The analysis of irregularly observed stochastic astronomical time-series – I. Basics of linear stochastic differential equations

摘要

The theory of low-order linear stochastic differential equations is reviewed. Solutions to theseequations give the continuous time analogues of discrete time autoregressive time-series. Explicitforms for the power spectra and covariance functions of first- and second-order forms aregiven. A conceptually simple method is described for fitting continuous time autoregressivemodels 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 observationsof the two hydrogen-deficient stars FQ Aqr and NO Ser are analysed. In the case ofFQ Aqr the best-fitting model is of second order, and describes a quasi-periodicity of about20 d with an e-folding time of 3.7 d. The NO Ser data are best fitted by a first-order modelwith an e-folding time of 7.2 d.