For testing hypothesis on the covariance operator of functional time series, we suggest to use the full functional information and to avoid dimension reduction techniques. The limit distribution follows from the central limit theorem of the weak convergence of the partial sum process in general Hilbert space applied to the product space. In order to obtain critical values for tests, we generalise bootstrap results from the independent to the dependent case. This results can be applied to covariance operators, autocovariance operators and cross covariance operators. We discuss one sample and changepoint tests and give some simulation results.

中文翻译：

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函数时间序列的自举协方差算子

为了检验函数时间序列协方差算子的假设，我们建议使用完整的函数信息并避免降维技术。极限分布遵循应用于乘积空间的一般希尔伯特空间中部分求和过程的弱收敛的中心极限定理。为了获得测试的临界值，我们将自举结果从独立案例推广到相关案例。这个结果可以应用于协方差算子、自协方差算子和交叉协方差算子。我们讨论了一个样本和变化点测试，并给出了一些模拟结果。