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CN 34-1054/N

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Granger causality test in quantiles and conditional VaR estimation of continuously rising and falling returns

  • Dept. of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

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https://doi.org/10.3969/j.issn.0253-2778.2016.11.007
  • Received Date: 30 May 2016
  • Accepted Date: 05 July 2016
  • Rev Recd Date: 05 July 2016
  • Publish Date: 30 November 2016
    Abstract

  • Abstract

    High-frequency financial data analysis has received more and more attention. Stationary of continuously rising and falling returns and durations from one-minute intraday high frequency SSE Composite Index and SZSE Component Index was analyzed and their distributions were fitted by exponential distribution, Gamma distribution and Weibull distribution with bad results. Influence factors of continuously rising and falling returns were studied based on quantile Granger causality test. The findings show that the possibility of a big rise followed by a big fall is high, but continuously rising extreme return is not affected by previous continuously falling return. The longer the durations of continuously rising or falling returns, the smaller the risk of continuously falling return is. The longer the duration of the last continuously rising process, the lower the extreme return of the next continuously rising process. Continuously falling duration has no effect on previous continuously rising extreme return. Finally, the prediction of conditional VaR for continuously falling return shows that the quantile regression model has good power to predict conditional VaR.

    Abstract

    High-frequency financial data analysis has received more and more attention. Stationary of continuously rising and falling returns and durations from one-minute intraday high frequency SSE Composite Index and SZSE Component Index was analyzed and their distributions were fitted by exponential distribution, Gamma distribution and Weibull distribution with bad results. Influence factors of continuously rising and falling returns were studied based on quantile Granger causality test. The findings show that the possibility of a big rise followed by a big fall is high, but continuously rising extreme return is not affected by previous continuously falling return. The longer the durations of continuously rising or falling returns, the smaller the risk of continuously falling return is. The longer the duration of the last continuously rising process, the lower the extreme return of the next continuously rising process. Continuously falling duration has no effect on previous continuously rising extreme return. Finally, the prediction of conditional VaR for continuously falling return shows that the quantile regression model has good power to predict conditional VaR.
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    • References(25)
  • [1]
    GENCAY R, DACOROGNA M, MULLER U A, et al. An Introduction to High-Frequency Finance[M]. San Diego, CA：Academic Press, 2001.
    [2]
    SALVATIERRA I D L, PATTONA J. Dynamic copula models and high frequency data[J]. Journal of Empirical Finance, 2015, 30: 120-135.
    [3]
    HANSEN P R, HOREL G, LUNDEA, et al. A Markova chain estimator of multivariate volatility from high frequency data[M]// The Fascination of Probability, Statistics and Their Applications. Switzerland: Springer International Publishing, 2016: 361-394.
    [4]
    KOTKATVUORI-RNBERG J. Measuring actual daily volatility from high frequency intraday returns of the S&P futures and index observations[J]. Expert Systems with Applications, 2016, 43: 213-222.
    [5]
    HANSEN P R, HUANG Z. Exponential garch modeling with realized measures of volatility[J]. Journal of Business & Economic Statistics, 2016, 34(2): 269-287.
    [6]
    雷鸣, 缪柏其. 运用生存模型对上证指数涨跌天数的研究[J]. 运筹与管理, 2003, 12(6): 87-91.
    LEI Ming, MIAO Baiqi. Study of successive rises and falls of days with survival analysis[J]. Operations Research and Management Science, 2003, 12(6): 87-91.
