GARCH models play an extremely important role in financial time series.However,the parameter estimation of the multivariate GARCH model is challenging because the parameter number is square of the dimension of the mod...GARCH models play an extremely important role in financial time series.However,the parameter estimation of the multivariate GARCH model is challenging because the parameter number is square of the dimension of the model.In this paper,the model of structural vector autoregressive moving⁃average(ARMA)with GARCH is discussed and an efficient multivariate impulse response estimation method is proposed.First,the causal structure of the model was identified and the independent component of error term vector was estimated by DirectLiNGAM algorithm.Then,the relationship between conditional heteroscedasticity of the independent component of error term vector and that of residual vector was constructed,and the estimation of the impulse response of conditional volatility of multivariate GARCH models was translated to the estimation of the impulse response of error term vector.The independency among the independent components was translated to the impulse response estimation of the univariate case and the causal structure was maintained.Finally,the proposed estimation method was used to estimate the volatility of stock market,which proved that the method is computational efficient.展开更多
This paper introduces the new class of periodic multivariate GARCH models in their periodic BEKK specification.Semi-polynomial Markov chains combined with algebraic geometry are used to obtain some properties like irr...This paper introduces the new class of periodic multivariate GARCH models in their periodic BEKK specification.Semi-polynomial Markov chains combined with algebraic geometry are used to obtain some properties like irreducibility.We impose weak conditions to obtain the strict periodic stationarity and the geometric ergodicity of the process,via the theory of positive linear operators on a cone:it is supposed that zero belongs to the support of the driving noise density which is absolutely continuous with respect to the Lebesgue measure and the spectral radius of a matrix built from the periodic coefficients of the model is smaller than one.展开更多
This paper proposes a method for modelling volatilities(conditional covariance matrices)of high dimensional dynamic data.We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH...This paper proposes a method for modelling volatilities(conditional covariance matrices)of high dimensional dynamic data.We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH models to establish a model to describe the dynamics of high dimensional volatilities.Sparsity condition and thresholding technique are applied to the estimation of the error covariance matrices,and quasi maximum likelihood estimation(QMLE)method is used to estimate the parameters of the common factor conditional covariance matrix.Asymptotic theories are developed for the proposed estimation.Monte Carlo simulation studies and real data examples are presented to support the methodology.展开更多
This paper investigates the linkage of returns and volatilities between the United States and Chinese stock markets from January 2010 to March 2020.We use the dynamic conditional correlation(DCC)and asymmetric Baba–E...This paper investigates the linkage of returns and volatilities between the United States and Chinese stock markets from January 2010 to March 2020.We use the dynamic conditional correlation(DCC)and asymmetric Baba–Engle–Kraft–Kroner(BEKK)GARCH models to calculate the time-varying correlations of these two markets and examine the return and volatility spillover effects between these two markets.The empirical results show that there are only unidirectional return spillovers from the U.S.stock market to the Chinese stock market.The U.S.stock market has a consistently positive spillover to China’s next day’s morning trading,but its impact on China’s next day’s afternoon trading appears to be insignificant.This finding implies that information in the U.S.stock market impacts the performance of the Chinese stock market differently in distinct semi-day trading.Moreover,with respect to the volatility,there are significant bidirectional spillover effects between these two markets.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.61573014)
文摘GARCH models play an extremely important role in financial time series.However,the parameter estimation of the multivariate GARCH model is challenging because the parameter number is square of the dimension of the model.In this paper,the model of structural vector autoregressive moving⁃average(ARMA)with GARCH is discussed and an efficient multivariate impulse response estimation method is proposed.First,the causal structure of the model was identified and the independent component of error term vector was estimated by DirectLiNGAM algorithm.Then,the relationship between conditional heteroscedasticity of the independent component of error term vector and that of residual vector was constructed,and the estimation of the impulse response of conditional volatility of multivariate GARCH models was translated to the estimation of the impulse response of error term vector.The independency among the independent components was translated to the impulse response estimation of the univariate case and the causal structure was maintained.Finally,the proposed estimation method was used to estimate the volatility of stock market,which proved that the method is computational efficient.
基金the support of the University of Science and Technology Houari Boumediene (USTHB) and the Ministry of Higher Education and Scientific Research, Algiers, Algeria for the PNR 25/08the support of the University of Médéa, Algeria
文摘This paper introduces the new class of periodic multivariate GARCH models in their periodic BEKK specification.Semi-polynomial Markov chains combined with algebraic geometry are used to obtain some properties like irreducibility.We impose weak conditions to obtain the strict periodic stationarity and the geometric ergodicity of the process,via the theory of positive linear operators on a cone:it is supposed that zero belongs to the support of the driving noise density which is absolutely continuous with respect to the Lebesgue measure and the spectral radius of a matrix built from the periodic coefficients of the model is smaller than one.
基金supported by the National Natural Science Foundation of China(Nos.11731015,11701116)Innovative Team Project of Ordinary Universities in Guangdong Province(No.2020WCXTD018)Guangzhou University Research Fund(Nos.YG2020029,YH202108)。
文摘This paper proposes a method for modelling volatilities(conditional covariance matrices)of high dimensional dynamic data.We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH models to establish a model to describe the dynamics of high dimensional volatilities.Sparsity condition and thresholding technique are applied to the estimation of the error covariance matrices,and quasi maximum likelihood estimation(QMLE)method is used to estimate the parameters of the common factor conditional covariance matrix.Asymptotic theories are developed for the proposed estimation.Monte Carlo simulation studies and real data examples are presented to support the methodology.
文摘This paper investigates the linkage of returns and volatilities between the United States and Chinese stock markets from January 2010 to March 2020.We use the dynamic conditional correlation(DCC)and asymmetric Baba–Engle–Kraft–Kroner(BEKK)GARCH models to calculate the time-varying correlations of these two markets and examine the return and volatility spillover effects between these two markets.The empirical results show that there are only unidirectional return spillovers from the U.S.stock market to the Chinese stock market.The U.S.stock market has a consistently positive spillover to China’s next day’s morning trading,but its impact on China’s next day’s afternoon trading appears to be insignificant.This finding implies that information in the U.S.stock market impacts the performance of the Chinese stock market differently in distinct semi-day trading.Moreover,with respect to the volatility,there are significant bidirectional spillover effects between these two markets.
