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題名 運用向量自我迴歸模型與最大交叉相關預測時間序列
Forecasting of Time Series based on Vector Autoregression Model and Maximum Cross-correlation作者 陳寬旻 貢獻者 洪英超
陳寬旻關鍵詞 領先關係
自我向量迴歸
交叉相關
Wald檢定
預測平方誤差
Granger causality
Vector autoregressive (VAR) model
Cross-correlation
Wald test
Mean prediction squared errors (MPSE)日期 2012 上傳時間 1-Jul-2013 17:01:31 (UTC+8) 摘要 對具時間序列型態的多變量資料進行預測時，模型的選取至關重要。長年以來，文獻中多以向量自我迴歸模型(VAR 模型)進行預測。其缺點是：(i)模型選取複雜；(ii)參數估計不易；(iii)模型假設常不符；(iv)估計模型所需資料量較大。本文提供了一個新的多變量時間序列預測方法，此方法主要建構在最大交叉相關性之上，資料僅需在短期時間內滿足相當程度的線性關係。本文並與時間序列應用相當廣泛的向量自我迴歸模型預測方法做比較，希望提供使用者實務分析上的預測方法選取準則。藉由台灣國內各股票型基金淨值以及各基金所含之股票型投資組合資料，本文比較此二種方法對於基金淨值的波動所提供之預測效果。以各預測方法之預測平方誤差作為評量標準，本文發現利用最大交叉相關的方法之預測效果較向量自我迴歸模型更佳。
The selection of methods plays an important role in the prediction based on time-series data. In most literature reviews, the vector autoregression model(VAR) has been a popular choice for prediction for many years. There are some disadvantages of this method: (i) the model selection procedure can be really complex; (ii) the model assumptions are difficult to validate; (iii) it requires a large amount of data for model building. The objective of this thesis is to provide an new multivariate-time series prediction method based on the concept of maximum cross-correlation. It requires merely the assumption of “fair linearity” between two time series under investigation. This thesis also compares the proposed method to the vector autoregressive (VAR) model which is widely used in time series analysis with the expectation to provide a new prediction method in practical data analysis. We use data from the Taiwan equity funds and the portfolio of those funds to compare the prediction performances of these two methods. Using the mean prediction squared errors (MPSE) as assessment criterion, the prediction method based on the maximum cross-correlation best performs under all prediction periods.參考文獻 [1] H. Boudjellaba, J.N.Dufour and R. Roy (1992). Testing causality between two vectors in multivariate autoregressive moving average models. American Statistical Assocication, 87, pp.1082-1090.[2] P. J. Brockwell and R. A. Davis (2009) Time Series: Theory and Methods, Springer.[3] T. Conlon, H. J. Ruskin, and M. Crane (2010) Cross-Correlation Dynamics in Financial Time Series. Physica A, 388, pp.705-714.[4] P. h. Franses (1998). Time Series Models for Business and Economic Forecasting, Cambridge University Press, Cambridge.[5] M. G. Dekimpe and D. M. Hanssens (1999), Sustained spending and persistent response: A new look at long-term marketing protability, Journal of Marketing Research, 36, pp.397-412.[6] M. G. Dekimpe and D. M. Hanssens (1995) The persistence of marketing effects on sales, Marketing Science, 14, pp.1-21.[7] W. Enders (1995). Applied Econometric Time Series, JohnWiley and Sons, INC., New York.[8] C.W.J. Granger (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Journal of Econometrica, vol. 37, No. 3, pp.424-438.[9] C.W.J. Granger (1980). Testing for causality: a personal viewpoint. Journal of Economic Dynamics and Control, 2, pp.329-352.[10] J. Geweke (1984). Inference and causality in economic time series. In: Griliches Z, Intriligator MM (eds) Handbook of econometrics, vol. 2, pp.1101-1144.[11] C. Horváth, M. Kornelis and P. S. H. Leeang (2002). Whatmarketing scholars should know about time series analysis. SOM Research Report No. 02F17, University of Groningen.[12] C. Horváth, P. S. H. Leeang, J. E. Wieringa and D. R. Wittink (2003). Dynamic analysis of a marketing system based on aggregated and pooled store data. Paper under review.[13] C. Hsiao (1982). Autoregressive modeling and causal ordering of econometric variables. Journal of Economic Dynamics and Control, 4, pp.243-259.[14] Y.C. Hung, N.F. Tseng (2012). Extracting informative variables in the validation of two-group causal relationship, to appear in Computational Statistics. [15] J.F. Hair, W.C. Black, B.J. Babin and R.E. Anderson (2010). Multivariate Analysis, Pearson Education.[16] H. Hotelling (1935). Demand Functions with Limited Budgets. Journal of Econometrica, vol. 3, No. 1, pp.66-78.[17] W.K. Härdle and L. Simar (2012). Applied multivariate statistical analysis, New York, Springer Verlag.[18] M.H. Kutner, C.J. Nachtsheim and J. Neter (2008). Applied linear regression models, McGraw Hill, New York.[19] H. Lütkepohl (2005). New introduction to multiple time series analysis, Springer, Berlin.[20] H. Lütkepohl and M.M. Burda (1997). Modified Wald tests under nonregular conditions. Journal of Econometrica, 78, pp.315-332.[21] H. Lütkepohl (1991). Introduction to Multiple Time Series Analysis. Springer Verlag, Berlin.[22] M. Moriarty and G. Salamon (1980) Estimation and forecast performance of a multivariate time series model of sales, Journal of marketing research, 17, pp.558.[23] S.G. Makridakis, S.C. Wheelwright and V.E. McGee (1983). Forecasting: methods and applications, Wiley, New York.[24] R. Mosconi and C. Giannine (1992). Non-causality in cointegrated system: representation. Estimation and testing. Oxford Bulletin of Economics and Statistics, 54, pp.399-417.[25] D.R. Osborn (1984). Causality testing and its implication for dynamic econometric models. Journal of Econometrica, 94, pp.82-96.[26] J. Pearl (2000). Causality: models, reasoning, and inference. Cambridge University Press, Cambridge.[27] C. A. Sims (1980) Macroeconomics and reality, Journal of Econometrica, 48, pp.1-48.[28] S. Srinivasan and F.M. Bass (2001) Diagnosing competitive responsiveness: Disentangling retailer-induced and manufacturer-induced actions. Paper presented at the MSI Conference on Competitive Responsiveness, Boston.[29] S. M. Simkin (1974) Methods for deriving LOSVDs. Astronomy & Astrophysics, 31, pp.129.[30] H. Takada and F. M. Bass (1998) Multiple time series analysis of competitive marketing behavior, Journal of Business Research, 43, pp.97-107.[31] A. Wald(1939).Contributions to the Theory of Statistical Estimation and Testing Hypotheses". Annals of Mathematical Statistics , vol. 10, pp.299–326.[32] Y. H. Zhang, I. Cagnoni, A. Treves, A. Celotti, and L. Maraschi (2004) The Effects of Periodically Gapped Time Series on Cross-Correlation Lag Determinations. The Astrophysical Journal, 605, pp.98-104.[33] V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral and H.E. Stanley (1999) Universal and nonuniversal properties of cross correlations in financial time series, Physical Review Letters, 83, pp.1471-1474. 描述 碩士
國立政治大學
統計研究所
100354017
101資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100354017 資料類型 thesis dc.contributor.advisor 洪英超 zh_TW dc.contributor.author (Authors) 陳寬旻 zh_TW dc.creator (作者) 陳寬旻 zh_TW dc.date (日期) 2012 en_US dc.date.accessioned 1-Jul-2013 17:01:31 (UTC+8) - dc.date.available 1-Jul-2013 17:01:31 (UTC+8) - dc.date.issued (上傳時間) 1-Jul-2013 17:01:31 (UTC+8) - dc.identifier (Other Identifiers) G0100354017 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58668 - 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) 100354017 zh_TW dc.description (描述) 101 zh_TW dc.description.abstract (摘要) 對具時間序列型態的多變量資料進行預測時，模型的選取至關重要。長年以來，文獻中多以向量自我迴歸模型(VAR 模型)進行預測。其缺點是：(i)模型選取複雜；(ii)參數估計不易；(iii)模型假設常不符；(iv)估計模型所需資料量較大。本文提供了一個新的多變量時間序列預測方法，此方法主要建構在最大交叉相關性之上，資料僅需在短期時間內滿足相當程度的線性關係。本文並與時間序列應用相當廣泛的向量自我迴歸模型預測方法做比較，希望提供使用者實務分析上的預測方法選取準則。藉由台灣國內各股票型基金淨值以及各基金所含之股票型投資組合資料，本文比較此二種方法對於基金淨值的波動所提供之預測效果。以各預測方法之預測平方誤差作為評量標準，本文發現利用最大交叉相關的方法之預測效果較向量自我迴歸模型更佳。 zh_TW dc.description.abstract (摘要) The selection of methods plays an important role in the prediction based on time-series data. In most literature reviews, the vector autoregression model(VAR) has been a popular choice for prediction for many years. There are some disadvantages of this method: (i) the model selection procedure can be really complex; (ii) the model assumptions are difficult to validate; (iii) it requires a large amount of data for model building. The objective of this thesis is to provide an new multivariate-time series prediction method based on the concept of maximum cross-correlation. It requires merely the assumption of “fair linearity” between two time series under investigation. This thesis also compares the proposed method to the vector autoregressive (VAR) model which is widely used in time series analysis with the expectation to provide a new prediction method in practical data analysis. We use data from the Taiwan equity funds and the portfolio of those funds to compare the prediction performances of these two methods. Using the mean prediction squared errors (MPSE) as assessment criterion, the prediction method based on the maximum cross-correlation best performs under all prediction periods. en_US dc.description.tableofcontents 第一章 導論……………………………………………………...……01第二章 運用向量自我迴歸模型預測……………………….….…04第一節 向量自我迴歸模型……………………………………04第二節 領先關係……………………….……………………..…09第三節 領先關係檢定…………………………………....….…11第四節 定態檢定…………………………………………..….…13第三章 運用最大交叉相關預測……………………….……..……19第一節 時間序列的交叉相關……………………….……...…19第二節 運用最大交叉相關預測……………………….….…22第三節 討論…………………………………………..…….….…25第四章 實例分析…………………………………….....................….32第一節 運用向量自我迴歸模型預測………………….….…37第二節 運用最大交叉相關預測………………………..….…39第五章 分析討論………………………...………………………..…48參考文獻………………………………………………………….………54 zh_TW dc.format.extent 2546091 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/#G0100354017 en_US dc.subject (關鍵詞) 領先關係 zh_TW dc.subject (關鍵詞) 自我向量迴歸 zh_TW dc.subject (關鍵詞) 交叉相關 zh_TW dc.subject (關鍵詞) Wald檢定 zh_TW dc.subject (關鍵詞) 預測平方誤差 zh_TW dc.subject (關鍵詞) Granger causality en_US dc.subject (關鍵詞) Vector autoregressive (VAR) model en_US dc.subject (關鍵詞) Cross-correlation en_US dc.subject (關鍵詞) Wald test en_US dc.subject (關鍵詞) Mean prediction squared errors (MPSE) en_US dc.title (題名) 運用向量自我迴歸模型與最大交叉相關預測時間序列 zh_TW dc.title (題名) Forecasting of Time Series based on Vector Autoregression Model and Maximum Cross-correlation en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [1] H. Boudjellaba, J.N.Dufour and R. Roy (1992). Testing causality between two vectors in multivariate autoregressive moving average models. American Statistical Assocication, 87, pp.1082-1090.[2] P. J. Brockwell and R. A. Davis (2009) Time Series: Theory and Methods, Springer.[3] T. Conlon, H. J. Ruskin, and M. Crane (2010) Cross-Correlation Dynamics in Financial Time Series. Physica A, 388, pp.705-714.[4] P. h. Franses (1998). Time Series Models for Business and Economic Forecasting, Cambridge University Press, Cambridge.[5] M. G. Dekimpe and D. M. Hanssens (1999), Sustained spending and persistent response: A new look at long-term marketing protability, Journal of Marketing Research, 36, pp.397-412.[6] M. G. Dekimpe and D. M. Hanssens (1995) The persistence of marketing effects on sales, Marketing Science, 14, pp.1-21.[7] W. Enders (1995). Applied Econometric Time Series, JohnWiley and Sons, INC., New York.[8] C.W.J. Granger (1969). Investigating Causal Relations by Econometric Models and Cross-spectral Methods. Journal of Econometrica, vol. 37, No. 3, pp.424-438.[9] C.W.J. Granger (1980). Testing for causality: a personal viewpoint. Journal of Economic Dynamics and Control, 2, pp.329-352.[10] J. Geweke (1984). Inference and causality in economic time series. In: Griliches Z, Intriligator MM (eds) Handbook of econometrics, vol. 2, pp.1101-1144.[11] C. Horváth, M. Kornelis and P. S. H. Leeang (2002). Whatmarketing scholars should know about time series analysis. SOM Research Report No. 02F17, University of Groningen.[12] C. Horváth, P. S. H. Leeang, J. E. Wieringa and D. R. Wittink (2003). Dynamic analysis of a marketing system based on aggregated and pooled store data. Paper under review.[13] C. Hsiao (1982). Autoregressive modeling and causal ordering of econometric variables. Journal of Economic Dynamics and Control, 4, pp.243-259.[14] Y.C. Hung, N.F. Tseng (2012). Extracting informative variables in the validation of two-group causal relationship, to appear in Computational Statistics. [15] J.F. Hair, W.C. Black, B.J. Babin and R.E. Anderson (2010). Multivariate Analysis, Pearson Education.[16] H. Hotelling (1935). Demand Functions with Limited Budgets. Journal of Econometrica, vol. 3, No. 1, pp.66-78.[17] W.K. Härdle and L. Simar (2012). Applied multivariate statistical analysis, New York, Springer Verlag.[18] M.H. Kutner, C.J. Nachtsheim and J. Neter (2008). Applied linear regression models, McGraw Hill, New York.[19] H. Lütkepohl (2005). New introduction to multiple time series analysis, Springer, Berlin.[20] H. Lütkepohl and M.M. Burda (1997). Modified Wald tests under nonregular conditions. Journal of Econometrica, 78, pp.315-332.[21] H. Lütkepohl (1991). Introduction to Multiple Time Series Analysis. Springer Verlag, Berlin.[22] M. Moriarty and G. Salamon (1980) Estimation and forecast performance of a multivariate time series model of sales, Journal of marketing research, 17, pp.558.[23] S.G. Makridakis, S.C. Wheelwright and V.E. McGee (1983). Forecasting: methods and applications, Wiley, New York.[24] R. Mosconi and C. Giannine (1992). Non-causality in cointegrated system: representation. Estimation and testing. Oxford Bulletin of Economics and Statistics, 54, pp.399-417.[25] D.R. Osborn (1984). Causality testing and its implication for dynamic econometric models. Journal of Econometrica, 94, pp.82-96.[26] J. Pearl (2000). Causality: models, reasoning, and inference. Cambridge University Press, Cambridge.[27] C. A. Sims (1980) Macroeconomics and reality, Journal of Econometrica, 48, pp.1-48.[28] S. Srinivasan and F.M. Bass (2001) Diagnosing competitive responsiveness: Disentangling retailer-induced and manufacturer-induced actions. Paper presented at the MSI Conference on Competitive Responsiveness, Boston.[29] S. M. Simkin (1974) Methods for deriving LOSVDs. Astronomy & Astrophysics, 31, pp.129.[30] H. Takada and F. M. Bass (1998) Multiple time series analysis of competitive marketing behavior, Journal of Business Research, 43, pp.97-107.[31] A. Wald(1939).Contributions to the Theory of Statistical Estimation and Testing Hypotheses". Annals of Mathematical Statistics , vol. 10, pp.299–326.[32] Y. H. Zhang, I. Cagnoni, A. Treves, A. Celotti, and L. Maraschi (2004) The Effects of Periodically Gapped Time Series on Cross-Correlation Lag Determinations. The Astrophysical Journal, 605, pp.98-104.[33] V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral and H.E. Stanley (1999) Universal and nonuniversal properties of cross correlations in financial time series, Physical Review Letters, 83, pp.1471-1474. zh_TW