    [7]
    雷鸣, 叶五一, 缪柏其, 等. 生存分析与股指涨跌的概率推断[J]. 管理科学学报, 2010, 13(4): 57-66.
    LEI Ming, YE Wuyi, MIAO Baiqi, et al. Survival analysis and the probability inference about the stock index[J]. Journal of Management Sciences in China, 2010, 13(4): 57-66.
    [8]
    胡心瀚, 叶五一, 缪柏其. 基于Copula-ACD 模型的股票连涨和连跌收益率风险分析[J]. 系统工程理论与实践, 2010, 30(2): 298-304.
    HU Xinhan, YE Wuyi, MIAO Baiqi. Risk analysis of continuously rising and falling stock yield based on Copula-ACD method[J]. Systems Engineering: Theory & Practice, 2010, 30(2): 298-304.
    [9]
    叶五一, 李磊, 缪柏其. 高频连涨连跌收益率的相依结构以及CVaR分析[J]. 中国管理科学, 2013, 21(1): 8-15.
    YE Wuyi, LI Lei, MIAO Baiqi. Dependence structure and CVaR analysis of continuously rising and falling return[J]. Chinese Journal of Management Science, 2013, 21(1): 8-15.
    [10]
    黄飞, 谭常春. 运用变点理论对连涨连跌收益率的 Bayes 分析[J]. 合肥工业大学学报: 自然科学版, 2014, 37(2): 248-252.
    HUANG Fei, TAN Changchun. Application of change point theory in successive rises and falls of returns with Bayes analysis[J]. Journal of Hefei University of Technology (Natural Science), 2014, 37(2): 248-252.
    [11]
    GRANGERC W J. Investigating causal relations by econometric models and cross-spectral methods [J]. Econometrica, 1969, 37: 424-438.
    [12]
    GRANGER C W J. Some recent developments in a concept of causality[J]. Journal of Econometrics, 1988, 39: 199-211.
    [13]
    WANG X, ZHENG T, ZHU Y. Money-output Granger causal dynamics in China[J]. Economic Modelling, 2014, 43: 192-200.
    [14]
    ALZAHRANI M, MASIH M, AL-TITI O. Linear and non-linear Granger causality between oil spot and futures prices: A wavelet based test[J]. Journal of International Money and Finance, 2014, 48: 175-201.
    [15]
    CHUANG C C, KUAN C M, LIN H. Causality in quantiles and dynamic stock return-volume relations[J]. Journal of Banking & Finance, 2009, 33(7): 1 351-1 360.
    [16]
    HU M, LIANG H. A copula approach to assessing Granger causality[J]. Neuroimage, 2014, 100: 125-134.
    [17]
    YANG Z, TU A H, ZENG Y. Dynamic linkages between Asian stock prices and exchange rates: New evidence from causality in quantiles[J]. Applied Economics, 2014, 46(11): 1 184-1 201.
    [18]
    LEE T H, YANG W. Granger-causality in quantiles between financial markets: Using copula approach[J]. International Review of Financial Analysis, 2014, 33: 70-78.
    [19]
    吴亮, 邓明. 中国股票市场收益率与交易量的非对称因果关系研究——基于分位数Granger因果检验[J]. 上海金融, 2014 (6): 75-81.
    [20]
    罗雪玲. 中美股市的联动性分析——基于沪深 300 与道琼斯工业平均指数的实证研究[J]. 成都理工大学学报: 社会科学版, 2014, 22(1): 67-72.
    LUO Xueling. Analysis of the co-movement between Chinas and U.S. stock markets: Based on the CSI 300 and the Dow Jones Industrial Average Index[J]. Journal of Chengdu University of Technology (Social Sciences), 2014, 22(1): 67-72.
    [21]
    CHERNOZHUKOV V, UMANTSEVL. Conditional value-at-risk: Aspects of modeling and estimation[J]. Empirical Economics, 2001, 26(1): 271-292.
    [22]
    GIACOMINI R, KOMUNJER I. Evaluation and combination of conditional quantile forecasts[J]. Journal of Business & Economic Statistics, 2005, 23(4): 416-431.
    [23]
    DUFFIE D, PAN J. An overview of value at risk[J]. The Journal of Derivatives, 1997, 4(3): 7-49.
    [24]
    KOENKER R, BASSETT Jr G. Regression quantiles[J]. Econometrica, 1978, 46(1): 33-50.
    [25]
    KUPIEC P H. Techniques for verifying the accuracy of risk measurement models[J]. The Journal of Derivatives, 1995, 3(2): 73-84.
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    [1]
    GENCAY R, DACOROGNA M, MULLER U A, et al. An Introduction to High-Frequency Finance[M]. San Diego, CA：Academic Press, 2001.
    [2]
    SALVATIERRA I D L, PATTONA J. Dynamic copula models and high frequency data[J]. Journal of Empirical Finance, 2015, 30: 120-135.
    [3]
    HANSEN P R, HOREL G, LUNDEA, et al. A Markova chain estimator of multivariate volatility from high frequency data[M]// The Fascination of Probability, Statistics and Their Applications. Switzerland: Springer International Publishing, 2016: 361-394.
