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首页> 外文期刊>Journal of Time Series Analysis >HIGHER-ORDER ACCURATE SPECTRAL DENSITY ESTIMATION OF FUNCTIONAL TIME SERIES
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HIGHER-ORDER ACCURATE SPECTRAL DENSITY ESTIMATION OF FUNCTIONAL TIME SERIES

机译：函数时间序列的高阶精确谱密度估计

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摘要

Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel estimators based on the notion of a flat-top kernel. The new class of estimators employs the inverse Fourier transform of a flat-top function as the weight function employed to smooth the periodogram. It is shown that using a flat-top kernel yields a bias reduction and results in a higher-order accuracy in terms of optimizing the integrated mean square error (IMSE). Notably, the higher-order accuracy of flat-top estimation comes at the sacrifice of the positive semi-definite property. Nevertheless, we show how a flat-top estimator can be modified to become positive semi-definite (even strictly positive definite) in finite samples while retaining its favorable asymptotic properties. In addition, we introduce a data-driven bandwidth selection procedure realized by an automatic inspection of the estimated correlation structure. Our asymptotic results are complemented by a finite-sample simulation where the higher-order accuracy of flat-top estimators is manifested in practice.
机译：在弱相关函数时间序列的频域框架下，关键要素是频谱密度内核，该内核封装了过程的二阶动力学。我们基于平顶核的概念提出了一类频谱密度核估计器。新型估计器将平顶函数的傅立叶逆变换用作权重函数，以平滑周期图。结果表明，在优化积分均方误差（IMSE）方面，使用平顶核可降低偏差并提高精度。值得注意的是，平顶估计的高阶精度来自牺牲正半定性。然而，我们展示了如何在有限样本中将平顶估计量修改为正半定（甚至严格为正定），同时保持其良好的渐近性质。另外，我们介绍了一种通过自动检查估计的相关结构来实现的数据驱动带宽选择程序。我们的渐近结果得到了有限样本模拟的补充，在有限样本模拟中，平顶估计器的高阶精度在实践中得到了体现。

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