Symmetric positive semi-definite Fourier estimator of instantaneous variance-covariance matrix

2023/04/10 by Jirô Akahori, Akahori, Jirô, Nien-Lin Liu +7
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #FOS: Economics and business #Methodology (stat.ME) #Random Matrices and Applications #Spatial and Panel Data Analysis #Statistical Finance (q-fin.ST)

paper · pdf · doi:10.48550/arxiv.2304.04372

openalex publication_date 2023/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we propose an estimator of spot covariance matrix which ensure symmetric positive semi-definite estimations. The proposed estimator relies on a suitable modification of the Fourier covariance estimator in Malliavin and Mancino (2009) and it is consistent for suitable choices of the weighting kernel. The accuracy and the ability of the estimator to produce positive semi-definite covariance matrices is evaluated with an extensive numerical study, in comparison with the competitors present in the literature. The results of the simulation study are confirmed under many scenarios, that consider the dimensionality of the problem, the asynchronicity of data and the presence of several specification of market microstructure noise.

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