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：在本文中，我们提出了一种估计现货协方差矩阵的估计器，它确保了对称正半定估计。所提出的估计器依赖于对Malliavin和Mancino（2009年）中傅里叶协方差估计器的适当修改，并且在适当选择加权核的情况下是一致的。通过与文献中的竞争对手进行广泛的数值研究评估估计器的准确性和产生正半定协方差矩阵的能力。模拟研究的结果在考虑问题的维度、数据的异步性以及市场微观结构噪声的多个规范的情况下得到了证实。