Time Series with Mixed Spectra

Li, Ta‐Hsin

doi:10.1201/b15154

Cited by 30 publications

(39 citation statements)

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“…Note that the classical Fisher's test [20] standardizes the periodogram ordinates by the estimated PSD of a white noise. Standardization (2) can be seen as a generalization of this approach (see [24] for a recent review). The estimate S E (ν) can be parametric or non-parametric.…”

Section: B Unknown Noise Statistics: Related Workmentioning

confidence: 99%

“…A further complication arises when multiple sinusoids are present under the alternative, as they perturb the estimation of the noise PSD [5], [27]. Standardized tests for this case can be found in [21], [22], [24], [27]- [29]. These tests are however non adaptive in the number of sinusoids (which must be set a priori) and designed for white noise.…”

Section: B Unknown Noise Statistics: Related Workmentioning

confidence: 99%

“…Even if such approaches are relatively straightforward to implement, characterizing the distribution of P (ν k | S E,AR ) is more difficult than in the case of P (ν k |P L ), owing essentially to the stochastic nature of o AR in (24). In practice, the 'whitening' effect of S E,AR is efficient because the selection procedures have good fitting properties (they are approximately consistent, i.e.,Ŝ E,AR ≈ −→ S E as N −→ +∞).…”

Section: Hc ⋆ and Bjmentioning

confidence: 99%

See 2 more Smart Citations

A Study of Periodograms Standardized Using Training Datasets and Application to Exoplanet Detection

Sulis

Mary

Bigot

2017

IEEE Trans. Signal Process.

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When the noise affecting time series is colored with unknown statistics, a difficulty for sinusoid detection is to control the true significance level of the test outcome. This paper investigates the possibility of using training data sets of the noise to improve this control. Specifically, we analyze the performances of various detectors applied to periodograms standardized using training data sets. Emphasis is put on sparse detection in the Fourier domain and on the limitation posed by the necessarily finite size of the training sets available in practice. We study the resulting false alarm and detection rates and show that standardization leads in some cases to powerful constant false alarm rate tests. The study is both analytical and numerical. Although analytical results are derived in an asymptotic regime, numerical results show that theory accurately describes the tests' behaviour for moderately large sample sizes. Throughout the paper, an application of the considered periodogram standardization is presented for exoplanet detection in radial velocity data.

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Section: B Unknown Noise Statistics: Related Workmentioning

confidence: 99%

Section: B Unknown Noise Statistics: Related Workmentioning

confidence: 99%

Section: Hc ⋆ and Bjmentioning

confidence: 99%

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A Study of Periodograms Standardized Using Training Datasets and Application to Exoplanet Detection

Sulis

Mary

Bigot

2017

IEEE Trans. Signal Process.

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“…As remarked after the proposition, the error rate becomes O(T −3/2 ) for g(T ) equal to or greater than O(T 1/6 ). In the closely related time series setting, the unwindowed periodogram achieves the same rate when g(T ) is greater than O(T 1/2 ) (Theorem 6.8b of [13]). We will therefore examine ν − ν λ ∞ as a function of T at the frequency resolutions corresponding to g(T ) ∈ {6, T 1/6 , T 1/2 }.…”

Section: 1mentioning

confidence: 95%

Super-resolution Estimation of Cyclic Arrival Rates

2016

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Exploiting the fact that most arrival processes exhibit cyclic behaviour, we propose a simple procedure for estimating the intensity of a nonhomogeneous Poisson process. The estimator is the super-resolution analogue to Shao and Lii [19,20], which is a sum of p sinusoids where p and the amplitude and phase of each wave are not known and need to be estimated. This results in an interpretable yet flexible specification that is suitable for use in modelling as well as in high resolution simulations.Our estimation procedure sits in between classic periodogram methods and atomic/total variation norm thresholding. Through a novel use of window functions in the point process domain, our approach attains super-resolution without semidefinite programming. Under suitable conditions, finite sample guarantees can be derived for our procedure. These resolve some open questions and expand existing results in spectral estimation literature.

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“…Even if some of these estimators are asymptotically unbiased, the unavoidable injection of estimation noise in the denominator of the standardized periodogram makes the statistical characterization of the test statistics difficult. One can resort to Monte Carlo or bootstrap simulations [17] to evaluate the thresholds empirically (see [18], Chap.7 for examples of gaps between theoretical and empirical thresholds), but this procedure may not be tractable for massive time series (large N ). In Astronomy, preprocessing stages aimed at "whitening" the noise (e.g.…”

Section: Introductionmentioning

confidence: 99%

Using hydrodynamical simulations of stellar atmospheres for periodogram standardization: Application to exoplanet detection

Sulis¹,

Mary²,

Bigot³

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Our aim is to devise a detection method for exoplanet signatures (multiple sinusoids) that is both powerful and robust to partially unknown statistics under the null hypothesis. In the considered application, the noise is mostly created by the stellar atmosphere, with statistics depending on the complicated interplay of several parameters. Recent progresses in hydrodynamic (HD) simulations show however that realistic stellar noise realizations can be numerically produced off-line by astrophysicists. We propose a detection method that is calibrated by HD simulations and analyze its performances. A comparison of the theoretical results with simulations on synthetic and real data shows that the proposed method is powerful and robust.

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Time Series with Mixed Spectra

Cited by 30 publications

References 0 publications

A Study of Periodograms Standardized Using Training Datasets and Application to Exoplanet Detection

A Study of Periodograms Standardized Using Training Datasets and Application to Exoplanet Detection

Super-resolution Estimation of Cyclic Arrival Rates

Using hydrodynamical simulations of stellar atmospheres for periodogram standardization: Application to exoplanet detection

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