Deep learning has increasingly been studied as a black-box method for audio effects modeling. While successful for some effects like equalizers or guitar amplifiers, learning long-range dependencies remains challenging. We discuss the disparity between streamed target and windowed target, and introduce the state prediction network, a general method addressing long-range dependencies in stateful models. We propose a novel model architecture, conduct hyperparameter search, and compare it with stateless and recurrent state-of-the-art models. Our architecture achieves better spectral accuracy with reduced training costs.