簡易檢索 / 詳目顯示

研究生: 廖又璉
論文名稱: 多變量ARMA模型選模方法之比較
指導教授: 徐南蓉
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 統計學研究所
Institute of Statistics
論文出版年: 2007
畢業學年度: 95
語文別: 中文
論文頁數: 46
中文關鍵詞: 多變量時間數列選模準則
外文關鍵詞: vector ARMA, final equation form, LASSO, order selection
相關次數: 點閱:1下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • VARMA模型由於能描述變數間的相關性及動態結構,並能有效的預測時間數列的走勢,因此巳被廣泛地應用在各學科中。但由於VARMA模型中有參數數目極多及non-identifiable等問題,因此在統計推論上極為不易,至今仍無一套公認最佳的選模準則及推論方法。有鑑於此,本文回顧過去發展出的數種著名選模方法,逐一介紹,並提出可能的修正方式,期能找出更有效的選模方法。


    第一章 緒論與文獻回顧 1第二章 向量自迴歸移動平均模型 4 2.1 標準式 4 2.2 迴歸式 5 2.3 最終方程式 6 第三章 各類選模方法之介紹與比較 7 3.1 交叉相關矩陣法 7 3.2 偏自迴歸矩陣法 8 3.3 訊息準則法 9 3.4 ESCCM法 10 3.5 SCAN法 13 3.6 HR法 16 3.7 PKK法 18 3.8 綜合比較 21 第四章 LASSO在VARMA選模上的應用 22 4.1 LASSO法 22 4.2 模擬 23 4.2.1 單變量例子 24 4.2.2 多變量例子 31 4.2.3 模擬結論 40 第五章 結論與後續研究 40 參考文獻 41

    Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automation and Control, 19, 716-723

    Barlett, M. S. (1946). On the theoretical specification and sampling properties of
    autocorrelated time series. Journal of the Royal Statistical Society B, 8, 27-41.

    Burg, J. P. (1975). Maximum entropy spectral analysis. PhD dissertation, Stanford University.

    Chenlei, L. , Lin, Y. and Wahba, G.. (2004). A note on the lasso and related procedures in model selection. Technical report.

    Craven, P. and Wahba, G. (1979). Smoothing noisy data with spline functions. Numerische Mathematik, 31, 377-403.

    Dufour, J. M. and Jouini, T. (2005). Asymptotic distribution of a simple linear estimator for VARMA models in echelon form. Statistical Modeling and Analysis for complex data problems , first edition, Springer, New York.

    Dufour, J. M. and Pelletier, D. (2002). Linear methods for estimating varma models with a macroeconomic application. Proceedings of the Business and Economic Statistics Section of the American Statistical Association, Washington, D.C., 2659-2664

    Durbin, J. (1960). The fitting of time-series models. Review of the international Institute of Statistics, 28, 233-244.

    Efron, B., Hastie, T., Johnstone, I. and Tishirani, R. (2004). Least Angle Regression. The Annals of Statistics, 32, 407-451.

    Flores de Frutos, R. and Serrano, G. R. (2002). A generalized least squares estimation method for VARMA models. Statistics, 36(4), 303–316.

    Hannan, E. J. and Deistler, M. (1988). The Statistical Theory of Linear Systems. John Wiley & Sons., New York.

    Hannan, E. J. and Kavalieris, L.(1984a). A method for autoregressive-moving average estimation. Biometrika, 71(2), 273-280.

    Hannan, E. J. and Kavalieris, L. (1984b). Multivariate linear time series models. Advances in Applied Probability, 16, 492–561.

    Hannan, E. J. and Kavalieris, L. (1986). Regression, autoregression models. Journal of Time Series Analysis, 7(1), 27–49.

    Hannan, E. J., Kavalieris, L. and Mackisack, M. (1986). Recursive estimation of linear systems. Biometrika, 73(1), 119–133.

