學術產出-Theses
Article View/Open
Publication Export
-
題名 以非樞紐統計量為基礎之格蘭傑因果關係檢定
Granger Causality Test Based on Non-pivotal Statistics作者 姚惠元
Yao, Huei-Yuan貢獻者 洪英超
Hung, Ying-Chao
姚惠元
Yao, Huei-Yuan關鍵詞 格蘭傑因果關係
Modified Wald 檢定
非樞紐統計量
向量自迴歸
Granger causality
Modified Wald test
Nonpivotal statistic
Vector autoregression日期 2022 上傳時間 1-Aug-2022 17:14:43 (UTC+8) 摘要 格蘭傑因果關係是一個透過結合向量自迴歸模型中所有變數的資訊於衡量兩組時間序列間可預測性的經典統計分析工具，傳統分析格蘭傑因果關係的推論方法為 Wald 類型的檢定方法，然而這些檢定方法可能會面臨以下問題: 一、需要挑選微調參數，二、當預估測之共變異數矩陣為奇異矩陣時，用於推論的臨界值會失效。在這篇論文中，我們發展了一個基於非樞紐統計量的格蘭傑因果關係檢定，此方法不僅避免了以上兩個問題，相較於 Wald 類型的檢定，我們的方法有更佳的檢定力，最後我們也通過幾個模擬例子和實際資料分析驗證此方法的有效性。
Granger causality is a classical tool for measuring predictability from one group of time series to another by incorporating information of variables described by a vector autoregressive (VAR) model. Traditional methods for validating Granger causality are based on the Wald type tests, which may encounter a problem with (i) tuning parameter selection or (ii) test-statistic inflation when the true covariance matrix is singular or near-singular. In this study, we propose an alternative procedure for testing Granger causality based on non-pivotal statistics. The proposed hypothesis testing method is valuable in that (i) it does not require any calibration of tuning parameters (thus saving huge computational cost); and (ii) it yields very competitive power values as compared with the Wald type tests. Finally, a number of simulation examples and a real data set are used to illustrate and evaluate the proposed method.參考文獻 Akaike, H. (1998). Information theory and an extension of the maximum likelihood principle. In Selected papers of hirotugu akaike, pages 199–213. Springer.Amblard, P.-O. and Michel, O. J. (2011). On directed information theory and grangercausality graphs. Journal of computational neuroscience, 30(1):7–16.Anderson, T. W. (1963). Asymptotic theory for principal component analysis. The Annalsof Mathematical Statistics, 34(1):122–148.Andrews, D. W. (1987). Asymptotic results for generalized wald tests. EconometricTheory, 3(3):348–358.Basu, S., Shojaie, A., and Michailidis, G. (2015). Network granger causality with inherentgrouping structure. The Journal of Machine Learning Research, 16(1):417–453.Boudjellaba, H., Dufour, J.-M., and Roy, R. (1992). Testing causality between two vectors in multivariate autoregressive moving average models. Journal of the AmericanStatistical Association, 87(420):1082–1090.Dagenais, M. G. and Dufour, J.-M. (1991). Invariance, nonlinear models, and asymptotictests. Econometrica: Journal of the Econometric Society, pages 1601–1615.Davis, R. A., Zang, P., and Zheng, T. (2016). Sparse vector autoregressive modeling.Journal of Computational and Graphical Statistics, 25(4):1077–1096.Dufour, J.-M. (2003). Identification, weak instruments, and statistical inference in econometrics. Canadian Journal of Economics/Revue canadienne d’économique, 36(4):767–808.Dufour, J.-M., Pelletier, D., and Renault, É. (2006). Short run and long run causality intime series: inference. Journal of Econometrics, 132(2):337–362.Dufour, J.-M. and Renault, E. (1998). Short run and long run causality in time series:theory. Econometrica, pages 1099–1125.Dufour, J.-M., Renault, E., and Zinde-Walsh, V. (2013). Wald tests when restrictions arelocally singular. arXiv preprint arXiv:1312.0569.Ferguson, T. S. (2017). A course in large sample theory. Routledge.Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.Granger, C. W. (1969). Investigating causal relations by econometric models and crossspectral methods. Econometrica: journal of the Econometric Society, pages 424–438.Hannan, E. J. and Quinn, B. G. (1979). The determination of the order of an autoregression.Journal of the Royal Statistical Society: Series B (Methodological), 41(2):190–195.Hung, Y.