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題名 長期追蹤資料之分位數迴歸分析：探討股票波動性與流動性的影響因素
Quantile Regression Analysis of Longitudinal Data: Investigating the Determinants of Stock Volatility and Liquidity
作者 涂筱宜
Tu, Shiau-Yi
貢獻者 鄭宗記
Cheng, Tsung-Chi
涂筱宜
Tu, Shiau-Yi
關鍵詞 長期追蹤資料
分位數迴歸
線性混合效應模型
有限混合模型
赤池資訊準則
貝氏資訊準則
波動性
流動性
Longitudinal Data
Quantile Regression
Linear Mixed Effects Model
Finite Mixture Model
Akaike Information Criterion
Bayesian Information Criterion
Volatility
Liquidity
日期 2025
上傳時間 4-Aug-2025 15:11:21 (UTC+8)
摘要 本研究以2014年第一季至2024年第二季台灣 1003 家上市公司的縱向資料為基礎，旨在探討影響個股波動性與流動性的因素，並捕捉在不同市場風險情境下的異質性反應。傳統迴歸方法多聚焦於平均效應，難以掌握極端情境下的非對稱性與潛在結構變異。本研究採用分位數迴歸模型作為主要分析工具，涵蓋 0.1 至 0.9 分位，全面剖析 ETF 持股比例、市值、股價等因素在不同分位下的影響力。研究建構了四種模型架構進行比較，包括傳統分位數迴歸（QR）、時間固定效應模型（TC）、時間變動效應模型（TV）以及結合兩者特性的 TCTV模型，並透過赤池資訊準則（AIC）與貝氏資訊準則（BIC）評估其適配性。實證結果顯示，多項變數在市場極端情境下對個股波動性與流動性具有顯著影響，部分變數呈現顯著非對稱效應，強調分位數模型在捕捉市場風險異質性及提升政策敏感度上的重要性。總體而言，TCTV 模型結合個股間的結構性異質性與時間序列上的動態轉換，能更全面刻劃市場波動性與流動性的潛在異質性與演變機制，展現優異的解釋力與擬合度，亦為後續跨市場比較與模型應用提供重要依據。
This study is based on longitudinal data from 1,003 listed companies in Taiwan spanning from the first quarter of 2014 to the second quarter of 2024. It aims to investigate the factors influencing individual stock volatility and liquidity, and to capture heterogeneous responses under different market risk scenarios. Traditional regression methods often focus on mean effects, making it difficult to grasp asymmetries and latent structural variations under extreme conditions. Therefore, this study adopts the quantile regression as the main analytical tool, covering quantiles from 0.1 to 0.9, to comprehensively analyze the influence of factors such as ETF ownership ratio, market capitalization and stock price across different quantiles. The study constructs and compares four model frameworks, including the traditional quantile regression (QR), the Time-constant model (TC), the Time-varying model (TV), and the TCTV model that combines features of both. Model fit is assessed using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The empirical results show that several variables have significant effects on stock volatility and liquidity under extreme market conditions, with some exhibiting sigificant asymmetric effects, highlighting the importance of quantile models in capturing market risk heterogeneity and enhancing the sensitivity of policy supervision. Overall, the TCTV model combines structural heterogeneity across individual stocks and dynamic transitions in the time series dimension, enabling a more comprehensive depiction of the underlying heterogeneity and evolving mechanisms of market volatility and liquidity. It demonstrates excellent explanatory power and model fit, and also provides an important basis for future cross-market comparisons and model applications.