    [4]
    KOTKATVUORI-RNBERG J. Measuring actual daily volatility from high frequency intraday returns of the S&P futures and index observations[J]. Expert Systems with Applications, 2016, 43: 213-222.
    [5]
    HANSEN P R, HUANG Z. Exponential garch modeling with realized measures of volatility[J]. Journal of Business & Economic Statistics, 2016, 34(2): 269-287.
    [6]
    雷鸣, 缪柏其. 运用生存模型对上证指数涨跌天数的研究[J]. 运筹与管理, 2003, 12(6): 87-91.
    LEI Ming, MIAO Baiqi. Study of successive rises and falls of days with survival analysis[J]. Operations Research and Management Science, 2003, 12(6): 87-91.
    [7]
    雷鸣, 叶五一, 缪柏其, 等. 生存分析与股指涨跌的概率推断[J]. 管理科学学报, 2010, 13(4): 57-66.
    LEI Ming, YE Wuyi, MIAO Baiqi, et al. Survival analysis and the probability inference about the stock index[J]. Journal of Management Sciences in China, 2010, 13(4): 57-66.
    [8]
    胡心瀚, 叶五一, 缪柏其. 基于Copula-ACD 模型的股票连涨和连跌收益率风险分析[J]. 系统工程理论与实践, 2010, 30(2): 298-304.
    HU Xinhan, YE Wuyi, MIAO Baiqi. Risk analysis of continuously rising and falling stock yield based on Copula-ACD method[J]. Systems Engineering: Theory & Practice, 2010, 30(2): 298-304.
    [9]
    叶五一, 李磊, 缪柏其. 高频连涨连跌收益率的相依结构以及CVaR分析[J]. 中国管理科学, 2013, 21(1): 8-15.
    YE Wuyi, LI Lei, MIAO Baiqi. Dependence structure and CVaR analysis of continuously rising and falling return[J]. Chinese Journal of Management Science, 2013, 21(1): 8-15.
    [10]
    黄飞, 谭常春. 运用变点理论对连涨连跌收益率的 Bayes 分析[J]. 合肥工业大学学报: 自然科学版, 2014, 37(2): 248-252.
    HUANG Fei, TAN Changchun. Application of change point theory in successive rises and falls of returns with Bayes analysis[J]. Journal of Hefei University of Technology (Natural Science), 2014, 37(2): 248-252.
    [11]
    GRANGERC W J. Investigating causal relations by econometric models and cross-spectral methods [J]. Econometrica, 1969, 37: 424-438.
    [12]
    GRANGER C W J. Some recent developments in a concept of causality[J]. Journal of Econometrics, 1988, 39: 199-211.
    [13]
    WANG X, ZHENG T, ZHU Y. Money-output Granger causal dynamics in China[J]. Economic Modelling, 2014, 43: 192-200.
    [14]
    ALZAHRANI M, MASIH M, AL-TITI O. Linear and non-linear Granger causality between oil spot and futures prices: A wavelet based test[J]. Journal of International Money and Finance, 2014, 48: 175-201.
    [15]
    CHUANG C C, KUAN C M, LIN H. Causality in quantiles and dynamic stock return-volume relations[J]. Journal of Banking & Finance, 2009, 33(7): 1 351-1 360.
    [16]
    HU M, LIANG H. A copula approach to assessing Granger causality[J]. Neuroimage, 2014, 100: 125-134.
    [17]
    YANG Z, TU A H, ZENG Y. Dynamic linkages between Asian stock prices and exchange rates: New evidence from causality in quantiles[J]. Applied Economics, 2014, 46(11): 1 184-1 201.
    [18]
    LEE T H, YANG W. Granger-causality in quantiles between financial markets: Using copula approach[J]. International Review of Financial Analysis, 2014, 33: 70-78.
    [19]
    吴亮, 邓明. 中国股票市场收益率与交易量的非对称因果关系研究——基于分位数Granger因果检验[J]. 上海金融, 2014 (6): 75-81.
    [20]
    罗雪玲. 中美股市的联动性分析——基于沪深 300 与道琼斯工业平均指数的实证研究[J]. 成都理工大学学报: 社会科学版, 2014, 22(1): 67-72.
    LUO Xueling. Analysis of the co-movement between Chinas and U.S. stock markets: Based on the CSI 300 and the Dow Jones Industrial Average Index[J]. Journal of Chengdu University of Technology (Social Sciences), 2014, 22(1): 67-72.
    [21]
    CHERNOZHUKOV V, UMANTSEVL. Conditional value-at-risk: Aspects of modeling and estimation[J]. Empirical Economics, 2001, 26(1): 271-292.
    [22]
    GIACOMINI R, KOMUNJER I. Evaluation and combination of conditional quantile forecasts[J]. Journal of Business & Economic Statistics, 2005, 23(4): 416-431.
    [23]
    DUFFIE D, PAN J. An overview of value at risk[J]. The Journal of Derivatives, 1997, 4(3): 7-49.
    [24]
    KOENKER R, BASSETT Jr G. Regression quantiles[J]. Econometrica, 1978, 46(1): 33-50.
    [25]
    KUPIEC P H. Techniques for verifying the accuracy of risk measurement models[J]. The Journal of Derivatives, 1995, 3(2): 73-84.
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