Estimation and Inference of Fractional Continuous-Time Model with Discrete-Sampled Data
Xiaohu Wang (),
Weilin Xiao () and
Jun Yu ()
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Xiaohu Wang: The Chinese University of Hong Kong
Weilin Xiao: Zhejiang University
No 17-2019, Economics and Statistics Working Papers from Singapore Management University, School of Economics
This paper proposes a two-stage method for estimating parameters in a para-metric 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 pro-posed 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 frac-tional continuous-time model performs better than the autoregressive fractionally integrated moving average (ARFIMA) model out-of-sample.
Keywords: Rough Volatility; Hurst Parameter; Second-order Difference; Different Time Scales; Method of Moments; ARFIMA (search for similar items in EconPapers)
JEL-codes: C15 C22 C32 (search for similar items in EconPapers)
Pages: 50 pages
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
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Persistent link: https://EconPapers.repec.org/RePEc:ris:smuesw:2019_017
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