參考文獻 Abrevaya, J., & Dahl, C. M. (2008). The effects of birth inputs on birthweight: Evidence from quantile estimation on panel data. Journal of Business and Economic Statistics, 26, 379–397. Allen, D. E., Singh, A. K., Powell, R. J., McAleer, M., Taylor, J., & Thomas, L. (2013). Return-volatility relationship: Insights from linear and non-linear quantile regression (No. 13-020/III). Tinbergen Institute Discussion Paper. Alfó, M., Marino, M. F., Ranalli, M. G., & Salvati, N. (2023). lqmix: An R package for longitudinal data analysis via linear quantile mixtures. arXiv preprint arXiv:2302.11363. Amihud, Y. (2002). Illiquidity and stock returns: cross-section and time-series effects. Journal of Financial Markets, 5(1), 31-56. Baur, D., & Schulze, N. (2005). Coexceedances in financial markets—A quantile regression analysis of contagion. Emerging Markets Review, 6(1), 21–43. Ben‐David, I., Franzoni, F., & Moussawi, R. (2018). Do ETFs increase volatility?. The Journal of Finance, 73(6), 2471-2535. Beyerlein, A., von Kries, R., Ness, A. R., & Ong, K. K. (2011). Genetic markers of obesity risk:Stronger associations with body composition in overweight compared to normal-weight children. PLOS ONE, 6(4), e19057. Buchinsky, M. (1994). Changes in the US wage structure 1963– 1987: Application of quantile regression. Econometrica: Journal of the Econometric Society, 405– 458. Chen, J., & Xu, L. (2023). Do exchange-traded fund activities destabilize the stock market? Evidence from the China Securities Index 300 stocks. Economic Modelling, 127, 106450. Choi, B., Jin, S., & Hahn, J. (2022). Exchange-Traded Funds ownership and stock volatility. Korean Journal of Financial Studies, 51(3), 245–280. Cnaan, A., Laird, N. M., and Slasor, P. (1997). Tutorial in Biostatistics: Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data. Statistics in Medicine, 16, 2349-2380. Dannhauser, C. D. (2017). The impact of innovation: Evidence from corporate bond exchange-traded funds (ETFs). Journal of Financial Economics, 125(3), 537– 560. Eide, E., & Showalter, M. H. (1998). The effect of school quality on student performance: A quantile regression approach. Economics Letters, 58(3), 345– 350. Farcomeni, A. (2012). Quantile regression for longitudinal data based on latent Markov subject-specific parameters. Statistics and Computing, 22. Fisher, R.A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd. Fitzmaurice, G. M., Laird, N. M., & Ware, J. H. (2012). Applied Longitudinal Analysis. John Wiley & Sons. Florackis, C., Gregoriou, A., & Kostakis, A. (2011). Trading frequency and asset pricing on the London Stock Exchange: Evidence from a new price impact ratio. Journal of Banking & Finance, 35(12), 3335-3350. Geraci, M. (2019). Modelling and estimation of nonlinear quantile regression with clustered data. Computational Statistics & Data Analysis, 136, 30–46. Geraci, M., & Bottai, M. (2007). Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics, 8(1), 140-154. Garman, M. B., & Klass, M. J. (1980). On the estimation of security price volatilities from historical data. Journal of Business, 67-78. Galarza, C. E., Lachos, V. H., & Bandyopadhyay, D. (2017). Quantile regression in linear mixed models: a stochastic approximation EM approach. Statistics and Its Interface, 10(3), 471. Glosten, L., Nallareddy, S., & Zou, Y. (2021). ETF activity and informational efficiency of underlying securities. Management Science, 67(1), 22–47. Henderson, C. R. (1950). Estimation of genetic parameters. Annals of Mathematical Statistics, 21(2), 309-310. Israeli, D., Lee, C. M., & Sridharan, S. A. (2017). Is there a dark side to exchange traded funds? An information perspective. Review of Accounting Studies, 22, 1048– 1083. Koenker, R. (2003). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74-89. Koenker, R., & Bache, S. H. (2014). rqpd: Regression quantiles for panel data. R package version 0.6/r10. Koenker, R., and Bassett, Jr., G. (1978). Regression quantiles. Econometrica, 46, 33–50. Koenker, R., Portnoy, S., Ng, P. T., Zeileis, A., Grosjean, P., & Ripley, B. D. (2018). Package ‘quantreg’. Reference manual. Available at R-CRAN: https://cran.r-project.org/web/packages/quantreg/quantreg.pdf Laborda, J., Laborda, R., & de la Cruz, J. (2024). Can ETFs affect US financial stability? A quantile cointegration analysis. Financial Innovation, 10(1), 64. Laird, N. (1978). Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association, 73(364), 805–811. Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 963–974. Liebi, L. J. (2020). The effect of ETFs on financial markets: a literature review. Financial Markets and Portfolio Management, 34(2), 165-178. Lindsay, B. G. (1983a). The geometry of mixture likelihoods: a general theory. The Annals of Statistics, 86–94. Lindsay, B. G. (1983b). The geometry of mixture likelihoods, part II: the exponential family. The Annals of Statistics, 783–792. Littell, R. C., Pendergast, J., and Natarajan, R. (2000). Modelling covariance structure in the analysis of repeated measures data. Statistics in Medicine, 19, 1793-1819. Marino, M. F., Tzavidis, N., and Alfo, M. (2018). Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences. Statistical Methods in Medical Research, 27, 2231–2246. Meteyard, L., & Davies, R. A. (2020). Best practice guidance for linear mixed-effects models in psychological science. Journal of Memory and Language, 112, 104092. Parkinson, M. (1980). The extreme value method for estimating the variance of the rate of return. Journal of Business, 61-65. Raudenbush, S. W. (2002). Hierarchical linear models: Applications and data analysis methods. Advanced Quantitative Techniques in the Social Sciences Series/SAGE. Rogers, L. C. G., & Satchell, S. E. (1991). Estimating variance from high, low and closing prices. The Annals of Applied Probability, 504-512. Saæglam, M., Tuzun, T., & Wermers, R. (2021). Do ETFs increase liquidity? (No. 21-03). CFR Working Paper. Taylor, J. W. (1999). A quantile regression approach to estimating the distribution of multiperiod returns. Journal of Derivatives, 7(1), 64. Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. MIT Press. Wu, J., Zhou, M., & Lv, D. (2025). ETF ownership and stock price crash risk: Evidence from China. Applied Economics Letters, 32(6), 757–762. Yu, K., and Moyeed, R. A. (2001). Bayesian quantile regression. Statistics and Probability Letters, 54, 437–447.
