NONLINEAR PROPERTIES OF MEASLES EPIDEMIC DATA ASSESSED WITH A KERNEL NONPARAMETRIC IDENTIFICATION APPROACH

Kernel nonparametric nonlinear autoregression was applied to measles data from the pre-vaccination era (1944-1966). A slowly sliding time window covered 20 overlapping segments of the series. In the case of data from Birmingham the order of the model was higher than 22 for all windows and the reconstructed noise free realizations were periodic with the most probable period being equal to 3 years, though values of 2, 4 and 6 years were also obtained. For London data 6 windows were with low orders (below 5). Low order noise free realizations were chaotic. The rest presented periodic solutions corresponding to 1, 2, and 3-years cycles. Our results are consistent with views about dynamical transitions among measles data. The method is reliable and puts practically no restrictions regarding data properties. We recommend its use for further exploration of epidemic data from different origin.