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題名 利用混合頻率群組因子模型分析台灣產業對整體經濟的影響
Analysis of the impact of Taiwan's industries on the overall economy by using mixed-frequency group factor model
作者 李卓穎
Lee, Jhuo-Ying
貢獻者 徐士勛
李卓穎
Lee, Jhuo-Ying
關鍵詞 群組因子模型
混合頻率資料
主成分分析
Group factor model
Mixed-frequency data
Principal component analysis
日期 2025
上傳時間 1-Jul-2025 15:35:06 (UTC+8)
摘要 近年來，因子模型已成為總體經濟與金融領域分析潛在共同驅動因素的重要工具，特別適用於大量維度的追蹤資料。然而，傳統因子模型大多假設所有變數受相同因子影響，忽略資料可能存在的群組結構與異質性，進而降低解釋力。此外，經濟資料常以不同時間頻率發布，如月頻率、季頻率及年頻率，若未妥善整合混合頻率資訊，將可能造成估計偏誤與資訊損失。有鑑於此，Andreou et al. (2019) 提出混合頻率群組因子模型（Mixed-Frequency Group Factor Model），有效結合高頻與低頻資料，並捕捉群組內外之共同與特定因子。本研究即以該方法為基礎，應用於台灣經濟資料，探討工業與非工業部門是否存在共同驅動因素，或各部門經濟表現之群組特定因子。 實證部分，我們選取1984-2023年間，台灣工業部門29種行業之月頻率工業生產指數增減率，以及非工業部門32種行業之年度實質GDP增減率，構成高頻與低頻群組。透過Bai and Ng (2002)提出之資訊準則決定各群組總因子數量，採用主成分分析（PCA）與典型相關分析（CCA）估計共同與特定因子，並運用貝氏資訊準則（BIC）與調整$R$平方比較各類因子組合之模型適配度。結果顯示，單一共同因子無法充分解釋台灣各產業經濟表現之波動；但納入群組特定因子後，模型解釋能力顯著提升。此外，經由ACF檢驗發現共同因子具持續性，特定因子則反映短期波動。本研究驗證了混合頻率群組因子模型於台灣資料之適用性，期盼能作為後續實證應用參考。
In recent years, factor models have become an essential tool in macroeconomics for analyzing potential common driving factors, but traditional approaches are limited by ignoring group structures and the challenges of mixed-frequency data, which can reduce explanatory power and cause estimation bias. This study applies the Mixed-Frequency Group Factor Model (Andreou et al., 2019) to Taiwan economic data to investigate common and group-specific factors between the industrial and non-industrial sectors. For the empirical analysis, we use data from 1984 to 2023, comprising the monthly growth rate of the industrial production index for 29 industries in industrial sector (the high-frequency group) and the annual real GDP growth rate for 32 industries in the non-industrial sector (the low-frequency group) of Taiwan. The information criteria proposed by Bai and Ng (2002) are used to determine the total number of factors for each group. We employ Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) to estimate the common and specific factors, and then use the Bayesian Information Criterion (BIC) and adjusted R-squared to compare the model fit for various factor combinations. The results indicate that a single common factor cannot adequately explain the economic fluctuations across Taiwan's industries; however, the model's explanatory power is significantly improved by including group-specific factors. Moreover, an ACF test reveals that the common factor exhibits persistence, whereas the specific factors reflect short-term fluctuations. This research validates the applicability of the Mixed-Frequency Group Factor Model to Taiwanese data, with the hope that it will serve as a reference for future empirical applications.
