Koen, Chris2013-12-022013-12-022005Koen, 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): 887-8960035-8711http://hdl.handle.net/10566/889The 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.en© 2005 copyright Oxford University Press. This file may be freely used for educational purposes, as long as it is not altered in any way. Acknowledgement of the authors and the source is required.Methods: data analysisMethods: statisticalArticle