The analysis of indexed astronomical time series – X. Significance testing of O − C data

It is assumed that O − C (‘observed minus calculated’) values of periodic variable stars are determined by three processes, namely measurement errors, random cycle‐to‐cycle jitter in the period, and possibly long‐term changes in the mean period. By modelling the latter as a random walk, the covariances of all O − C values can be calculated. The covariances can then be used to estimate unknown model parameters, and to choose between alternative models. Pseudo‐residuals which could be used in model fit assessment are also defined. The theory is illustrated by four applications to spotted stars in eclipsing binaries.