Fourier transform methods for pathwise covariance estimation in the presence of jumps

Christa Cuchiero and Josef Teichmann

Stochastic Processes and their Applications, 2015, vol. 125, issue 1, 116-160

Abstract: We provide a new non-parametric Fourier procedure to estimate the trajectory of the instantaneous covariance process (from discrete observations of a multidimensional price process) in the presence of jumps extending the seminal work of Malliavin and Mancino (2002, 2009). Our approach relies on a modification of (classical) jump-robust estimators of integrated realized covariance to estimate the Fourier coefficients of the covariance trajectory. Using Fourier–Féjer inversion we reconstruct the path of the instantaneous covariance. We prove consistency and a central limit theorem (CLT) and in particular that the asymptotic estimator variance is smaller by a factor 2/3 in comparison to classical local estimators.

Keywords: Non-parametric spot variance estimation; Fourier analysis; Jump–diffusion; Jump-robust estimation techniques (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (16)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:125:y:2015:i:1:p:116-160

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DOI: 10.1016/j.spa.2014.07.023

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