen_US
dc.creator (作者) 劉瑞芝zh_TW
dc.creator (作者) Liou, Ruey Chihen_US
dc.date (日期) 1993en_US
dc.date.accessioned 29-四月-2016 16:44:14 (UTC+8)-
dc.date.available 29-四月-2016 16:44:14 (UTC+8)-
dc.date.issued (上傳時間) 29-四月-2016 16:44:14 (UTC+8)-
dc.identifier (其他 識別碼) B2002004203en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/89028-
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) G80354019zh_TW
dc.description.abstract (摘要) 時間序列在過去二十年當中，受到熱列地討論，而絕大多數的文獻都是研究線性時間序列模式。但在現實生活中，很多時間序列並不符合線性的假設，因此近十年來很多學者致力研究非線性時間序列模式。其中有一種雙線性模式，因其性質與線性模式類似，故引起了廣泛注意。在本篇文章中我們是採用Subba Rao 和Gabr(1984)提出的迭代等式以及高斯－賽德迭代法估計參數，再配合 Subba Rao(1981)提出的巢狀搜尋程序，來選取雙線性模式的階數。將其選模結果與AIC、BIC以及修正後的 PKK 選模法比較。zh_TW
dc.description.tableofcontents 第一章 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
     第二章 雙線性模式
      2.1 向量型式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
      2.2 特殊型式. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
     第三章 模式選取
      3.1 參數估計. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11
      3.2 Subba Rao和Gabr選模法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
      3.3 PKK選模法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
     第四章 模擬結果與分析
      4.1 模擬過程. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
      4.2 Subba Rao和Gabr選模結果與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
      4.3 修正PKK、AIC與BIC選模結果與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .31
     第五章 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .34
     參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44		zh_TW
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#B2002004203en_US
dc.subject (關鍵詞) 雙線性時間序列zh_TW
dc.subject (關鍵詞) 模式選取zh_TW
dc.subject (關鍵詞) Bilinear time seriesen_US
dc.subject (關鍵詞) Model selectionen_US
dc.title (題名) 雙線性時間序列模式選取之研究zh_TW
dc.title (題名) Model Selection of Bilinear Time Seriesen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Bhaskara Rao, [vl., and Subba Rao, T ., and Walker, A.IVl.(1983), "On the
     Existence of some Bilinear Time Series Models," Journal of Time Series
     Analysis, 4,95-110.
     Brockett, R.W.(1976), "Volterra Series and Geometric Control Theory," A•uto`matica,
     12, 167-176.
     Granger, C.W.J.,and Andersen, A.P.(1978),An Introduction to Bilinear Time
     Series Analysis) Vandenhoeck and Ruprecht: Gottingen.
     Haggan, V. and Ozaki) T. (1981) , " rvIodelling Non-linear RanclOln Vi brations
     Using an Amplitude-dependent Autoregressive Tirne Series Model,"
     Biometrika, 68, 189-196.
     Koreisha, S., and Pukklia, T.(1990), "A Generalized Least -Squares Approach
     for Estimation of Autoregressive Moving-Average Models," J ournal
     of Time Series Analysis, 11, 139-151.
     Eumar, K. (1986), "On the Identification of some Bilinear Time Series rdodels,"
     Journal of Ti`me Series Analysis, 7, 117-122.
     Li, W.K. (1984), "On the Autocorrelation Strnct ure and Identification of
     some Bilinear T ime Series," Jo urnal of T i`me S eries Analysis, 5 172-
     181.
     Liu, J., and Brockwell, P,J.(1988), "On the General Bilinear Time Series
     Ivlodels," Journal of Applied Probability, 25, 553-564.
     
     Pham Dinh, T., and Tran, L.(1981), On the First Order Bilinear Time
     Series Moclels," Journal of Applied Probability, 18, 617-627
     Priestley, M.B.(1988),Non-Linear and Non-Stationary Time Series Analysis)
     Academic Press: London.
     Pukkila, T.M., and Koreisha, S., and Kallinen, A.(1990), :`The Identification
     of ARMA Models," Biornetrika, 77, 537-548.
     Pukkila, T,IvI., and Krishnaiah , P.R.(1988), "On the Use of Autorgressive
     Order Determination Criteria in Univariate "White~ oise Tests," IEEE
     Transaction, on Aco`lLstics) Speech, Signal Processing, 36, 764-774.
     Quinn, B. G. (1982), " Stationarity and Invertibility of Simple Bilinear Mod-els, Stochastic Processes and their Applications, 12,225-229.
     Subba Rao, T. (1981), "On the Theory of Bilinear Time Series Model," Jour-nal of The Royal Statistical Society Series B ; 43, 244-255.
     Subba Rao, T., and Eduarda A. da Silva, M.(1992), "Identification of Bilinear
     Time Series Models," Statistica Sinica, 2, 479-494.
     Subba Rao, T., and Gabr, M.M.(1980), `A Test for Linearity of Stationary
     Tinle Series ," Journal of Time Series Analysis, 1, 145-158.
     Subba Rao, T., and Gabr, }VLNI.(1984),An Introd`uction to Bispectral Analysis
     and Bilinear Time Series NIodels) Springer-Verlag: Berlin.
     Tong, H., and Lim, K.S.(1980), "Threshold Autoregression, Limit Cycles
     and Cyclical Data," Journal of The Royal Statistical Society Series
     B, 42,245-2 92.
     Tsay, R.S .(1986), "Nonlinearity Tests for Time Series," Biometrika, 73, 461-
     466.		zh_TW