Estimation of the coherence time of stochastic oscillations from modest samples
Loading...
Date
2012
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Oxford University Press
Abstract
‘Quasi-periodic’ or ‘solar-like’ oscillations can be described by three parameters – a characteristic
frequency, a coherence time (or ‘quality factor’) and the variance of the random
driving process. This paper is concerned with the estimation of these quantities, particularly
the coherence time, from modest sample sizes (observations covering of the order of a hundred
or fewer oscillation periods). Under these circumstances, finite sample properties of the periodogram
(bias and covariance) formally invalidate the commonly used maximum-likelihood
procedure. It is shown that it none the less gives reasonable results, although an appropriate
covariance matrix should be used for the standard errors of the estimates. Tailoring the frequency
interval used, and oversampling the periodogram, can substantially improve parameter
estimation. Maximum-likelihood estimation in the time-domain has simpler statistical properties,
and generally performs better for the parameter values considered in this paper. The
effects of added measurement errors are also studied. An example analysis of pulsating star
data is given.
Description
Keywords
Methods: statistical, Stars: oscillations
Citation
Koen, C. (2012). Estimation of the coherence time of stochastic oscillations from modest samples. Monthly Notices of the Royal Astronomical Society, 419(2): 1197-1218