We present a new method of modelling time-series data based on the running optimal average (ROA). By identifying the effective number of parameters for the ROA model, in terms of the shape and width of its window function and the times and accuracies of the data, we enable a Bayesian analysis, optimising the ROA width, along with other model parameters, by minimising the Bayesian Information Criterion (BIC) and sampling joint posterior parameter distributions using MCMC methods. For analysis of quasar lightcurves, our implementation of ROA modelling can inter-calibrate lightcurve data from different telescopes, estimate the shape and thus the power-density spectrum of the lightcurve, and measure time delays among lightcurves at different wavelengths or from different images of a lensed quasar. Our noise model implements a robust treatment of outliers and error-bar adjustments to account for additional variance or poorly-quantified uncertainties. Tests with simulated data validate the parameter uncertainty estimates. We compare ROA delay measurements with results from cross-correlation and from JAVELIN, which models lightcurves with a prior on the power-density spectrum. We analyse published COSMOGRAIL lightcurves of multi-lensed quasar lightcurves and present the resulting measurements of the inter-image time delays and detection of microlensing effects.
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