描述 碩士
國立政治大學
統計學系
112354019
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0112354019
資料類型 thesis
dc.contributor.advisor 鄭宗記zh_TW
dc.contributor.advisor Cheng, Tsung-Chien_US
dc.contributor.author (Authors) 涂筱宜zh_TW
dc.contributor.author (Authors) Tu, Shiau-Yien_US
dc.creator (作者) 涂筱宜zh_TW
dc.creator (作者) Tu, Shiau-Yien_US
dc.date (日期) 2025en_US
dc.date.accessioned 4-Aug-2025 15:11:21 (UTC+8)-
dc.date.available 4-Aug-2025 15:11:21 (UTC+8)-
dc.date.issued (上傳時間) 4-Aug-2025 15:11:21 (UTC+8)-
dc.identifier (Other Identifiers) G0112354019en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/158713-
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) 112354019zh_TW
dc.description.abstract (摘要) 本研究以2014年第一季至2024年第二季台灣 1003 家上市公司的縱向資料為基礎，旨在探討影響個股波動性與流動性的因素，並捕捉在不同市場風險情境下的異質性反應。傳統迴歸方法多聚焦於平均效應，難以掌握極端情境下的非對稱性與潛在結構變異。本研究採用分位數迴歸模型作為主要分析工具，涵蓋 0.1 至 0.9 分位，全面剖析 ETF 持股比例、市值、股價等因素在不同分位下的影響力。研究建構了四種模型架構進行比較，包括傳統分位數迴歸（QR）、時間固定效應模型（TC）、時間變動效應模型（TV）以及結合兩者特性的 TCTV模型，並透過赤池資訊準則（AIC）與貝氏資訊準則（BIC）評估其適配性。實證結果顯示，多項變數在市場極端情境下對個股波動性與流動性具有顯著影響，部分變數呈現顯著非對稱效應，強調分位數模型在捕捉市場風險異質性及提升政策敏感度上的重要性。總體而言，TCTV 模型結合個股間的結構性異質性與時間序列上的動態轉換，能更全面刻劃市場波動性與流動性的潛在異質性與演變機制，展現優異的解釋力與擬合度，亦為後續跨市場比較與模型應用提供重要依據。zh_TW
dc.description.abstract (摘要) This study is based on longitudinal data from 1,003 listed companies in Taiwan spanning from the first quarter of 2014 to the second quarter of 2024. It aims to investigate the factors influencing individual stock volatility and liquidity, and to capture heterogeneous responses under different market risk scenarios. Traditional regression methods often focus on mean effects, making it difficult to grasp asymmetries and latent structural variations under extreme conditions. Therefore, this study adopts the quantile regression as the main analytical tool, covering quantiles from 0.1 to 0.9, to comprehensively analyze the influence of factors such as ETF ownership ratio, market capitalization and stock price across different quantiles. The study constructs and compares four model frameworks, including the traditional quantile regression (QR), the Time-constant model (TC), the Time-varying model (TV), and the TCTV model that combines features of both. Model fit is assessed using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The empirical results show that several variables have significant effects on stock volatility and liquidity under extreme market conditions, with some exhibiting sigificant asymmetric effects, highlighting the importance of quantile models in capturing market risk heterogeneity and enhancing the sensitivity of policy supervision. Overall, the TCTV model combines structural heterogeneity across individual stocks and dynamic transitions in the time series dimension, enabling a more comprehensive depiction of the underlying heterogeneity and evolving mechanisms of market volatility and liquidity. It demonstrates excellent explanatory power and model fit, and also provides an important basis for future cross-market comparisons and model applications.en_US
dc.description.tableofcontents 謝辭 i 摘要 ii Abstract iii 第一章 緒論 1 第一節 研究背景 1 第二節 研究動機 2 第二章 長期追蹤資料與分位數迴歸 5 第一節 線性混合效應模型 5 第二節 分位數迴歸 7 第三節 長期追蹤資料之分位數迴歸 9 第四節 模型比較準則 14 第三章 ETF 之波動性與流動性 16 第一節 指數股票型基金 16 第二節 變數介紹 18 第四章 實證資料分析 25 第一節 自變數介紹 26 第二節 波動性分析結果 27 第三節 流動性分析結果 67 第四節 模型比較 96 第五節 各自變數於各分位數下模型顯著情況 101 第五章 結論 128 參考文獻 131 附錄 135zh_TW
dc.format.extent 8536628 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0112354019en_US
dc.subject (關鍵詞) 長期追蹤資料zh_TW
dc.subject (關鍵詞) 分位數迴歸zh_TW
dc.subject (關鍵詞) 線性混合效應模型zh_TW
dc.subject (關鍵詞) 有限混合模型zh_TW
dc.subject (關鍵詞) 赤池資訊準則zh_TW
dc.subject (關鍵詞) 貝氏資訊準則zh_TW
