The total electron content TEC plays a vital role in solving many technological problems, especially in eliminating the influence of the ionosphere on positioning accuracy. The constant development of deep learning models significantly increased the accuracy of TEC forecasting solutions, but also increased the computational costs, which are undesirable for traditional single-frequency GPS users. The given brief review of publications revealed significant shortcomings of deep learning models and led to the need to develop methods that provide a trade-off between the complexity of the architectures and the computational costs. For this purpose several architecture options are considered, including the autoregressive (AR) model, the autoregressive integrated moving average (ARIMA) model, the simplest shallow neural network based on a dense architecture, the deep convolutional bidirectional neural network, the deep recurrent neural network, the hybrid model consisting of an AR-model and a shallow neural network. It is shown that the hybrid of autoregressive and neural network models, combining analytical and numerical approaches to forecasting, provides high accuracy comparable to the accuracy of deep bidirectional neural networks, while having a relatively small number of trainable parameters, several orders of magnitude smaller than the considered deep models, which makes it possible to use and retrain it on computers of medium and low power.