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Abstract:
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We propose a mixture-of-experts approach to modelling the spectral density of a non-stationary time series, where the non-stationarity is with respect to space, time and other covariates. This research is motivated by the need to identify and predict influenza "signatures" across Western Australia. This is achieved by developing a novel nonparametric spatial-temporal model for influenza counts in Western Australia. The underlying spectra are modelled as functions of time, space, and covariates such as the type of influenza virus, weather conditions and the demographic data, using a mixture formulation. The number of components in the mixture is assumed to be unknown but finite. The Whittle likelihood is used as an approximation to the true likelihood and Gaussian process priors for the mixture components are used to model the spectra as functions of frequency. The frequentist properties of the technique are examined via simulation. Initial analysis of the real example reveals that there are distinct influenza signatures in WA. These signatures depend not only on space and time but also on covariates such as workforce movement patterns
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