參考文獻 吳易樺、黃朝熙、劉子衙（2014）。時間序列模型對我國產業成長預測之優劣比較。應用經濟論叢，96，35-68。https://doi.org/10.3966/054696002014120096002 Andreou, E., Gagliardini, P., Ghysels, E., & Rubin, M. (2019). Inference in group factor models with an application to mixed‐frequency data. Econometrica, 87(4), 1267-1305. https://doi.org/10.3982/ECTA14690 Andreou, E., Gagliardini, P., Ghysels, E., & Rubin, M. (2020). Mixed-frequency macro–finance factor models: Theory and applications. Journal of Financial Econometrics, 18(3), 585-628. https://doi.org/10.1093/jjfinec/nbaa015 Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica, 71(1), 135-171. https://doi.org/10.1111/1468-0262.00392 Bai, J., & Ando, T. (2013). Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors [Unpublished manuscript]. MPRA Paper No. 52785, University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/52785/ Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191-221. https://doi.org/10.1111/1468-0262.00273 Bykhovskaya, A., & Gorin, V. (2024). Canonical correlation analysis: Review. arXiv preprint arXiv:2411.15625. https://doi.org/10.48550/arXiv.2411.15625 Chen, K. H., & Yang, H. Y. (2010). Appraising the Economic Impact of the “Opening up to Mainland Chinese Tourist Arrivals” Policy on Taiwan with a Tourism-CGE Model. Asia Pacific Journal of Tourism Research, 15(2), 155–175. https://doi.org/10.1080/10941661003629961 Chen, P. (2010). A grouped factor model [Unpublished manuscript]. MPRA Paper No. 36082. University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/36082/ Chen, P. (2012). Common factors and specific factors [Unpublished manuscript]. MPRA Paper No. 36114. University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/36114/ Flury, B. N. (1984). Common principal components in k groups. Journal of the American Statistical Association, 79(388), 892-898. https://doi.org/10.1080/01621459.1984.10477108 Foerster, A. T., Sarte, P. D. G., & Watson, M. W. (2011). Sectoral versus aggregate shocks: A structural factor analysis of industrial production. Journal of Political Economy, 119(1), 1-38. https://doi.org/10.1086/659311 Gou, Z., & Fyfe, C. (2000). Generalised canonical correlation analysis. In International Conference on Intelligent Data Engineering and Automated Learning (pp. 164-173). Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44491-2_25 Goyal, A., Pérignon, C., & Villa, C. (2008). How common are common return factors across the NYSE and Nasdaq?. Journal of Financial Economics, 90(3), 252-271. https://doi.org/10.1016/j.jfineco.2008.01.004 Harris, R. J. (2001). A primer of multivariate statistics (3rd ed.). Psychology Press. https://doi.org/10.4324/9781410600455 Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6), 417-441. https://psycnet.apa.org/doi/10.1037/h0071325 Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3/4), 321–377. https://doi.org/10.2307/2333955 Jackson, J. E. (2005). A user's guide to principal components (2nd ed.). Wiley. https://doi.org/10.1002/0471725331 Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). Springer. https://doi.org/10.1007/b98835 Jörg, B., & Sandra, E. (2016). Analyzing international business and financial cycles using multi-level factor models: A comparison of alternative approaches. In Dynamic factor models (Vol. 35, pp. 177-214). Emerald Group Publishing Limited. https://doi.org/10.1108/s0731-905320150000035005 Kose, M. A., Otrok, C., & Whiteman, C. H. (2003). International business cycles: World, region, and country-specific factors. American Economic Review, 93(4), 1216-1239. https://doi.org/10.1257/000282803769206278 Kose, M. A., Otrok, C., & Whiteman, C. H. (2008). Understanding the evolution of world business cycles. Journal of International Economics, 75(1), 110–130. https://doi.org/10.1016/j.jinteco.2007.10.002 Pearson, K. (1901). LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin philosophical magazine and journal of science, 2(11), 559-572. https://doi.org/10.1080/14786440109462720 Schott, J. R. (1991). Some tests for common principal component subspaces in several groups. Biometrika, 78(4), 771-777. https://doi.org/10.1093/biomet/78.4.771 Stock, J. H., & Watson, M. W. (2002). Forecasting using principal components from a large number of predictors. Journal of the American statistical association, 97(460), 1167-1179. https://doi.org/10.1198/016214502388618960 Thompson, B. (1984). Canonical correlation analysis: Uses and interpretation. Sage. https://doi.org/10.4135/9781412983570 Tucker, L. R. (1958). An inter-battery method of factor analysis. Psychometrika, 23(2), 111-136. https://doi.org/10.1007/BF02289009 Wang, P. (2012). Large dimensional factor models with a multi-level factor structure: Identification, estimation, and inference [Unpublished manuscript]. Hong Kong University of Science and Technology.
