A simple test for periodic signals in red noise

By S. Vaughan. 2004

296 citations recorded by the source corpus.

We demonstrate a simple method for testing the significance of peaks in the periodogram of red noise data. The procedure was designed to test for spurious periodicities in X-ray light curves of active galaxies, but can be used quite generally to test for periodic components against a background noise spectrum assumed to have a power law shape. The method provides a simple and fast test of the significance of candidate periodic signals in short, well-sampled time series such as those obtained from XMM-Newton observations of Seyfert galaxies, without the need for Monte Carlo simulations. A full account is made of the number of trials and the uncertainties inherent to the model fitting. Ignoring these subtle effects can lead to substantially overestimated significances. These difficulties motivate us to demand high standards of detection (minimum >99.9 per cent confidence) for periodicities in sources that normally show red noise spectra. The method also provides a simple means to estimate the power spectral index, which may be an interesting parameter itself, regardless of the presence/absence of periodicities.

Subfields: Applied Mathematics, Atmospheric Science, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/8af1465951b3968941afe31a99066c3df20ac798

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Andrey Korotayev
2. S. Tsirel
3. I. McHardy
4. D. Emmanoulopoulos
5. I. Papadakis
6. P. Uttley
7. S. Vaughan

In Atmospheric Science

1. Andrey Korotayev
2. S. Tsirel
3. I. Papadakis
4. D. Emmanoulopoulos
5. I. McHardy

In Global and Planetary Change

1. Andrey Korotayev
2. S. Tsirel
3. I. Papadakis
4. D. Emmanoulopoulos
5. I. McHardy
6. S. Vaughan

Citations in the corpus

• A Spectral Analysis of World GDP Dynamics: Kondratieff Waves, Kuznets Swings, Juglar and Kitchin Cycles in Global Economic Development, and the 2008–2009 Economic Crisis (2010, methodology): “The simplest method (Vaughan 2005) employs (the symbols are ours throughout) the following equation: f(ω) ≈ a + b /ωn, (A2) that assumes an arbitrary exponent, but that does not take into account either the finiteness of the correlation distance (α > 0), or the presence of the white noise in the…”
• Generating artificial light curves: revisited and updated (2013, methodology): “This is the approach used in this work and detailed references can be found in (e.g. Anderson et al. 1990; Vaughan 2005; Barret & Vaughan 2012).”
• Observations of Turbulent Magnetic Reconnection within a Solar Current Sheet (2018, background): “This type of fluctuation is also known as red “noise”, which is an intrinsic property of a random physical process, most likely due to turbulence, that can be described by a power-law spectrum with a negative slope (Vaughan 2005; Inglis et al. 2015; Ning 2017).”
• A Bayesian test for periodic signals in red noise (2009, methodology): “In a previous paper, Vaughan (2005) (henceforth V05), we proposed what is essentially a generalisation of Fisher’s method to the case where the noise spectrum is a power law:SR(f) = βf−α (whereα andβ are the power law index and normalisation parameters).”
• X-ray reverberation around accreting black holes (2014, background): “An alternative approach, which converges more quickly to Gaussian-distributed errors, is to bin log(Pn,m), which also necessitates adding a constant bias to the binned logpower, see Papadakis & Lawrence (1993); Vaughan (2005) for details.”
• Fluctuations in functional connectivity associated with interictal epileptiform discharges (IEDs) in intracranial EEG (2021, unknown): “While it is mathematically possible to have meaningful changes in phase synchrony between signals without prominent oscillations[68], we do not observe consistent changes in these processes during IEDs.”