dc.subject (關鍵詞) 波動性zh_TW
dc.subject (關鍵詞) 流動性zh_TW
dc.subject (關鍵詞) Longitudinal Dataen_US
dc.subject (關鍵詞) Quantile Regressionen_US
dc.subject (關鍵詞) Linear Mixed Effects Modelen_US
dc.subject (關鍵詞) Finite Mixture Modelen_US
dc.subject (關鍵詞) Akaike Information Criterionen_US
dc.subject (關鍵詞) Bayesian Information Criterionen_US
dc.subject (關鍵詞) Volatilityen_US
dc.subject (關鍵詞) Liquidityen_US
dc.title (題名) 長期追蹤資料之分位數迴歸分析：探討股票波動性與流動性的影響因素zh_TW
dc.title (題名) Quantile Regression Analysis of Longitudinal Data: Investigating the Determinants of Stock Volatility and Liquidityen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Abrevaya, J., & Dahl, C. M. (2008). The effects of birth inputs on birthweight: Evidence from quantile estimation on panel data. Journal of Business and Economic Statistics, 26, 379–397. Allen, D. E., Singh, A. K., Powell, R. J., McAleer, M., Taylor, J., & Thomas, L. (2013). Return-volatility relationship: Insights from linear and non-linear quantile regression (No. 13-020/III). Tinbergen Institute Discussion Paper. Alfó, M., Marino, M. F., Ranalli, M. G., & Salvati, N. (2023). lqmix: An R package for longitudinal data analysis via linear quantile mixtures. arXiv preprint arXiv:2302.11363. Amihud, Y. (2002). Illiquidity and stock returns: cross-section and time-series effects. Journal of Financial Markets, 5(1), 31-56. Baur, D., & Schulze, N. (2005). Coexceedances in financial markets—A quantile regression analysis of contagion. Emerging Markets Review, 6(1), 21–43. Ben‐David, I., Franzoni, F., & Moussawi, R. (2018). Do ETFs increase volatility?. The Journal of Finance, 73(6), 2471-2535. Beyerlein, A., von Kries, R., Ness, A. R., & Ong, K. K. (2011). Genetic markers of obesity risk:Stronger associations with body composition in overweight compared to normal-weight children. PLOS ONE, 6(4), e19057. Buchinsky, M. (1994). Changes in the US wage structure 1963– 1987: Application of quantile regression. Econometrica: Journal of the Econometric Society, 405– 458. Chen, J., & Xu, L. (2023). Do exchange-traded fund activities destabilize the stock market? Evidence from the China Securities Index 300 stocks. Economic Modelling, 127, 106450. Choi, B., Jin, S., & Hahn, J. (2022). Exchange-Traded Funds ownership and stock volatility. Korean Journal of Financial Studies, 51(3), 245–280. Cnaan, A., Laird, N. M., and Slasor, P. (1997). Tutorial in Biostatistics: Using the general linear mixed model to analyse unbalanced repeated measures and longitudinal data. Statistics in Medicine, 16, 2349-2380. Dannhauser, C. D. (2017). The impact of innovation: Evidence from corporate bond exchange-traded funds (ETFs). Journal of Financial Economics, 125(3), 537– 560. Eide, E., & Showalter, M. H. (1998). The effect of school quality on student performance: A quantile regression approach. Economics Letters, 58(3), 345– 350. Farcomeni, A. (2012). Quantile regression for longitudinal data based on latent Markov subject-specific parameters. Statistics and Computing, 22. Fisher, R.A. (1925). Statistical Methods for Research Workers. Edinburgh: Oliver and Boyd. Fitzmaurice, G. M., Laird, N. M., & Ware, J. H. (2012). Applied Longitudinal Analysis. John Wiley & Sons. Florackis, C., Gregoriou, A., & Kostakis, A. (2011). Trading frequency and asset pricing on the London Stock Exchange: Evidence from a new price impact ratio. Journal of Banking & Finance, 35(12), 3335-3350. Geraci, M. (2019). Modelling and estimation of nonlinear quantile regression with clustered data. Computational Statistics & Data Analysis, 136, 30–46. Geraci, M., & Bottai, M. (2007). Quantile regression for longitudinal data using