描述 碩士
國立政治大學
經濟學系
112258024
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0112258024
資料類型 thesis
dc.contributor.advisor 徐士勛zh_TW
dc.contributor.author (Authors) 李卓穎zh_TW
dc.contributor.author (Authors) Lee, Jhuo-Yingen_US
dc.creator (作者) 李卓穎zh_TW
dc.creator (作者) Lee, Jhuo-Yingen_US
dc.date (日期) 2025en_US
dc.date.accessioned 1-Jul-2025 15:35:06 (UTC+8)-
dc.date.available 1-Jul-2025 15:35:06 (UTC+8)-
dc.date.issued (上傳時間) 1-Jul-2025 15:35:06 (UTC+8)-
dc.identifier (Other Identifiers) G0112258024en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/157862-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 經濟學系zh_TW
dc.description (描述) 112258024zh_TW
dc.description.abstract (摘要) 近年來，因子模型已成為總體經濟與金融領域分析潛在共同驅動因素的重要工具，特別適用於大量維度的追蹤資料。然而，傳統因子模型大多假設所有變數受相同因子影響，忽略資料可能存在的群組結構與異質性，進而降低解釋力。此外，經濟資料常以不同時間頻率發布，如月頻率、季頻率及年頻率，若未妥善整合混合頻率資訊，將可能造成估計偏誤與資訊損失。有鑑於此，Andreou et al. (2019) 提出混合頻率群組因子模型（Mixed-Frequency Group Factor Model），有效結合高頻與低頻資料，並捕捉群組內外之共同與特定因子。本研究即以該方法為基礎，應用於台灣經濟資料，探討工業與非工業部門是否存在共同驅動因素，或各部門經濟表現之群組特定因子。 實證部分，我們選取1984-2023年間，台灣工業部門29種行業之月頻率工業生產指數增減率，以及非工業部門32種行業之年度實質GDP增減率，構成高頻與低頻群組。透過Bai and Ng (2002)提出之資訊準則決定各群組總因子數量，採用主成分分析（PCA）與典型相關分析（CCA）估計共同與特定因子，並運用貝氏資訊準則（BIC）與調整$R$平方比較各類因子組合之模型適配度。結果顯示，單一共同因子無法充分解釋台灣各產業經濟表現之波動；但納入群組特定因子後，模型解釋能力顯著提升。此外，經由ACF檢驗發現共同因子具持續性，特定因子則反映短期波動。本研究驗證了混合頻率群組因子模型於台灣資料之適用性，期盼能作為後續實證應用參考。zh_TW
dc.description.abstract (摘要) In recent years, factor models have become an essential tool in macroeconomics for analyzing potential common driving factors, but traditional approaches are limited by ignoring group structures and the challenges of mixed-frequency data, which can reduce explanatory power and cause estimation bias. This study applies the Mixed-Frequency Group Factor Model (Andreou et al., 2019) to Taiwan economic data to investigate common and group-specific factors between the industrial and non-industrial sectors. For the empirical analysis, we use data from 1984 to 2023, comprising the monthly growth rate of the industrial production index for 29 industries in industrial sector (the high-frequency group) and the annual real GDP growth rate for 32 industries in the non-industrial sector (the low-frequency group) of Taiwan. The information criteria proposed by Bai and Ng (2002) are used to determine the total number of factors for each group. We employ Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) to estimate the common and specific factors, and then use the Bayesian Information Criterion (BIC) and adjusted R-squared to compare the model fit for various factor combinations. The results indicate that a single common factor cannot adequately explain the economic fluctuations across Taiwan's industries; however, the model's explanatory power is significantly improved by including group-specific factors. Moreover, an ACF test reveals that the common factor exhibits persistence, whereas the specific factors reflect short-term fluctuations. This research validates the applicability of the Mixed-Frequency Group Factor Model to Taiwanese data, with the hope that it will serve as a reference for future empirical applications.en_US
