分位数向量自回归分布滞后模型及脉冲响应分析
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摘要
为研究多个时间序列条件分位数之间的关联关系,将向量自回归分布滞后模型扩展到分位数体系下,提出了分位数向量自回归分布滞后模型:QVARDL(p, q),给出其数学表示、参数估计、滞后阶数选择、脉冲响应分析等一整套建模方法.选取世界范围内主要国家(地区)资本市场作为研究对象,将建立的模型与方法应用于解释美国次贷危机的影响,结果表明:美国次贷危机在世界范围内产生了深远影响,但对不同国家(地区)的资本市场在影响程度、影响方式、响应时期等方面有着不同的表现.这一发现,有助于理解美国次贷危机的传播规律.
In practice, it is important to explore the correlations among conditional quantiles of multiple time series. To this end, this paper presents a quantile vector autoregressive distributed lag(QVARDL) model.The QVARDL model is an extension of vector autoregressive distributed lag model under the framework of quantile. Related methods are further studied for modelling the QVARDL(p, q). Such methods mainly contain mathematical expression, parameter estimation, lag order selection, impulse response analysis, etc. Empirical studies show that the QVARDL model is able to investigate the impacts of the U.S. subprime mortgage crisis throughout the world. The U.S. subprime mortgage crisis has had a profound impact on the capital markets of different countries(regions), but it shows various performances in terms of the depth, the mode, and response period. The empirical findings help to understand the propagation law of the U.S. subprime mortgage crisis.
In practice, it is important to explore the correlations among conditional quantiles of multiple time series. To this end, this paper presents a quantile vector autoregressive distributed lag(QVARDL) model.The QVARDL model is an extension of vector autoregressive distributed lag model under the framework of quantile. Related methods are further studied for modelling the QVARDL(p, q). Such methods mainly contain mathematical expression, parameter estimation, lag order selection, impulse response analysis, etc. Empirical studies show that the QVARDL model is able to investigate the impacts of the U.S. subprime mortgage crisis throughout the world. The U.S. subprime mortgage crisis has had a profound impact on the capital markets of different countries(regions), but it shows various performances in terms of the depth, the mode, and response period. The empirical findings help to understand the propagation law of the U.S. subprime mortgage crisis.
引文
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[2]刘向丽,程刚,成思危,等.中国期货市场日内效应分析.系统工程理论与实践, 2008, 28(8):63–80.Liu X L, Cheng G, Cheng S W, et al. Intraday effects analysis of Chinese futures markets. Systems Engineering:Theory&Practice,2008, 28(8):63–80.(in Chinese)
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[10] Xu Q, Niu X, Jiang C, et al. The Phillips curve in the US:A nonlinear quantile regression approach. Economic Modelling, 2015, 49:186–197.
[11]许启发,陈士俊,蒋翠侠,等.极端VaR风险测度的新方法:QRNN+POT.系统工程学报, 2016, 31(1):33–44.Xu Q F, Chen S J, Jiang C X, et al. A new method for extreme value at risk measure:QRNN+POT. Journal of Systems Enginerring,2016, 31(1):33–44.(in Chinese)
[12] Koenker R, Xiao Z. Quantile autoregression. Journal of the American Statistical Association, 2006, 101(475):980–990.
[13]陈磊,曾勇,杜化宇.石油期货收益率的分位数建模及其影响因素分析.中国管理科学, 2012, 20(3):35–40.Chen L, Zeng Y, Du H Y. Modeling the quantile of oil futures return and analyzing the dynamics of quantile. Chinese Journal of Management Science, 2012, 20(3):35–40.(in Chinese)
[14] Engle R F, Manganelli S. CAViaR:Conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics, 2004, 22(4):367–381.
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[16] Gouri′eroux C, Jasiak J. Dynamic quantile models. Journal of Econometrics, 2008, 147(1):198–205.
[17]叶五一,缪柏其.基于动态分位点回归模型的金融传染分析.系统工程学报, 2012, 27(2):214–223.Ye W Y, Liao B Q. Analysis of financial contagion based on dynamic quantile regression model. Journal of Systems Engineering,2012, 27(2):214–223.(in Chinese)
[18] Galvao Jr A F, Montes-Rojas G, Park S Y. Quantile autoregressive distributed lag model with an application to house price returns.Oxford Bulletin of Economics and Statistics, 2013, 75(2):307–321.
