Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting

Forecasting high-dimensional time series plays a crucial role in many applications such as demand forecasting and financial predictions. Modern real-world datasets can have millions of correlated time-series that evolve together, i.e they are extremely high dimensional (one dimension for each individual time-series). Thus there is need for exploiting these global patterns and coupling them with local calibration for better prediction. However, most recent deep learning approaches in the literature are one-dimensional, i.e, even though they are trained on the whole dataset, during prediction, the future forecast for a single dimension mainly depends on past values from the same dimension. In this paper, we seek to correct this deficiency and propose DeepGLO, a deep forecasting model which thinks globally and acts locally. In particular, DeepGLO is a hybrid model that combines a global matrix factorization model regularized by a temporal deep network with a local deep temporal model that captures patterns specific to each dimension. The global and local models are combined via a data-driven attention mechanism for each dimension. The proposed deep architecture used is a variation of temporal convolution termed as leveled network which can be trained effectively on high-dimensional but diverse time series, where different time series can have vastly different scales, without a priori normalization or rescaling. Empirical results demonstrate that DeepGLO outperforms state-of-the-art approaches on various datasets; for example, we see more than 30% improvement in WAPE over other methods on a real-world dataset that contains more than 100K-dimensional time series.