The dynamics of many viral infections, including rotaviral infections (RIs), are known to have a complex non-linear, non-stationary structure with strong seasonality indicative of virus and host sensitivity to environmental conditions. However, analytical tools suitable for the identification of seasonal peaks are limited. We introduced a two-step procedure to determine seasonal patterns in RI and examined the relationship between daily rates of rotaviral infection and ambient temperature in cold climates in three Russian cities: Chelyabinsk, Yekaterinburg, and Barnaul from 2005 to 2011. We described the structure of temporal variations using a new class of singular spectral analysis (SSA) models based on the “Caterpillar” algorithm. We then fitted Poisson polyharmonic regression (PPHR) models and examined the relationship between daily RI rates and ambient temperature. In SSA models, RI rates reached their seasonal peaks around 24 February, 5 March, and 12 March (i.e., the 55.17 ± 3.21, 64.17 ± 5.12, and 71.11 ± 7.48 day of the year) in Chelyabinsk, Yekaterinburg, and Barnaul, respectively. Yet, in all three cities, the minimum temperature was observed, on average, to be on 15 January, which translates to a lag between the peak in disease incidence and time of temperature minimum of 38–40 days for Chelyabinsk, 45–49 days in Yekaterinburg, and 56–59 days in Barnaul. The proposed approach takes advantage of an accurate description of the time series data offered by the SSA-model coupled with a straightforward interpretation of the PPHR model. By better tailoring analytical methodology to estimate seasonal features and understand the relationships between infection and environmental conditions, regional and global disease forecasting can be further improved.

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Abstract. In the paper, an adaptive algorithm for time series forecasting based on the selection of an analogue period is proposed. A distinctive feature of the algorithm is the use of training sample of forecasts for the automatic selection of optimal parameters of its work. The algorithm was employed for prediction of the hydrological time series of inflow to Novosibirsk Reservoir (the Ob River). The efficiency of its use (an increase in the accuracy of forecasts) is demonstrated compared with the basic algorithm.

The algorithm of the adaptive resonant theory ART-2 is based on the ideas of dynamic clustering and the unsupervised learning model. The classic application of the ART-2 algorithm is related to the solution of pattern recognition problems in the framework of the neural network approach. The article proposes a modification of the adaptive resonance theory ART-2 as applied to the solution of the time series (TS) prediction problem. A description of the TS forecasting algorithm based on ART-2, its properties and application features, as well as the results of a study of TS free electricity prices of the “day-ahead market” (DAM) in Russia is here. The obtained results allow us to conclude about the prospects of using ART-2 to study the structure and prediction of TS with a periodic (seasonal) component.