Narrow-Band Analysis of Nonstationary Processes
Narrow-Band Analysis of Nonstationary Processes
复制标题
非平稳过程的窄带分析
DOI：
10.1214/aos/1013699988
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
P. Robinson
中科院分区：
文献类型：
--
作者：
P. Robinson
研究了一类非平稳过程的平均周期图和交叉周期图的行为。该过程包括非平稳的任何阶的分数，以及渐近平稳的分数。交叉周期图可以包括两个可能不同阶数的非平稳过程，或者一个非平稳过程和一个渐近平稳过程。平均发生在整个频带上，或者发生在随着样本大小增加而缓慢退化到零频率的频带上。在某些情况下，它被发现没有渐近差异，特别是我们表明如何在二维空间的集成订单的平均值和方差的变化的行为。结果只采用本地零假设的基础弱平稳序列的频谱。它示出了如何的结果可以应用在分数阶协整未知的整合。
The behaviour of averaged periodograms and cross-periodograms of a broad class of nonstationary processes is studied. The processes include nonstationary ones that are fractional of any order, as well as asymptotically stationary fractional ones. The cross-periodogram can involve two nonstationary processes of possibly different orders, or a nonstationary and an asymptotically stationary one. The averaging takes place either over the whole frequency band, or over one that degenerates slowly to zero frequency as sample size increases. In some cases it is found to make no asymptotic difference, and in particular we indicate how the behaviour of the mean and variance changes across the two-dimensional space of integration orders. The results employ only local-to-zero assumptions on the spectra of the underlying weakly stationary sequences. It is shown how the results can be applied in fractional cointegration with unknown integration orders.