TY - JOUR

T1 - Detecting multiple periodicities in observational data with the multifrequency periodogram – I. Analytic assessment of the statistical significance

AU - Baluev, R.V.

PY - 2013

Y1 - 2013

N2 - We consider the ‘multifrequency’ periodogram, in which the putative signal is modelled as a sum of two or more sinusoidal harmonics with independent frequencies. It is useful in cases when the data may contain several periodic components, especially when their interaction with each other and with the data sampling patterns might produce misleading results. Although the multifrequency statistic itself was constructed earlier, for example by G. Foster in his CLEANest algorithm, its probabilistic properties (the detection significance levels) are still poorly known and much of what is deemed known is not rigorous. These detection levels are nonetheless important for data analysis. We argue that to prove the simultaneous existence of all n components revealed in a multiperiodic variation, it is mandatory to apply at least $2^n − 1$ significance tests, among which most involve various multifrequency statistics, and only $n$ tests are single-frequency ones. The main result of this paper is an analytic estimation

AB - We consider the ‘multifrequency’ periodogram, in which the putative signal is modelled as a sum of two or more sinusoidal harmonics with independent frequencies. It is useful in cases when the data may contain several periodic components, especially when their interaction with each other and with the data sampling patterns might produce misleading results. Although the multifrequency statistic itself was constructed earlier, for example by G. Foster in his CLEANest algorithm, its probabilistic properties (the detection significance levels) are still poorly known and much of what is deemed known is not rigorous. These detection levels are nonetheless important for data analysis. We argue that to prove the simultaneous existence of all n components revealed in a multiperiodic variation, it is mandatory to apply at least $2^n − 1$ significance tests, among which most involve various multifrequency statistics, and only $n$ tests are single-frequency ones. The main result of this paper is an analytic estimation

KW - methods:analytical methods:data analysis methods:statistical

U2 - 10.1093/mnras/stt1617

DO - 10.1093/mnras/stt1617

M3 - Article

VL - 436

SP - 807

EP - 818

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 1

ER -