Time series, periodograms, and significance
Time series, periodograms, and significance
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时间序列、周期图和显着性
DOI：
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发表时间：
1999
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影响因子：
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通讯作者：
G. Hernández
中科院分区：
文献类型：
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作者：
G. Hernández
地球物理学文献表明，从测量数据中提取相干振荡有意义信息的方法使用广泛且相互冲突。这使得很难，如果不是不可能的话，将不同作者报告的调查结果联系起来。因此，我们已经进行了严格的调查的测试和方法，用于确定存在的统计上显着的相干振荡周期图来自时间序列。统计显著性检验仅在对测量中存在的独立频率执行时有效。周期图中可能的独立频率的数量和显著性检验都是由自由度的数量决定的，自由度是时间序列中存在的真正独立测量的数量，而不是测量中的样本点的数量。自由度的数量是数据的固有属性，必须根据时间序列的序列相干性来确定。作为这项调查的一部分，进行了详细的研究，清楚地说明了明显无辜的和常用的过滤，去趋势和逐渐减少的数据对周期图分析的有害影响，以及由此产生的解释统计学意义的困难。为了清楚起见，包含不均匀间隔的测量、间隙等的实际现场测量的具体示例，以及合成的例子，已被用来说明周期图的方法，和陷阱，导致（统计）的显着性测试相干振荡的存在。在这项调查的见解是：（1）时间序列的概念是（统计上）受其自身序列相干性限制的频带，因此具有临界采样率，该临界采样率定义了实验的适当统计设计的必要要求之一;（2）设计一个临界检验，以确定可用于描述时间序列的最大有效频率数，同时保持测试样本的方差不变;（3）证明数据的操作给所述数据的统计学显著性解释带来了不必要的困难;以及（4）通过使用常规Lomb-Scargle显著性检验获得的显著性结果中的明显差异的解决和校正，与长期存在的Schuster-Walker和Fisher检验相比，
The geophysical literature shows a wide and conflicting usage of methods employed to extract meaningful information on coherent oscillations from measurements. This makes it difficult, if not impossible, to relate the findings reported by different authors. Therefore, we have undertaken a critical investigation of the tests and methodology used for determining the presence of statistically significant coherent oscillations in periodograms derived from time series. Statistical significance tests are only valid when performed on the independent frequencies present in a measurement. Both the number of possible independent frequencies in a periodogram and the significance tests are determined by the number of degrees of freedom, which is the number of true independent measurements, present in the time series, rather than the number of sample points in the measurement. The number of degrees of freedom is an intrinsic property of the data, and it must be determined from the serial coherence of the time series. As part of this investigation, a detailed study has been performed which clearly illustrates the deleterious effects that the apparently innocent and commonly used processes of filtering, de-trending, and tapering of data have on periodogram analysis and the consequent difficulties in the interpretation of the statistical significance thus derived. For the sake of clarity, a specific example of actual field measurements containing unevenly-spaced measurements, gaps, etc., as well as synthetic examples, have been used to illustrate the periodogram approach, and pitfalls, leading to the (statistical) significance tests for the presence of coherent oscillations. Among the insights of this investigation are: (1) the concept of a time series being (statistically) band limited by its own serial coherence and thus having a critical sampling rate which defines one of the necessary requirements for the proper statistical design of an experiment; (2) the design of a critical test for the maximum number of significant frequencies which can be used to describe a time series, while retaining intact the variance of the test sample; (3) a demonstration of the unnecessary difficulties that manipulation of the data brings into the statistical significance interpretation of said data; and (4) the resolution and correction of the apparent discrepancy in significance results obtained by the use of the conventional Lomb-Scargle significance test, when compared with the long-standing Schuster-Walker and Fisher tests.