Least-squares spectral analysis, an alternative to the classical Fourier transform, is a method of analyzing unequally spaced and non-stationary time series'/> Least-Squares Wavelet Analysis of Unequally Spaced and Non-stationary Time Series and Its Applications
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Least-Squares Wavelet Analysis of Unequally Spaced and Non-stationary Time Series and Its Applications

机译：不平等间隔和非静止时间序列及其应用的最小二乘小波分析

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AbstractLeast-squares spectral analysis, an alternative to the classical Fourier transform, is a method of analyzing unequally spaced and non-stationary time series in their first and second statistical moments. However, when a time series has components with low or high amplitude and frequency variability over time, it is not appropriate to use either the least-squares spectral analysis or Fourier transform. On the other hand, the classical short-time Fourier transform and the continuous wavelet transform do not consider the covariance matrix associated with a time series nor do they consider trends or datum shifts. Moreover, they are not defined for unequally spaced time series. A new method of analyzing time series, namely, the least-squares wavelet analysis is introduced, which is a natural extension of the least-squares spectral analysis. This method decomposes a time series to the time–frequency domain and obtains its spectrogram. In addition, the probability distribution function of the spectrogram is derived that identifies statistically significant peaks. The least-squares wavelet analysis can analyze any non-stationary and unequally spaced time series with components of low or high amplitude and frequency variability, including datum shifts, trends, and constituents of known forms, by taking into account the covariance matrix associated with the time series. The outstanding performance of the proposed method on synthetic time series and a very long baseline interferometry series is demonstrated, and the results are compared with the weighted wavelet Z-transform.
机译： ara id =“par1”>最小二乘频谱分析，校园傅里叶变换的替代方法是在他们的第一和第二统计时刻分析不平等间隔和非静止时间序列的方法。然而，当时间序列随时间具有低或高幅度和频率变化的时间序列时，使用最小二乘频谱分析或傅里叶变换是不合适的。另一方面，经典的短时傅里叶变换和连续小波变换不考虑与时间序列相关的协方差矩阵，也不考虑他们考虑趋势或基准移位。此外，它们未被定义为不均等间隔时间序列。介绍了一种分析时间序列的新方法，即引入了最小二乘小波分析，这是最小二乘光谱分析的自然延伸。该方法将时间序列分解给时频域并获得其频谱图。另外，推导出谱图的概率分布函数，其识别统计上显着的峰。最小二乘小波分析可以通过考虑与之相关的协方差矩阵时间序列。对合成时间序列和非常长的基线干涉测量系列的提出方法的出色性能进行了说明，并将结果与​​加权小波Z变换进行比较。

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