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本文研究了金融高频时间序列的长记忆特征,介绍了已实现波动率、长记忆随机波动模型以及参数估计方法。由于长记忆随机波动模型(Long Memory Stochastic Volatility Model,LMSV)模型中参数较多,常用的参数估计方法不能解决参数估计问题,故采用半参数估计方法——Local Whittle估计。通过上海证券交易所上证综指2000年一2008年每五分钟的数据,选择ADF单位根检验验证了金融高频时间序列的平稳性,自相关图、重标极差法、对数周期图法验证了长记忆性,利用LMSV模型对中国股市的长记忆特征进行了参数估计,与广泛使用的自回归分整移动平均模型(Auto—Regressive Fractional Integrated Moving Average,ARFIMA)进行了对比,得到的长记忆参数d的估计结果均符合长记忆性的定义,发现LMSV模型在实际应用中的有效性。
In this paper, we study the long memory features of financial high frequency time series, introduce the volatility, long-memory stochastic volatility model and parameter estimation methods. Due to the large number of parameters in the Long Memory Stochastic Volatility Model (LMSV) model, the commonly used parameter estimation method can not solve the problem of parameter estimation. Therefore, the semi-parametric estimation method, the Local Whittle Estimation, is adopted. According to the data of every five minutes of Shanghai Stock Exchange in 2000-2008, ADF unit root test was used to verify the stability of high-frequency financial series, autocorrelation diagram, repackage method, logarithmic cycle diagram method The long memory is validated. The LMSV model is used to estimate the parameters of long memory in China’s stock market. Compared with the widely used Auto-Regressive Fractional Integrated Moving Average (ARFIMA) The results of memory parameter d are in accordance with the definition of long memory, and find the validity of LMSV model in practical application.