-C., Tseng, N.-F., and Balakrishnan, N. (2014). Trimmed granger causality between two groups of time series. Electronic Journal of Statistics, 8(2):1940–1972.Lozano, A. C., Abe, N., Liu, Y., and Rosset, S. (2009). Grouped graphical granger modeling for gene expression regulatory networks discovery. Bioinformatics, 25(12):i110–i118.Lütkepohl, H. (2000). Bootstrapping impulse responses in var analyses. In COMPSTAT,pages 109–119. Springer.Lütkepohl, H. (2005). New introduction to multiple time series analysis. Springer Science& Business Media.Lütkepohl, H. and Burda, M. M. (1997). Modified wald tests under nonregular conditions.Journal of Econometrics, 78(2):315–332.Quinn, B. G. (1980). Order determination for a multivariate autoregression. Journal ofthe Royal Statistical Society: Series B (Methodological), 42(2):182–185.Ratsimalahelo, Z. (2005). Generalised wald type tests of nonlinear restrictions. IFACProceedings Volumes, 38(1):100–105.Schwarz, G. (1978). Estimating the dimension of a model. The annals of statistics, pages461–464.Sims, C. A. (1980). Macroeconomics and reality. Econometrica: journal of the Econometric Society, pages 1–48.Tank, A., Covert, I., Foti, N., Shojaie, A., and Fox, E. (2018). Neural granger causality.arXiv preprint arXiv:1802.05842.Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of theRoyal Statistical Society: Series B (Methodological), 58(1):267–288.Vicente, R., Wibral, M., Lindner, M., and Pipa, G. (2011). Transfer entropy—a modelfree measure of effective connectivity for the neurosciences. Journal of computationalneuroscience, 30(1):45–67.Von Weyl, H. (1909). Über beschränkte quadratische formen, deren differenz vollstetigist. Rendiconti del Circolo Matematico di Palermo (1884-1940), 27(1):373–392.Xiao, H. and Wu, W. B. (2012). Covariance matrix estimation for stationary time series.The Annals of Statistics, 40(1):466–493.Yuen, T., Wong, H., and Yiu, K. F. C. (2018). On constrained estimation of graphical timeseries models. Computational Statistics & Data Analysis, 124:27–52. 描述 碩士
國立政治大學
統計學系
109354004資料來源 http://thesis.lib.nccu.edu.tw/record/#G0109354004 資料類型 thesis dc.contributor.advisor 洪英超 zh_TW dc.contributor.advisor Hung, Ying-Chao en_US dc.contributor.author (Authors) 姚惠元 zh_TW dc.contributor.author (Authors) Yao, Huei-Yuan en_US dc.creator (作者) 姚惠元 zh_TW dc.creator (作者) Yao, Huei-Yuan en_US dc.date (日期) 2022 en_US dc.date.accessioned 1-Aug-2022 17:14:43 (UTC+8) - dc.date.available 1-Aug-2022 17:14:43 (UTC+8) - dc.date.issued (上傳時間) 1-Aug-2022 17:14:43 (UTC+8) - dc.identifier (Other Identifiers) G0109354004 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/141003 - 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) 109354004 zh_TW dc.description.abstract (摘要) 格蘭傑因果關係是一個透過結合向量自迴歸模型中所有變數的資訊於衡量兩組時間序列間可預測性的經典統計分析工具，傳統分析格蘭傑因果關係的推論方法為 Wald 類型的檢定方法，然而這些檢定方法可能會面臨以下問題: 一、需要挑選微調參數，二、當預估測之共變異數矩陣為奇異矩陣時，用於推論的臨界值會失效。在這篇論文中，我們發展了一個基於非樞紐統計量的格蘭傑因果關係檢定，此方法不僅避免了以上兩個問題，相較於 Wald 類型的檢定，我們的方法有更佳的檢定力，最後我們也通過幾個模擬例子和實際資料分析驗證此方法的有效性。 zh_TW dc.description.abstract (摘要) Granger causality is a classical tool for measuring predictability from one group of time series to another by incorporating information of variables described by a vector autoregressive (VAR) model. Traditional methods for validating Granger causality are based on the Wald type tests, which may encounter a problem with (i) tuning parameter selection or (ii) test-statistic inflation when the true covariance matrix is singular or near-singular. In this study, we propose an alternative procedure for testing Granger causality based on non-pivotal statistics. The proposed hypothesis testing method is valuable in that (i) it does not require any calibration of tuning parameters (thus saving huge