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

Paper: arXiv 2304.04372

Authors: Jirô Akahori, Nien-Lin Liu, Maria Elvira Mancino, Tommaso Mariotti, Yukie Yasuda

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a mathematically rigorous modification to the Malliavin-Mancino Fourier covariance estimator to guarantee positive semi-definiteness. It supports its theoretical framework with a solid, high-dimensional simulation study addressing asynchronous trading and microstructure noise.

Research Flowchart

  flowchart TD
    A[Research Goal: Ensure Symmetric Positive Semi-Definite Spot Covariance Estimations] --> B[Data Inputs: Asynchronous High-Frequency Equity Prices with Noise]
    B --> C[Methodology: Modified Fourier Covariance Estimator using Weighting Kernels]
    C --> D[Computational Process: Extensive Numerical Simulation Study]
    D --> E[Outcomes: Consistent, PSD Matrix Estimations Across Dimensionalities]