Journal article

Malliavin--Mancino Estimators Implemented with Nonuniform Fast Fourier Transforms

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Publication Details

Author list: Chang Patrick, Pienaar Etienne, Gebbie Tim

Publisher: Society for Industrial and Applied Mathematics

Publication year: 2020

Journal: SIAM Journal on Scientific Computing

Volume number: 42

Issue number: 6

Start page: B1378

End page: B1403

Total number of pages: 26

ISSN: 1064-8275

eISSN: 1095-7197



We implement and test kernel averaging nonuniform fast Fourier transform (NUFFT) methods to enhance the performance of correlation and covariance estimation on asynchronously sampled event data using the Malliavin--Mancino Fourier estimator. The methods are benchmarked for Dirichlet and Fejér Fourier basis kernels. We consider test cases formed from geometric Brownian motions to replicate synchronous and asynchronous data for benchmarking purposes. We consider three standard averaging kernels to convolve the event data for synchronization via oversampling for use with the FFT: the Gaussian kernel, the Kaiser--Bessel kernel, and the exponential of semicircle kernel. First, this allows us to demonstrate the performance of the estimator with different combinations of basis kernels and averaging kernels. Second, we investigate and compare the impact of the averaging scales explicit in each averaging kernel and its relationship with the time-scale averaging implicit in the Malliavin--Mancino estimator. Third, we compare the relationship between time-scale averaging based on the number of Fourier coefficients used in the estimator to a theoretical model of the Epps effect. We briefly demonstrate the methods on trade-and-quote (TAQ) data from the Johannesburg Stock Exchange to make an initial visualization of the correlation dynamics for various time scales under market microstructure.

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Last updated on 2020-09-11 at 21:24