the asymmetric Laplace distribution. Biostatistics, 8(1), 140-154. Garman, M. B., & Klass, M. J. (1980). On the estimation of security price volatilities from historical data. Journal of Business, 67-78. Galarza, C. E., Lachos, V. H., & Bandyopadhyay, D. (2017). Quantile regression in linear mixed models: a stochastic approximation EM approach. Statistics and Its Interface, 10(3), 471. Glosten, L., Nallareddy, S., & Zou, Y. (2021). ETF activity and informational efficiency of underlying securities. Management Science, 67(1), 22–47. Henderson, C. R. (1950). Estimation of genetic parameters. Annals of Mathematical Statistics, 21(2), 309-310. Israeli, D., Lee, C. M., & Sridharan, S. A. (2017). Is there a dark side to exchange traded funds? An information perspective. Review of Accounting Studies, 22, 1048– 1083. Koenker, R. (2003). Quantile regression for longitudinal data. Journal of Multivariate Analysis, 91(1), 74-89. Koenker, R., & Bache, S. H. (2014). rqpd: Regression quantiles for panel data. R package version 0.6/r10. Koenker, R., and Bassett, Jr., G. (1978). Regression quantiles. Econometrica, 46, 33–50. Koenker, R., Portnoy, S., Ng, P. T., Zeileis, A., Grosjean, P., & Ripley, B. D. (2018). Package ‘quantreg’. Reference manual. Available at R-CRAN: https://cran.r-project.org/web/packages/quantreg/quantreg.pdf Laborda, J., Laborda, R., & de la Cruz, J. (2024). Can ETFs affect US financial stability? A quantile cointegration analysis. Financial Innovation, 10(1), 64. Laird, N. (1978). Nonparametric maximum likelihood estimation of a mixing distribution. Journal of the American Statistical Association, 73(364), 805–811. Laird, N. M., & Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 963–974. Liebi, L. J. (2020). The effect of ETFs on financial markets: a literature review. Financial Markets and Portfolio Management, 34(2), 165-178. Lindsay, B. G. (1983a). The geometry of mixture likelihoods: a general theory. The Annals of Statistics, 86–94. Lindsay, B. G. (1983b). The geometry of mixture likelihoods, part II: the exponential family. The Annals of Statistics, 783–792. Littell, R. C., Pendergast, J., and Natarajan, R. (2000). Modelling covariance structure in the analysis of repeated measures data. Statistics in Medicine, 19, 1793-1819. Marino, M. F., Tzavidis, N., and Alfo, M. (2018). Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences. Statistical Methods in Medical Research, 27, 2231–2246. Meteyard, L., & Davies, R. A. (2020). Best practice guidance for linear mixed-effects models in psychological science. Journal of Memory and Language, 112, 104092. Parkinson, M. (1980). The extreme value method for estimating the variance of the rate of return. Journal of Business, 61-65. Raudenbush, S. W. (2002). Hierarchical linear models: Applications and data analysis methods. Advanced Quantitative Techniques in the Social Sciences Series/SAGE. Rogers, L. C. G., & Satchell, S. E. (1991). Estimating variance from high, low and closing prices. The Annals of Applied Probability, 504-512. Saæglam, M., Tuzun, T., & Wermers, R. (2021). Do ETFs increase liquidity? (No. 21-03). CFR Working Paper. Taylor, J. W. (1999). A quantile regression approach to estimating the distribution of multiperiod returns. Journal of Derivatives, 7(1), 64. Wooldridge, J. M. (2010). Econometric analysis of cross section and panel data. MIT Press. Wu, J., Zhou, M., & Lv, D. (2025). ETF ownership and stock price crash risk: Evidence from China. Applied Economics Letters, 32(6), 757–762. Yu, K., and Moyeed, R. A. (2001). Bayesian quantile regression. Statistics and Probability Letters, 54, 437–447.zh_TW