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Abstract

This paper introduces a novel approach to modelling non-white residual noise in discrete time series. We present a Markov chain Monte Carlo (MCMC) algorithm for combined posterior inference on signal and noise parameters. By choosing a conjugate prior distribution for the noise parameters, the additional Gibbs sampling steps have a particularly simple form and are easy to implement as well as fast to run. Furthermore, the sampling-based approach allows for easy inference on the autocovariance function. The model is illustrated using a well-known sunspot dataset as well as a simulated dataset of a chirp signal embedded in non-Normal, coloured noise where the spectrum is regarded as a nuisance parameter.