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| Abstract: |
| 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. |
| Key words: structural autoregressive moving-average multivariate GARCH independent component causal structure volatility |
| DOI：10.11916/j.issn.1005-9113.18077 |
| Clc Number:F224.9 |
| Fund: |
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| Descriptions in Chinese: |
| ARMA-GARCH模型的多元波动率估计 谢鹏飞，冶继民，王俊元 （西安电子科技大学, 数学与统计学院, 西安 710071） 创新点说明：本文提出了基于结构自回归移动平均（ARMA）模型和GARCH模型相结合的ARMA-GARCH模型。建立了误差项向量独立分量的条件异方差与残差向量的条件异方差之间的关系，并将多元GARCH模型条件波动率脉冲响应的估计转化为估计误差项向量独立分量的脉冲响应，同时保持了因果结构。 研究目的： GARCH模型在金融时间序列中起着极其重要的作用，然而，多元GARCH模型的待估参数随着维数的增加呈指数级增加，因此寻找简单有效的估计方法显得尤为重要。 研究方法： 基于结构向量自回归移动平均（ARMA）模型和GARCH模型相结合的ARMA-GARCH模型。本文提出一种有效的多变量脉冲响应估计方法。首先，使用DirectLiNGAM算法识别模型的因果结构和估计误差项向量的独立分量，并使用MSE对算法的性能进行评估。其次，建立了误差项向量独立分量的条件异方差与残差向量的条件异方差之间的关系，将多元GARCH模型的条件波动率脉冲响应的估计转化为估计误差项向量独立分量的脉冲响应，同时保持因果结构。 结果和结论： 将所提出的估计方法用于股市波动率的估计，结果表明所提出的估计方法具有较高的计算效率。 关键词：结构向量自回归；多元GARCH；独立成分；因果结构；波动率 |