[19] White H, Kim T H, Manganelli S. VAR for VaR:Measuring tail dependence using multivariate regression quantiles. Journal of Econometrics, 2015, 187:169–188.
[20] Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1973, 19(6):716–723.
[21] Schwarz G. Estimating the dimension of a model. The Annals of Statistics, 1978, 6(2):461–464.
[22] Yuan M. GACV for quantile smoothing splines. Computational Statistics and Data Analysis, 2006, 50(3):813–829.
[23] Li Y, Liu Y, Zhu J. Quantile regression in reproducing kernel hilbert spaces. Journal of the American Statistical Association, 2007,102(477):255–268.
[24] Hamilton J D. Time Series Analysis. Princeton:Princeton University Press, 1994:291–336.
[25]杨博理,龚朴,包晓辉.香港各地区房地产市场间的动态相关性研究.系统工程学报, 2016, 31(2):178–191.Yang B L, Gong P, Bao X H. Research on dynamic correlations among regional real estate markets of Hong Kong. Journal of Systems Engineering, 2016, 31(2):178–191.(in Chinese)
[26] Kupiec P. Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, 1995, 3(2):73–84.
[27] Christoffersen P, Pelletier D. Backtesting value-at-risk:A duration-based approach. Journal of Financial Econometrics, 2004, 2(1):84–108.
[28]黄友珀,唐振鹏,唐勇.基于藤copula–已实现GARCH的组合收益分位数预测.系统工程学报, 2016, 31(1):45–54.Huang Y P, Tang Z P, Tang Y. Portfolio quantile forecasts based on vine Copula and realized GARCH. Journal of Systems Engineering, 2016, 31(1):45–54.(in Chinese)
[29]郭华,王春峰,房振明.高频视角下微观交易信息对价格波动的影响.系统工程学报, 2014, 29(6):780–790.Guo H, Wang C F, Fang Z M. Impact of trade information on price volatility in the perspective of high-frequency data. Journal of Systems Engineering, 2014, 29(6):780–790.(in Chinese)
[2]刘向丽,程刚,成思危,等.中国期货市场日内效应分析.系统工程理论与实践, 2008, 28(8):63–80.Liu X L, Cheng G, Cheng S W, et al. Intraday effects analysis of Chinese futures markets. Systems Engineering:Theory&Practice,2008, 28(8):63–80.(in Chinese)
[3]王曦,邹文理,叶茂.中国治理通货膨胀的货币政策操作方式选择.中国工业经济, 2012, 29(8):5–17.Wang X, Zou W L, Ye M. The choice of monetary policy implemental procedure to curb inflation in China. China Industrial Economics, 2012, 29(8):5–17.(in Chinese)
[4]李湘梅,姚智爽.基于VAR模型的中国能源消费碳排放影响因素分析.生态经济, 2014, 30(1):39–44.Li X M, Yao Z S. Analysis of influential factors of carbon emissions for energy consumption in China based on vector autoregression model. Ecological Economy, 2014, 30(1):39–44.(in Chinese)
[5] Koenker R, Bassett G W. Regression quantiles. Econometrica, 1978, 46(1):33–50.
[6]王新宇,宋学锋,吴瑞明.基于AAVS-CAViaR模型的股市风险测量研究.系统工程学报, 2010, 25(3):326–333.Wang X Y, Song X F, Wu R M. Measuring stock market risk based on AAVS-CAViaR model. Journal of Systems Engineering, 2010,25(3):326–333.(in Chinese)
[7]许启发,蒋翠侠.分位数局部调整模型及应用.数量经济技术经济研究, 2011, 28(8):115–133.Xu Q F, Jiang C X. Quantile partial adjustment model and its application. The Journal of Quantitative&Technical Economics, 2011,28(8):115–133.(in Chinese)
[8]史金凤,刘维奇,杨威.基于分位数回归的金融市场稳定性检验.中国管理科学, 2011, 19(2):24–29.Shi J F, Liu W Q, Yang W. Test for financial market stability based on quantile regression model. Chinese Journal of Management Science, 2011, 19(2):24–29.(in Chinese)
[9]王新宇,杨广,宋学锋.我国创业板IPO首日高频量价分位相关的变点分析.系统工程理论与实践, 2013, 33(7):1717–1722.Wang X Y, Yang G, Song X F. Change point analysis to high frequency price-volume quantile dependence of IPOs on listing date in China’s growth enterprise market. Systems Engineering:Theory&Practice, 2013, 33(7):1717–1722.(in Chinese)
[10] Xu Q, Niu X, Jiang C, et al. The Phillips curve in the US:A nonlinear quantile regression approach. Economic Modelling, 2015, 49:186–197.
