论文标题
Malliavin-Mancino估计器以不均匀的快速傅立叶变换实现
Malliavin-Mancino estimators implemented with non-uniform fast Fourier transforms
论文作者
论文摘要
我们使用Malliaiavin-Mancino傅立叶估算器实施和测试内核，以增强异步采样事件数据的相关性和协方差估计的性能。这些方法是针对Dirichlet和FejérFourier基核的基准测试的。我们考虑从几何布朗动作形成的测试用例，以复制同步和异步数据以进行基准测试。我们考虑三个标准的平均内核来通过对快速傅立叶变换（FFT）的过度采样（FFT）进行交换事件数据：高斯内核，kaiser-bessel内核和半圆核的指数。首先，这使我们能够以不同的基础内核和平均内核的不同组合来证明估计器的性能。其次，我们调查并比较了每个平均内核中平均量表的影响及其在Malliavin-Mancino估计器中隐含的时间尺度平均之间的关系。第三，我们根据估计器中使用的傅立叶系数数量与EPPS效应的理论模型中的傅立叶系数数量进行了时间尺度平均之间的关系。我们简要说明了约翰内斯堡证券交易所的贸易和引号（TAQ）数据的方法，以对市场微观结构下各种时间表的相关性动态进行初步可视化。
We implement and test kernel averaging Non-Uniform 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 synchronisation via over-sampling for use with the Fast Fourier Transform (FFT): the Gaussian kernel, the Kaiser-Bessel kernel, and the exponential of semi-circle 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 between the time-scale averaging implicit in the Malliavin-Mancino estimator. Third, we demonstrate 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 visualisation of the correlation dynamics for various time-scales under market microstructure.
