得分驱动乘性成分已实现CARR模型及其实证研究

Score-driven Multiplicative Component Tealized CARR Model and its Empirical Study

本文对条件自回归极差(CARR)模型进行扩展,引入基于高频数据的已实现测度,设定条件极差具有乘性成分结构:将条件极差乘性分解为长期(趋势)成分和短期(暂时)成分,并采用得分驱动方法设定这两个成分的动态性,构建了得分驱动乘性成分已实现CARR(SD-MCRCARR)模型。基于上证综合指数和深证成分指数高频数据的实证研究表明,SD-MCRCARR模型相比其他基准模型(包括SD-CARR模型、SD-RCARR模型和SD-MCCARR模型)具有更好的数据拟合效果。利用稳健的损失函数及模型置信集(MCS)检验作为判断准则,实证比较了SD-MCRCARR模型与其他基准模型对波动率的预测能力。实证结果表明:SD-MCRCARR模型相比其他基准模型具有更好的波动率预测能力,而且SD-MCRCARR模型优越的波动率预测能力具有关于不同预测窗口和预测期的稳健性。

Modelling and forecasting volatility is important for many financial applications,such as asset alloca⁃tion,risk measurement and option pricing.It is well known that volatility is time-varying and highly persistent,and many models have been proposed to capture these stylized facts.The generalized autoregressive conditional heteroskedasticity(GARCH)model is among the most popular model.However,the model is return-based model that uses only daily closing prices to model and estimate volatility and fails to exploit the intraday informa⁃tion.An alternative approach for estimating volatility is to apply the daily price range,which is based on intraday high and low prices.The high-low price range has been proven to be a more efficient volatility estimator than the return-based one.The classical range volatility model,conditional autoregressive range(CARR)model,fails to exploits the intraday information in high-frequency data and belongs to the class of single component volatility models,which is incapable of capturing the dynamics of financial volatility adequately.An important feature of volatility is the high persistence(long memory property).To account for this salient stylized fact of volatility,the additive component GARCH volatility models have been proposed in the earlier literature.In recent years,multiplicative component volatility models have received a great deal of attention in the financial econometrics literature.The models feature a multiplicative decomposition of volatility into a short-run and a long-run component.It is claimed that the multiplicative component models are more attractive than the additive component models,which are able to capture complex volatility dynamics such as the high persistence of volatil⁃ity.By incorporating the realized measure,assuming a multiplicative component structure for the conditional range:the first component traces the long-run(secular)volatility trends,while the second component captures the short-run(transitory)movements in volatility,and adopting the score-driven approach to drive the dynamics of the two components,an extension of the CARR model is proposed,namely the score-driven multiplicative component realized CARR(SD-MCRCARR)model.The proposed SD-MCRCARR model that incorporates the realized measure(the intraday information of high-frequency data)as well as the multiplicative component volatility structure is able to quickly capture severe market fluctuation and to account for long-memory volatil⁃ity.In addition,the model builds upon the score-driven framework which builds a dynamic update mechanism exploiting information contained in the score of the conditional distribution(predictive likelihood)of the observa⁃tions.Also,an important advantage of the model is that the practical implementation of the model is simple since it is an observation-driven model and the likelihood function is available in closed form and therefore estimation can be easily performed by the maximum likelihood method.The empirical analysis using the highfrequency data of the Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index shows that the SD-MCRCARR model outperforms other benchmark models including the SD-CARR model,the SD-RCARR model and the SD-MCCARR model in the empirical fit.Further,the forecasting performance of the SD-MCRCARR model and the benchmark models are compared by using the robust loss functions and the model confidence set(MCS)test.The results show that the SD-MCRCARR model yields more accurate volatility forecasts than the benchmark models.Moreover,the superior forecast ability of the proposed SD-MCRCARR model is robust to alternative forecasting windows and forecasting horizons.