The analysis of indexed astronomical time series -- IV. Modelling period changes in sparsely observed variables

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Abstract
This paper attempts to place the modelling of period changes in variable stars on a sound quantitative basis. Two techniques for analysing observed sequences of a particular light-curve phase of interest (e.g. pulsational light maximum or eclipse minimum) are presented. The first is a maximum likelihood estimation procedure, suitable when the mean period is subject to changes that can be represented by a simple analytic functional form. The second method, state-space modelling, can be used in more general situations. Allowance is made for the effects of non-systematic random variations in the period, as well as for systematic long-term changes in the magnitude of measurement errors. The techniques are illustrated with simulated and real data.

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