In this study, a new bootstrapped hybrid artificial neural network is proposed for forecasting. This new neural network provides input significance, linearity and nonlinearity hypothesis tests in a unique network structure via a residual bootstrap approach. The network has three parts: linear, non-linear and a combination with associated weights and biases. These weights are used to test the input significance, linearity and nonlinearity hypotheses with this new method providing empirical distributions for forecasts and weights. The proposed method employs a bagging approach to obtain forecasts. It is then applied to real-time series including the M4 Competition data set and stock exchange time series where its performance is compared with appropriate benchmark methods including other popular neural networks. The proposed method results are less affected than other neural networks by initial random weights, which means that the results of the proposed method are more stable and precise. The new method provides improvements in forecasting accuracy over the established benchmarks.