Time-series forecasting is a key component in the automation and optimization of intelligent applications. It is not a trivial task, as there are various short-term and/or long-term temporal dependencies. Multiscale modeling has been considered as a promising strategy to solve this problem. However, the existing multiscale models either apply an implicit way to model the temporal dependencies or ignore the interrelationships between multiscale subseries. In this article, we propose a multiscale interactive recurrent network (MiRNN) to jointly capture multiscale patterns. MiRNN employs a deep wavelet decomposition network to decompose the raw time series into multiscale subseries. MiRNN introduces three key strategies (truncation, initialization, and message passing) to model the inherent interrelationships between multiscale subseries, as well as a dual-stage attention mechanism to capture multiscale temporal dependencies. Experiments on four real-world datasets demonstrate that our model achieves promising performance compared with the state-of-the-art methods.