[11]许启发,陈士俊,蒋翠侠,等.极端VaR风险测度的新方法:QRNN+POT.系统工程学报, 2016, 31(1):33–44.Xu Q F, Chen S J, Jiang C X, et al. A new method for extreme value at risk measure:QRNN+POT. Journal of Systems Enginerring,2016, 31(1):33–44.(in Chinese)
[12] Koenker R, Xiao Z. Quantile autoregression. Journal of the American Statistical Association, 2006, 101(475):980–990.
[13]陈磊,曾勇,杜化宇.石油期货收益率的分位数建模及其影响因素分析.中国管理科学, 2012, 20(3):35–40.Chen L, Zeng Y, Du H Y. Modeling the quantile of oil futures return and analyzing the dynamics of quantile. Chinese Journal of Management Science, 2012, 20(3):35–40.(in Chinese)
[14] Engle R F, Manganelli S. CAViaR:Conditional autoregressive value at risk by regression quantiles. Journal of Business and Economic Statistics, 2004, 22(4):367–381.
[15] Xu Q, Childs T. Evaluating forecast performances of the quantile autoregression models in the present global crisis in international equity markets. Applied Financial Economics, 2013, 23(2):105–117.
[16] Gouri′eroux C, Jasiak J. Dynamic quantile models. Journal of Econometrics, 2008, 147(1):198–205.
[17]叶五一,缪柏其.基于动态分位点回归模型的金融传染分析.系统工程学报, 2012, 27(2):214–223.Ye W Y, Liao B Q. Analysis of financial contagion based on dynamic quantile regression model. Journal of Systems Engineering,2012, 27(2):214–223.(in Chinese)
[18] Galvao Jr A F, Montes-Rojas G, Park S Y. Quantile autoregressive distributed lag model with an application to house price returns.Oxford Bulletin of Economics and Statistics, 2013, 75(2):307–321.
[19] White H, Kim T H, Manganelli S. VAR for VaR:Measuring tail dependence using multivariate regression quantiles. Journal of Econometrics, 2015, 187:169–188.
[20] Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1973, 19(6):716–723.
[21] Schwarz G. Estimating the dimension of a model. The Annals of Statistics, 1978, 6(2):461–464.
[22] Yuan M. GACV for quantile smoothing splines. Computational Statistics and Data Analysis, 2006, 50(3):813–829.
[23] Li Y, Liu Y, Zhu J. Quantile regression in reproducing kernel hilbert spaces. Journal of the American Statistical Association, 2007,102(477):255–268.
[24] Hamilton J D. Time Series Analysis. Princeton:Princeton University Press, 1994:291–336.
[25]杨博理,龚朴,包晓辉.香港各地区房地产市场间的动态相关性研究.系统工程学报, 2016, 31(2):178–191.Yang B L, Gong P, Bao X H. Research on dynamic correlations among regional real estate markets of Hong Kong. Journal of Systems Engineering, 2016, 31(2):178–191.(in Chinese)
[26] Kupiec P. Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, 1995, 3(2):73–84.
[27] Christoffersen P, Pelletier D. Backtesting value-at-risk:A duration-based approach. Journal of Financial Econometrics, 2004, 2(1):84–108.
[28]黄友珀,唐振鹏,唐勇.基于藤copula–已实现GARCH的组合收益分位数预测.系统工程学报, 2016, 31(1):45–54.Huang Y P, Tang Z P, Tang Y. Portfolio quantile forecasts based on vine Copula and realized GARCH. Journal of Systems Engineering, 2016, 31(1):45–54.(in Chinese)
[29]郭华,王春峰,房振明.高频视角下微观交易信息对价格波动的影响.系统工程学报, 2014, 29(6):780–790.Guo H, Wang C F, Fang Z M. Impact of trade information on price volatility in the perspective of high-frequency data. Journal of Systems Engineering, 2014, 29(6):780–790.(in Chinese)