Modeling and forecasting seasonal and trend time series is an important research topic in many areas of industrial and economic activity. In this study, we forecast the seasonal and trend time series using a quasi-linear autoregressive model. This quasi-linear autoregressive model belongs to a class of varying coefficient models in which its autoregressive coefficients are constructed by radial basis function networks. A combined genetic optimization and gradient-based optimization algorithm is applied for automatic selection of proper input variables and model-dependent variables, and optimizing the model parameters simultaneously. The model is tested by five monthly time series. We compare the results with those of other various methods, which show the effectiveness of the proposed approach for the seasonal time series. 
Seasonal and trend time series forecasting based on a quasi-linear autoregressive model