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考虑到交易周期对资产价格波动特征的重要影响,将小波多尺度分析引入广义自回归条件异方差(GARCH)建模理论,提出了多尺度广义自回归条件异方差模型和多尺度增广分整广义自回归条件异方差均值模型,同时通过改进迭代的步长参数,得到了收敛速度快于BHHH算法的数值优化方法.对上证综合指数进行实证分析,结果表明:该模型克服了GARCH理论无法同时揭示蕴含在资产价格内部的多时间尺度信息的缺陷,还能够捕获到资产收益率在不同时间尺度上的局部波动特征;改进后的算法对模型参数估值效果十分明显.这类模型有助于探究资产价格伴随交易周期演化的微观动力学机制.
Considering the important influence of transaction cycle on the fluctuation characteristics of asset prices, the multi-scale wavelet analysis is introduced into the GARCH model of generalized autoregressive conditional (GARCH) modeling. A multi-scale generalized autoregressive conditional heteroskedasticity model and multi- The generalized autoregressive conditional heteroskedasticity averaging model is proposed, and the numerical optimization method of convergence rate faster than BHHH algorithm is obtained by improving the iterative step parameters.An empirical analysis of the composite index shows that this model can not overcome the problem that GARCH theory can not simultaneously Revealing the shortcomings of multi-time scale information embedded in asset prices, and also capturing the local fluctuation characteristics of asset return on different time scales.The improved algorithm is very effective in model parameter estimation.These models are helpful to Explore the micro-dynamics of asset prices with the evolution of trading cycles.