当前位置: X-MOL 学术SIAM J. Sci. Comput. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Malliavin--Mancino Estimators Implemented with Nonuniform Fast Fourier Transforms
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2020-11-09 , DOI: 10.1137/20m1325903
Patrick Chang , Etienne Pienaar , Tim Gebbie

SIAM Journal on Scientific Computing, Volume 42, Issue 6, Page B1378-B1403, January 2020.
We implement and test kernel averaging nonuniform 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 synchronization via oversampling for use with the FFT: the Gaussian kernel, the Kaiser--Bessel kernel, and the exponential of semicircle 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 with the time-scale averaging implicit in the Malliavin--Mancino estimator. Third, we compare 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 visualization of the correlation dynamics for various time scales under market microstructure.


中文翻译:

使用非均匀快速傅立叶变换实现的Malliavin-Mancino估计器

SIAM科学计算杂志,第42卷,第6期,第B1378-B1403页,2020年1月。
我们实施并测试内核平均非均匀快速傅立叶变换(NUFFT)方法,以增强使用Malliavin-Mancino傅立叶估计器对异步采样事件数据进行相关和协方差估计的性能。该方法以Dirichlet和FejérFourier基核为基准。我们考虑由几何布朗运动形成的测试用例,以复制同步和异步数据以进行基准测试。我们考虑使用三个标准的平均内核来对事件数据进行卷积以通过与FFT一起使用的过采样进行同步:高斯内核,Kaiser-Bessel内核和半圆内核的指数。首先,这使我们可以用基本内核和平均内核的不同组合来演示估计器的性能。第二,我们研究并比较了每个平均内核中显式平均尺度的影响及其与Malliavin-Mancino估计量中隐含的时间尺度平均的关系。第三,我们将基于估计器中使用的傅立叶系数的数量的时标平均之间的关系与Epps效应的理论模型进行了比较。我们简要地演示了约翰内斯堡证券交易所的交易报价(TAQ)数据方法,以便在市场微观结构下初步可视化各种时间尺度的相关动态。我们将基于估计器中使用的傅立叶系数数量的时标平均之间的关系与Epps效应的理论模型进行了比较。我们简要地演示了约翰内斯堡证券交易所的交易报价(TAQ)数据方法,以便在市场微观结构下初步可视化各种时间尺度的相关动态。我们将基于估计器中使用的傅立叶系数数量的时标平均之间的关系与Epps效应的理论模型进行了比较。我们简要地演示了约翰内斯堡证券交易所的交易报价(TAQ)数据方法,以便在市场微观结构下初步可视化各种时间尺度的相关动态。
更新日期:2020-12-04
down
wechat
bug