Combined TBATS and SVM model of minimum and maximum air temperatures applied to wheat yield prediction at different locations in Europe.

• The combined SVM/TBATS model improves pure TBATS or SVM air temperature prediction. • Dynamics of the weather conditions influences SVM/TBATS long-term prediction. • The lengths of the learning/testing data sets should be individually estimated. • The SVM/TBATS model can be successfully used for filling gaps in time series data. • SVM/TBATS predicted and measured temperature values lead to similar modelled yield. This paper explores the idea of combining Trigonometric Exponential Smoothing State Space model with Box-Cox transformation, ARMA errors, Trend and Seasonal Components (TBATS) with Support Vector Machine (SVM) model to estimate time series of the minimum and maximum daily air temperatures in a period of six years for various climatic localizations in Europe. It was found that a combined SVM/TBATS model can predict not only seasonality but also local temperature variation between subsequent days observed in daily data. Because the SVM sub-model uses not only results of TBATS prediction as an input data, but also several meteorological values, such modelling cannot be treated as a future time series estimation. Therefore, it has a potential to be used for filling gaps in the air temperature data. As is shown in our results, the precision of air temperature prediction improves when using the combined SVM/TBATS modelling, compared with pure TBATS or SVM modelling. For various locations, which can be related with different climatic conditions, this improvement ranged from 3% up to 14% for the maximum daily air temperature and from 5% to 25% for the minimum daily air temperature. The temperature sums calculated on the base of air temperatures predicted with SVM/TBATS models and from measured values did not differ more than 300°C (less than 1°C per day) in majority of cases. The average error in wheat yield prediction by WOFOST and DNDC models did not exceed 12.8% and 13.3%, respectively. [ABSTRACT FROM AUTHOR]