Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome.

中文翻译：

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具有长程分形相关性的时间序列分割。


分段是一种数据分析的标准方法，用于识别将非平稳时间序列划分为同质段的变化点。然而，对于长程分形相关序列，大多数分割技术都会检测到虚假的变化点，这仅仅是由于相关性引起的异质性而不是真正的非平稳性。为了避免这种过度分割，我们提出了一种分割算法，它采用与要分割的序列具有相同相关程度的分数噪声建模的相关序列，而不是随机独立同分布序列作为同质性的参考。我们将我们的算法应用于具有长程相关性的人工序列，并表明它系统地仅检测由真实非平稳性产生的变化点，而不是由信号相关性产生的变化点。此外，我们将该方法应用于人类 21 号染色体长臂的序列，已知该序列具有长程分形相关性。我们仅获得了三个片段，这些片段清楚地对应于通过多尺度小波图揭示的不同 G + C 组成的三个区域。当对所有人类染色体序列进行分割时，也获得了类似的结果，表明人类基因组中存在以前未知的巨大组成上层结构。