The analysis of irregularly observed stochastic astronomical time-series – I. Basics of linear stochastic differential equations
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Date
2005
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Publisher
Oxford University Press
Abstract
The theory of low-order linear stochastic differential equations is reviewed. Solutions to these
equations give the continuous time analogues of discrete time autoregressive time-series. Explicit
forms for the power spectra and covariance functions of first- and second-order forms are
given. A conceptually simple method is described for fitting continuous time autoregressive
models to data. Formulae giving the standard errors of the parameter estimates are derived.
Simulated data are used to verify the performance of the methods. Irregularly spaced observations
of the two hydrogen-deficient stars FQ Aqr and NO Ser are analysed. In the case of
FQ Aqr the best-fitting model is of second order, and describes a quasi-periodicity of about
20 d with an e-folding time of 3.7 d. The NO Ser data are best fitted by a first-order model
with an e-folding time of 7.2 d.
Description
Keywords
Methods: data analysis, Methods: statistical
Citation
Koen, C. (2005). The analysis of irregularly observed stochastic astronomical time-series – I. Basics of linear stochastic differential equations. Monthly Notices of the Royal Astronomical Society, 361(3): 887-896