ETS framework smoothing controls.

Three exponential smoothing (ES) methods within the state-space forecasting (ETS) framework employed herein were automatically selected n times each, according to the Akaike's Information Criterion (AIC), to forecast Schistosoma haematobium–induced terminal hematuria consultation rate time-series (TS) for the district of Niono, Mali (1996–2004). The multiplicative error/ trendless/ aseasonal (MNN), multiplicative error/ damped additive trend/ aseasonal (MAdN), and multiplicative error/ damped multiplicative trend/ aseasonal (MMdN) ES methods were selected 45, 6, and 16 times, respectively. Though the estimated smoothing controls for each of these ES method are time-dependent, they fluctuate only slightly (Results). Thus, they are reported above as median and inter-quartile range (IQR) values. These three methods are remarkably similar. The MNN was the most frequently selected ES method (n = 45). Only the α value was listed for this method because it only has a level (lt) TS component; β and φ, are reserved for methods that have trend (rt) and rt-dampening TS components (i.e. MAdN and MMdN). For MAdN and MMdN methods, β≤α≪φ due to large dampening of minute rt TS components. Of note, smoothing controls differ in function across ES methods, their retained notation notwithstanding. In sum, only aseasonal methods with minute or inexistent rt plus significant lt TS components were automatically selected during the investigational period, suggesting that: 1) TS forcing by seasonal covariates is not limiting; and, 2) public health intervention, population behavior, migration, and irrigation management may govern S. haematobium–induced terminal hematuria consultation rate TS fluctuations in this district. The strength of the forecasting approach employed herein relies on the automatic and systematic AIC-directed switches between ES methods within the ETS framework as new observations accumulate, conferring an additional layer of flexibility to TS predictions.