Stochastic significance of peaks in the least-squares spectrum

Pagiatakis, Spiros

doi:10.1007/s001900050220

Cited by 78 publications

(64 citation statements)

References 13 publications

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“…The LSSA has its roots in [19,20]. Its advantages over classical Fourier analysis have already been presented in the literature and need not be repeated here (see, e.g., [21][22][23]). For the sake of comprehensiveness, we only present the fundamental formulas and emphasize the statistical properties of this method.…”

Section: Least Squares Spectral Analysismentioning

confidence: 99%

“…The LSSA spectrum is described by the percentage variance s(ω j ) of the spectral content of a specific cyclic frequency ω j , which is the ratio of the quadratic norm of the specific signal to the total quadratic norm of the series: [24,25]. Reference [22] showed that the probability density function (PDF) of the LS spectrum s(ω j ) is a beta distribution defined by two parameters α and β, where α = 1 and β depends on the number of data points (length of the series) and the number of unknown parameters estimated by the LS estimation (degrees of freedom of the LS system).…”

Section: Least Squares Spectral Analysismentioning

confidence: 99%

“…Moreover, the mean and the variance of the product spectrum can easily be defined. Let a random variable X denote the LS spectrum, which is distributed as beta(x; α, β), with α = 1 and β dependent upon the degrees of freedom of the linear LS system as follows [22,Theorem 3]:…”

Section: Least Squares Product Spectrummentioning

confidence: 99%

“…(4) For each SG segment corresponding to the AG experiment, the LSSA v5.02 software [22,23] is used for the following purposes: (a) offset detection and identification of the time they occur, (b) residual outlier detection and flagging, (c) detection of any periodicities or deterministic signals followed by their suppression, and (d) test on the variance factor using Chi-square test [24].…”

Section: Data Preprocessing and Filteringmentioning

confidence: 99%

See 3 more Smart Citations

On the Potential of Least Squares Response Method for the Calibration of Superconducting Gravimeters

El-Gelil

Pagiatakis

El-Rabbany

2012

International Journal of Geophysics

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One of the most important operating procedures after the installation of a superconducting gravimeter (SG) is its calibration. The calibration process can identify and evaluate possible time variability in the scale factor and in the hardware anti-aliasing filter response. The SG installed in Cantley, Canada is calibrated using two absolute gravimeters and the data are analysed in the time and frequency domains to estimate the SG scale factor. In the time domain, we use the weighted linear regression method whereas in the frequency domain we use the least squares response method. Rigorous statistical procedures are applied to define data disturbances, outliers, and realistic data noise levels. Using data from JILA-2 and FG5-236 separately, the scale factor is estimated in the time and frequency domains as −78.374 ± 0.012 μGal/V and −78.403 ± 0.075 μGal/V, respectively. The relative accuracy in the time domain is 0.015%. We cannot identify any significant periodicity in the scale factor. The hardware anti-aliasing filter response is tested by injecting known waves into the control electronics of the system. Results show that the anti-aliasing filter response is stable and conforms to the global geodynamics project standards.

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Section: Least Squares Spectral Analysismentioning

confidence: 99%

Section: Least Squares Spectral Analysismentioning

confidence: 99%

Section: Least Squares Product Spectrummentioning

confidence: 99%

Section: Data Preprocessing and Filteringmentioning

confidence: 99%

See 2 more Smart Citations

On the Potential of Least Squares Response Method for the Calibration of Superconducting Gravimeters

El-Gelil

Pagiatakis

El-Rabbany

2012

International Journal of Geophysics

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“…non-uniform sampling and noise. The detection of sinusoidal oscillations in this framework is basically a statistical hypothesis test, particularly a significance test of spectral peaks in the least squares spectrum (Pagiatakis 1999).…”

Section: Introductionmentioning

confidence: 99%

Detection of a sinusoidal oscillation of unknownfrequency in a time series – a geodetic approach

Lehmann¹

2014

Journal of Geodetic Science

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Geodetic and geophysical time series may contain sinusoidal oscillations of unknown angular frequency. Often it is required to decide if such sinusoidal oscillations are truly present in a given time series. Here we pose the decision problem as a statistical hypothesis test, an approach very popular in geodesy and other scientific disciplines. In the case of unknown angular frequencies such a test has not yet been proposed. We restrict ourselves to the detection of a single sinusoidal oscillation in a one-dimensional time series, sampled at non-uniform time intervals. We compare two solution methods: the likelihood ratio test for parameters in a Gauss-Markov model and the analysis of the Lomb-Scargle periodogram. Whenever needed, critical values of these tests are computed using the Monte Carlo method. We analyze an exemplary time series from an absolute gravimetric observation by various tests. Finally, we compare their statistical power. It is found that the results for the exemplary time series are comparable. The LR test is more flexible, but always requires the Monte Carlo method for the computation of critical values. The periodogram analysis is computationally faster, because critical values can be approximately deduced from the exponential distribution, at least if the sampling is nearly uniform.

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Transformative resonant moderation of geomagnetic polarity and strata

Omerbashich

2021

Preprint

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Claims of paleodata periodicity are many and controversial so that, for example, superimposing Phanerozoic (0-541 My) massextinction periods renders life on Earth impossible. This period hunt coincided with the modernization of geochronology which now ties geological timescales to orbital frequencies. Such tuneup simplifies energy-band (variance-) stratification of information contents, enabling separation of astronomical signal from any harmonics. Variance-based spectral analysis techniques can achieve this, such as the Gauss-Vaníček method favored by astronomers for resilience with even extreme data gaps. I thus show on diverse data (geomagnetic polarity, cratering, extinction episodes) that many-body subharmonic entrainment causes the Earth to respond to its astronomical forcing resonantly, so that the 2π-phase-shifted axial precession p=26 ky, and its Pi=2πp/i; i=1,…,n harmonics, are resonantly responsible for virtually all paleodata periods. This resonantly quasiperiodic nature of strata is shown co-triggered by the p'/4-lockstep to the p'=41-ky obliquity (also 2π-phase-shifted, to P'=3.5-My superperiod). For verification, residuals analysis after suppressing 2πp (and thus Pi, too) in the current polarity-reversals GPTS-95 timescale's calibration extending to end-Campanian (0-83 My) successfully detected weak signals of Earth-Mars planetary resonances, reported previously from older epochs. The only significant residual signal is intrinsic 26.5-My Rampino period -carrier wave of crushing deflections which, during Transformative Resonant Events (TRE), decimate strata to quasiperiodicity, co-responsible for polarity reversals and whose detection confirms geomagnetism overall ergodicity. The (2πp, Pi) resonant response of the Earth to orbital forcing is the longsought, energy-transfer mechanism of the Milankovitch theory -now a special case applicable to the current episode of Earth-Moon-Sun system resonant dynamics springing from the 1-40 My very long band. Fundamental system properties -2π-phaseshift, ¼ lockstep to a forcer, and discrete time translation symmetry (multiplied or halved periods) -previously were thought typical of a discrete time crystal, which here then appears unremarkable.

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Stochastic significance of peaks in the least-squares spectrum

Cited by 78 publications

References 13 publications

On the Potential of Least Squares Response Method for the Calibration of Superconducting Gravimeters

On the Potential of Least Squares Response Method for the Calibration of Superconducting Gravimeters

Detection of a sinusoidal oscillation of unknownfrequency in a time series – a geodetic approach

Transformative resonant moderation of geomagnetic polarity and strata

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