dc.description.tableofcontents 1 緒論 1 2 文獻回顧 3 2.1 前言 3 2.1.1 群組因子模型的發展概述 3 2.1.2 產業對經濟影響之分析方法流變 3 2.2 國際相關文獻 4 2.2.1 方法論 4 2.2.2 實證應用 5 2.3 重要參考文獻 7 2.4 總結與本研究定位 7 3 研究方法與模型 9 3.1 研究背景與方法選擇 9 3.2 群組因子模型 9 3.2.1 模型設定 9 3.2.2 模型假設 10 3.2.3 模型目標 11 3.3 主成分分析（PCA） 11 3.3.1 簡介 11 3.3.2 核心原理與基本概念 12 3.3.3 數學推導 13 3.4 典型相關分析（CCA） 17 3.4.1 簡介 17 3.4.2 核心原理與基本概念 17 3.4.3 數學推導 19 3.5 混合頻率群組因子模型 20 3.5.1 模型動機與概述 20 3.5.2 基本模型設定 21 3.5.3 高低頻資料整理 22 3.5.4 因子估計步驟 23 3.5.5 步驟一：使用PCA估計群組的整體因子空間 24 3.5.6 步驟二：使用CCA抓取共同因子 25 3.5.7 步驟三：使用PCA估計群組特定因子 26 4 實證分析 29 4.1 概述 29 4.2 資料 31 4.2.1 產業變數 31 4.2.2 時間序列變數 32 4.2.3 資料來源與說明 34 4.3 實證結果 35 4.3.1 因子數量估計 35 4.3.2 因子之間的關聯性 37 4.3.3 因子與產業間的相關性 42 5 結論與討論 52 参考文献 54 附錄 57zh_TW
dc.format.extent 8771963 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0112258024en_US
dc.subject (關鍵詞) 群組因子模型zh_TW
dc.subject (關鍵詞) 混合頻率資料zh_TW
dc.subject (關鍵詞) 主成分分析zh_TW
dc.subject (關鍵詞) Group factor modelen_US
dc.subject (關鍵詞) Mixed-frequency dataen_US
dc.subject (關鍵詞) Principal component analysisen_US
dc.title (題名) 利用混合頻率群組因子模型分析台灣產業對整體經濟的影響zh_TW
dc.title (題名) Analysis of the impact of Taiwan's industries on the overall economy by using mixed-frequency group factor modelen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) 吳易樺、黃朝熙、劉子衙（2014）。時間序列模型對我國產業成長預測之優劣比較。應用經濟論叢，96，35-68。https://doi.org/10.3966/054696002014120096002 Andreou, E., Gagliardini, P., Ghysels, E., & Rubin, M. (2019). Inference in group factor models with an application to mixed‐frequency data. Econometrica, 87(4), 1267-1305. https://doi.org/10.3982/ECTA14690 Andreou, E., Gagliardini, P., Ghysels, E., & Rubin, M. (2020). Mixed-frequency macro–finance factor models: Theory and applications. Journal of Financial Econometrics, 18(3), 585-628. https://doi.org/10.1093/jjfinec/nbaa015 Bai, J. (2003). Inferential theory for factor models of large dimensions. Econometrica, 71(1), 135-171. https://doi.org/10.1111/1468-0262.00392 Bai, J., & Ando, T. (2013). Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors [Unpublished manuscript]. MPRA Paper No. 52785, University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/52785/ Bai, J., & Ng, S. (2002). Determining the number of factors in approximate factor models. Econometrica, 70(1), 191-221. https://doi.org/10.1111/1468-0262.00273 Bykhovskaya, A., & Gorin, V. (2024). Canonical correlation analysis: Review. arXiv preprint arXiv:2411.15625. https://doi.org/10.48550/arXiv.2411.15625 Chen, K. H., & Yang, H. Y. (2010). Appraising the Economic Impact of the “Opening up to Mainland Chinese Tourist Arrivals” Policy on Taiwan with a Tourism-CGE Model. Asia Pacific Journal of Tourism Research, 15(2), 155–175. https://doi.org/10.1080/10941661003629961 Chen, P. (2010). A grouped factor model [Unpublished manuscript]. MPRA Paper No. 36082. University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/36082/ Chen, P. (2012). Common factors and specific factors [Unpublished manuscript]. MPRA Paper No. 36114. University Library of Munich, Germany. https://mpra.ub.uni-muenchen.de/36114/ Flury, B. N. (1984). Common