computational cost); and (ii) it yields very competitive power values as compared with the Wald type tests. Finally, a number of simulation examples and a real data set are used to illustrate and evaluate the proposed method. en_US dc.description.tableofcontents Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i摘要 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Background Knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1 The VAR Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 The Concept of Granger Causality . . . . . . . . . . . . . . . . . . . . . 53 Granger Causality Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1 Estimation of VAR Models . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.1 Least Square Estimate . . . . . . . . . . . . . . . . . . . . . . . 93.1.2 Order Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Hypothesis Testing of Granger Causality . . . . . . . . . . . . . . . . . . 113.2.1 Granger Causality Test . . . . . . . . . . . . . . . . . . . . . . . 123.2.2 Testing Zero Coefficients . . . . . . . . . . . . . . . . . . . . . . 123.2.3 The Wald-type Tests . . . . . . . . . . . . . . . . . . . . . . . . 133.2.4 Shortcomings of the Wald-Type Tests . . . . . . . . . . . . . . . 173.2.5 New Test Based on Non-pivotal Statistics . . . . . . . . . . . . . 184 Simulation and Numerical Analysis . . . . . . . . . . . . . . . . . . . . . . . 214.1 Conventional Granger Causality Test . . . . . . . . . . . . . . . . . . . . 214.1.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 214.1.2 Size of the Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 234.1.3 Power of the Tests . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Testing Non-linear Restrictions . . . . . . . . . . . . . . . . . . . . . . . 284.2.1 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2.2 Size of the Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2.3 Power of the Tests . . . . . . . . . . . . . . . . . . . . . . . . . 324.3 Real data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.1 Detail of Equation (3.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . 466.2 Proofs in Section 3.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.3 More on the Numerical Results . . . . . . . . . . . . . . . . . . . . . . . 496.3.1 The Power of Conventional Granger Causality Test . . . . . . . . 496.3.2 The Power of Testing Non-linear Restrictions . . . . . . . . . . . 546.3.3 Comparison with LASSO-type Methods . . . . . . . . . . . . . . 56References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 zh_TW dc.format.extent 1042517 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0109354004 en_US dc.subject (關鍵詞) 格蘭傑因果關係 zh_TW dc.subject (關鍵詞) Modified Wald 檢定 zh_TW dc.subject (關鍵詞) 非樞紐統計量 zh_TW dc.subject (關鍵詞) 向量自迴歸 zh_TW dc.subject (關鍵詞) Granger causality en_US dc.subject (關鍵詞) Modified Wald test en_US dc.subject (關鍵詞) Nonpivotal statistic en_US dc.subject (關鍵詞) Vector autoregression en_US dc.title (題名) 以非樞紐統計量為基礎之格蘭傑因果關係檢定 zh_TW dc.title (題名) Granger Causality Test Based on Non-pivotal Statistics en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) Akaike, H. (1998). Information theory and an extension of the maximum likelihood principle. In Selected papers of hirotugu akaike, pages 199–213. Springer.Amblard, P.-O. and Michel, O. J. (2011). On directed information theory and grangercausality graphs. Journal of computational neuroscience, 30(1):7–16.Anderson, T. W. (1963). Asymptotic theory for principal component analysis. The Annalsof Mathematical Statistics, 34(1):122–148.Andrews, D. W. (1987). Asymptotic results for generalized wald tests. EconometricTheory, 3(3):348–358.Basu, S., Shojaie, A., and Michailidis, G. (2015). Network granger causality with inherentgrouping structure. The Journal of Machine Learning Research, 16(1):417–453.Boudjellaba, H., Dufour, J.