    Hannan, E. J. and Quinn, B.G.. (1979). The determination of the order of an autoregression. Journal of the Royal Statistical Society B, 41, 190-195.

    Hannan, E. J. and Rissanen, R.(1982). Recursive estimation of mixed autoregressive -moving average order. Biometrika, 69, 81-94.

    Jones, R.H. (1978). Multivariate autoregression estimation using residuals. Applied Time Series Analysis, David F. Findley(ed.), Academic Press, New York, 139-162.

    Koreisha, S. G. and Pukkila, T. M. (1989). Fast linear estimation methods for vector autoregressive moving-average models. Journal of Time Series Analysis, 10(4), 325–339.

    Koreisha, S. G. and Pukkila, T. M. (1990a). A generalized least-squares approach for estimation of autoregressive-moving-average models. Journal of Time Series Analysis, 11(2), 139–151.

    Koreisha, S. G. and Pukkila, T. M. (1990b). Linear methods for estimating ARMA and regression models with serial correlation. Communications in Statistics, Part B -Simulation and Computation, 19(1), 71–102.

    Koreisha, S. G. and Pukkila, T. M. (1993). Determining the order of a vector autoregression when the number of component series is large. Journal of Time Series Analysis, 14, 47-69.

    Koreisha, S. G. and Pukkila, T. M. (1995).A comparison between different order- determination criteria for identification of ARIMA models. Journal of Business and Economic Statistics, 13(1), 127–131.

    Koreisha, S. G. and Pukkila, T. M. (2004). The specification of vector autoregressive moving average models.Journal of Statistical Computation and Simulation, 74, 547-565.

    Poskitt, D. S. and Salau, M. O.(1995). On the relationship between generalized least squares and Gaussian estimation of vector ARMA models. Journal of Time Series Analysis, 16, 617-645.

    Pukkila, T. , Koreisha, S. and Kallinen, A. (1990). The identification of ARMA models. Biometrika, 77, 537-548.

    Lütkepohl, H. and Claessen, H. (1997). Analysis of cointegrated VARMA processes. Journal of Econometrics, 80(2), 223–39.

    Lutkepohl, H. (1993). Introduction to multiple time series analysis, second edition, Springer-Verlag, New York.

    Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14, 465-471.

    Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.

    Stein, C. M. (1981), Estimation of the mean of a multivariate normal distribution, The Annals of Statistics, 9,1135-1151.

    Stone, M.(1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society, Series B, 36, 111-147.

    Hsu, N.J. ,Hung, H.L. and Chang, Y. M. (2006). Subset selection for vector autoregressive processes using lasso. Technical report.

    Tiao, G. C. and Tsay, R.S. (1983). Multiple time series modeling and extended sample cross-correlations. Journal of Business and Economic Statistics, 1, 43-56

    Tiao, G.C. and Tsay, R.S. (1985).A canonical correlation approach to modeling multivariate time series". American Statistical Association 1985 Proceedings of the Business and Economic Statistics Section, 112-120.

    Tiao, G. C. and Tsay, R.S. (1989). Model specification in multivariate time series. Journal of the Royal Statistical Society, Series B. 51, 157-213

    Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, 58,267-288.

    Tsay, R.S. and Tiao, G. C. (1984). Consistent estimates of autoregressive parameters and extended sample autocorrelation function for stationary and nonstationary ARMA models. Journal of American Statistical Association, 79, 84-96

    Tsay, R.S. and Tiao, G.C. (1985). Use of Canonical Analysis in Time Series Model Identification. Biometrika,72 ,299-315.

    Tsay, R.S. (1989a). Identifying Multivariate Time Series Models. Journal of Time Series Analysis, 10, 357-372.

    Tsay, R.S. (1989b). Parsimonious Parameterization of Vector Autoregressive Moving Average Models. Journal of Business & Economic Statistics, 7, 327-341.

    Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of American
    Statistical Association, 101, 1418-1429

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE