基于谱密度算子核滞后窗估计的一般白噪声检验
A general white noise test based on kernel lag-window estimates of the spectral density operator
摘要：
我们提出了一个通用的功能时间序列的白噪声测试的基础上估计之间的距离的谱密度算子的弱平稳时间序列和恒定的谱密度算子的不相关的时间序列。我们提出的估计是基于核滞后窗口型估计的谱密度算子。当观测到的时间序列是实可分希尔伯特空间中的强白噪声时，证明了检验统计量的渐近分布是标准正态的，并进一步证明了一般序列相关时间序列的检验统计量是发散的.这些结果恢复了Hong（1996）和Horváth等人（2013）的结果。为了实现测试，我们提出并研究了一些内核和带宽的选择，包括一个新的数据自适应带宽，以及数据自适应功率变换的检验统计量，提高了正常的近似在有限样本。仿真研究表明，所提出的方法具有良好的规模和提高功率相比，在文献中的其他方法，同时也提供了一个轻的计算负担。
英文摘要：
We propose a general white noise test for functional time series based on estimating a distance between the spectral density operator of a weakly stationary time series and the constant spectral density operator of an uncorrelated time series. The estimator that we propose is based on a kernel lag-window type estimator of the spectral density operator. When the observed time series is a strong white noise in a real separable Hilbert space, we show that the asymptotic distribution of the test statistic is standard normal, and we further show that the test statistic diverges for general serially correlated time series. These results recover as special cases those of Hong (1996) and Horváth et al. (2013). In order to implement the test, we propose and study a number of kernel and bandwidth choices, including a new data adaptive bandwidth, as well as data adaptive power transformations of the test statistic that improve the normal approximation in finite samples. A simulation study demonstrated that the proposed method has good size and improved power when compared to other methods available in the literature, while also offering a light computational burden.
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