-M., and Roy, R. (1992). Testing causality between two vectors in multivariate autoregressive moving average models. Journal of the AmericanStatistical Association, 87(420):1082–1090.Dagenais, M. G. and Dufour, J.-M. (1991). Invariance, nonlinear models, and asymptotictests. Econometrica: Journal of the Econometric Society, pages 1601–1615.Davis, R. A., Zang, P., and Zheng, T. (2016). Sparse vector autoregressive modeling.Journal of Computational and Graphical Statistics, 25(4):1077–1096.Dufour, J.-M. (2003). Identification, weak instruments, and statistical inference in econometrics. Canadian Journal of Economics/Revue canadienne d’économique, 36(4):767–808.Dufour, J.-M., Pelletier, D., and Renault, É. (2006). Short run and long run causality intime series: inference. Journal of Econometrics, 132(2):337–362.Dufour, J.-M. and Renault, E. (1998). Short run and long run causality in time series:theory. Econometrica, pages 1099–1125.Dufour, J.-M., Renault, E., and Zinde-Walsh, V. (2013). Wald tests when restrictions arelocally singular. arXiv preprint arXiv:1312.0569.Ferguson, T. S. (2017). A course in large sample theory. Routledge.Fox, J. (2015). Applied regression analysis and generalized linear models. Sage Publications.Granger, C. W. (1969). Investigating causal relations by econometric models and crossspectral methods. Econometrica: journal of the Econometric Society, pages 424–438.Hannan, E. J. and Quinn, B. G. (1979). The determination of the order of an autoregression.Journal of the Royal Statistical Society: Series B (Methodological), 41(2):190–195.Hung, Y.-C., Tseng, N.-F., and Balakrishnan, N. (2014). Trimmed granger causality between two groups of time series. Electronic Journal of Statistics, 8(2):1940–1972.Lozano, A. C., Abe, N., Liu, Y., and Rosset, S. (2009). Grouped graphical granger modeling for gene expression regulatory networks discovery. Bioinformatics, 25(12):i110–i118.Lütkepohl, H. (2000). Bootstrapping impulse responses in var analyses. In COMPSTAT,pages 109–119. Springer.Lütkepohl, H. (2005). New introduction to multiple time series analysis. Springer Science& Business Media.Lütkepohl, H. and Burda, M. M. (1997). Modified wald tests under nonregular conditions.Journal of Econometrics, 78(2):315–332.Quinn, B. G. (1980). Order determination for a multivariate autoregression. Journal ofthe Royal Statistical Society: Series B (Methodological), 42(2):182–185.Ratsimalahelo, Z. (2005). Generalised wald type tests of nonlinear restrictions. IFACProceedings Volumes, 38(1):100–105.Schwarz, G. (1978). Estimating the dimension of a model. The annals of statistics, pages461–464.Sims, C. A. (1980). Macroeconomics and reality. Econometrica: journal of the Econometric Society, pages 1–48.Tank, A., Covert, I., Foti, N., Shojaie, A., and Fox, E. (2018). Neural granger causality.arXiv preprint arXiv:1802.05842.Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of theRoyal Statistical Society: Series B (Methodological), 58(1):267–288.Vicente, R., Wibral, M., Lindner, M., and Pipa, G. (2011). Transfer entropy—a modelfree measure of effective connectivity for the neurosciences. Journal of computationalneuroscience, 30(1):45–67.Von Weyl, H. (1909). Über beschränkte quadratische formen, deren differenz vollstetigist. Rendiconti del Circolo Matematico di Palermo (1884-1940), 27(1):373–392.Xiao, H. and Wu, W. B. (2012). Covariance matrix estimation for stationary time series.The Annals of Statistics, 40(1):466–493.Yuen, T., Wong, H., and Yiu, K. F. C. (2018). On constrained estimation of graphical timeseries models. Computational Statistics & Data Analysis, 124:27–52. zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202200767 en_US
