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.

翻译：本文提出了一种确保对称正半定估计的瞬时协方差矩阵估计量。该估计量基于对Malliavin与Mancino（2009）中傅里叶协方差估计量的适当修正，并在选择合适权重核函数时具有一致性。我们通过广泛的数值研究，评估了该估计量产生正半定协方差矩阵的精度与能力，并与文献中现有方法进行了比较。模拟研究结果在多种场景下得到验证，这些场景考虑了问题维度、数据异步性以及市场微观结构噪声的多种设定。