principal components in k groups. Journal of the American Statistical Association, 79(388), 892-898. https://doi.org/10.1080/01621459.1984.10477108 Foerster, A. T., Sarte, P. D. G., & Watson, M. W. (2011). Sectoral versus aggregate shocks: A structural factor analysis of industrial production. Journal of Political Economy, 119(1), 1-38. https://doi.org/10.1086/659311 Gou, Z., & Fyfe, C. (2000). Generalised canonical correlation analysis. In International Conference on Intelligent Data Engineering and Automated Learning (pp. 164-173). Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44491-2_25 Goyal, A., Pérignon, C., & Villa, C. (2008). How common are common return factors across the NYSE and Nasdaq?. Journal of Financial Economics, 90(3), 252-271. https://doi.org/10.1016/j.jfineco.2008.01.004 Harris, R. J. (2001). A primer of multivariate statistics (3rd ed.). Psychology Press. https://doi.org/10.4324/9781410600455 Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6), 417-441. https://psycnet.apa.org/doi/10.1037/h0071325 Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3/4), 321–377. https://doi.org/10.2307/2333955 Jackson, J. E. (2005). A user's guide to principal components (2nd ed.). Wiley. https://doi.org/10.1002/0471725331 Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). Springer. https://doi.org/10.1007/b98835 Jörg, B., & Sandra, E. (2016). Analyzing international business and financial cycles using multi-level factor models: A comparison of alternative approaches. In Dynamic factor models (Vol. 35, pp. 177-214). Emerald Group Publishing Limited. https://doi.org/10.1108/s0731-905320150000035005 Kose, M. A., Otrok, C., & Whiteman, C. H. (2003). International business cycles: World, region, and country-specific factors. American Economic Review, 93(4), 1216-1239. https://doi.org/10.1257/000282803769206278 Kose, M. A., Otrok, C., & Whiteman, C. H. (2008). Understanding the evolution of world business cycles. Journal of International Economics, 75(1), 110–130. https://doi.org/10.1016/j.jinteco.2007.10.002 Pearson, K. (1901). LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin philosophical magazine and journal of science, 2(11), 559-572. https://doi.org/10.1080/14786440109462720 Schott, J. R. (1991). Some tests for common principal component subspaces in several groups. Biometrika, 78(4), 771-777. https://doi.org/10.1093/biomet/78.4.771 Stock, J. H., & Watson, M. W. (2002). Forecasting using principal components from a large number of predictors. Journal of the American statistical association, 97(460), 1167-1179. https://doi.org/10.1198/016214502388618960 Thompson, B. (1984). Canonical correlation analysis: Uses and interpretation. Sage. https://doi.org/10.4135/9781412983570 Tucker, L. R. (1958). An inter-battery method of factor analysis. Psychometrika, 23(2), 111-136. https://doi.org/10.1007/BF02289009 Wang, P. (2012). Large dimensional factor models with a multi-level factor structure: Identification, estimation, and inference [Unpublished manuscript]. Hong Kong University of Science and Technology.zh_TW