Isolating cyclical patterns in irregular time-series data

Times-series data which are observed at irregular time intervals often arise in economics and the bio-sciences. Existing methods for modelling these data have focused on the discretisation of continuous processes. A method is proposed for fitting cyclical components to irregular time-series data based on the continuous-discrete Kalman filter which incorporates numerical integration of the differential equations describing the model. The method is applied to seawater temperature data and empirical sampling distributions for parameter estimators are enumerated. The supporting sampling distributions suggest that the method yields estimates which have satisfactory statistical properties.