【题目】Estimating Fractional Continuous-Time Models with an Application to Realized VolatilityForecasting




【摘要】This paper proposes a two-stage method for estimating parameters in a parametric fractional continuous-time model based on discrete-sampled observations. In the first stage, the Hurst parameter is estimated based on the ratio of two second-order differences of observations from different time scales. In the second stage, the other parameters are estimated by the method of moments. All estimators have closed-form expressions and are easy to obtain. A large sample theory of the proposed estimators is derived under either the in-fill asymptotic scheme or the double asymptotic scheme. Extensive simulations show that the proposed theory performs well in finite samples. Two empirical studies are carried out. The first, based on the daily realized volatility of equities from 2011 to 2017, shows that the Hurst parameter is much lower than 0.5, which suggests that the realized volatility is too rough for continuous-time models driven by standard Brownian motion or fractional Brownian motion with Hurst parameter larger than 0.5. The second empirical study is of the daily realized volatility of exchange rates from 1986 to 1999. The estimate of the Hurst parameter is again much lower than 0.5. Moreover, the proposed fractional continuous-time model performs better than the autoregressive fractionally integrated moving average (ARFIMA) model out-of-sample.

【主讲人简介】王晓虎博士,香港中文大学大学经济系助理教授。他于2012年在新加坡管理大学获得经济学博士学位。他的主要研究兴趣在理论和应用计量经济学,尤其侧重为宏观和金融时间序列数据分析发展和提供新的计量方法。他已经在计量经济学国际顶级期刊Journal of Econometrics上发表多篇论文。


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