Recurrent and convolutional neural networks are the most common architectures used for time series forecasting in deep learning literature. These networks use parameter sharing by repeating a set of fixed architectures with fixed parameters over time or space. The result is that the overall architecture is time-invariant (shift-invariant in the spatial domain) or stationary. We argue that time-invariance can reduce the capacity to perform multi-step-ahead forecasting, where modelling the dynamics at a range of scales and resolutions is required. We propose ForecastNet which uses a deep feed-forward architecture to provide a time-variant model. An additional novelty of ForecastNet is interleaved outputs, which we show assist in mitigating vanishing gradients. ForecastNet is demonstrated to outperform statistical and deep learning benchmark models on several datasets.