Periodogram regression: A two-stage mixed effects approach for modelling multiple integer-valued time series of tropical cyclone frequency

Tropical cyclones (TC) are significant indicators of evolving climate dynamics. Two primary responses of interest are the cyclone frequency and intensity. In this paper we propose a novel integrated modelling framework for simultaneous modelling of TC frequency across several meteorological regions within Australasia. The key methodological insight is to model the second-order properties of multiple integer-valued time series in frequency domain, instead of parametric time domain models. We take a two-stage semiparametric approach, where large scale environmental variation is modelled using generalized linear models while the stochastic variation, including spatial heterogeneity, is estimated using spectral analysis of time series under a hierarchical generating model. Using longitudinal data analysis, we are able to jointly model periodicities in TC frequencies and their correlation with El Niño–Southern Oscillation (ENSO) cycles as well as the spatial variation between regions. We project the fitted model to obtain one-step-ahead forecasts under the principle of best linear unbiased estimation. This semiparametric approach allows us to obliterate the uniqueness matter of parametric integer-valued time series modelling. Additional methodological advantages include tests for spatial heterogeneity and temporal second-order stationarity. The data analysis corroborates previous findings on declining trend of tropical cyclone frequencies, in the short-term.