Nonparametric Likelihood for Volatility Under High Frequency Data

Lorenzo Camponovo, Yukitoshi Matsushita and Taisuke Otsu
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Lorenzo Camponovo: University of Surrey
Yukitoshi Matsushita: Tokyo Institute of Technology
Taisuke Otsu: London School of Economics

No 318, School of Economics Discussion Papers from School of Economics, University of Surrey

Abstract: We propose a nonparametric likelihood inference method for the integrated volatility under high frequency financial data. The nonparametric likelihood statistic, which contains the conventional statistics such as empirical likelihood and Pearson’s x^2 as special cases, is not asymptotically pivotal under the so-called infill asymptotics, where the number of high frequency observations in a fixed time interval increases to infinity. We show that multiplying a correction term recovers the x^2 limiting distribution. Furthermore, we establish Bartlett correction for our modified nonparametric likelihood statistic under the constant and general non-constant volatility cases. In contrast to the existing literature, the empirical likelihood statistic is not Bartlett correctable under the infill asymptotics. However, by choosing adequate tuning constants for the power divergence family, we show that the second order refinement to the order O(n^{-2}) can be achieved.

Pages: 16 pages
Date: 2018-02
New Economics Papers: this item is included in nep-ets and nep-mst
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https://repec.som.surrey.ac.uk/2018/DP03-18.pdf (application/pdf)

Related works:
Working Paper: Nonparametric likelihood for volatility under high frequency data (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:sur:surrec:0318

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