N-BEATS: Neural basis expansion analysis for interpretable time series forecasting

TL;DR

N-BEATS introduces a pure deep learning architecture for univariate time series forecasting that uses backward/forward residual blocks and a deep FC stack to achieve state-of-the-art results on M3, M4, and Tourism datasets without time-series-specific features. It provides two configurations—generic and interpretable—where the latter imposes trend and seasonality inductive biases via polynomial and Fourier bases to yield decomposed, human-understandable forecasts. The architecture supports extensive ensembling and multi-horizon training, and is framed within a meta-learning perspective to explain its generalization and transfer capabilities. Overall, the work demonstrates that deep learning can outperform traditional statistical methods in broad TS forecasting tasks and that interpretability can be achieved without sacrificing accuracy, with practical implications for forecasting practice and research into meta-learning analogies.

Abstract

We focus on solving the univariate times series point forecasting problem using deep learning. We propose a deep neural architecture based on backward and forward residual links and a very deep stack of fully-connected layers. The architecture has a number of desirable properties, being interpretable, applicable without modification to a wide array of target domains, and fast to train. We test the proposed architecture on several well-known datasets, including M3, M4 and TOURISM competition datasets containing time series from diverse domains. We demonstrate state-of-the-art performance for two configurations of N-BEATS for all the datasets, improving forecast accuracy by 11% over a statistical benchmark and by 3% over last year's winner of the M4 competition, a domain-adjusted hand-crafted hybrid between neural network and statistical time series models. The first configuration of our model does not employ any time-series-specific components and its performance on heterogeneous datasets strongly suggests that, contrarily to received wisdom, deep learning primitives such as residual blocks are by themselves sufficient to solve a wide range of forecasting problems. Finally, we demonstrate how the proposed architecture can be augmented to provide outputs that are interpretable without considerable loss in accuracy.

Figures (5)

• Figure 1: Proposed architecture. The basic building block is a multi-layer FC network with $\mathop{\mathrm{\textsc{ReLu}}}\nolimits$ nonlinearities. It predicts basis expansion coefficients both forward, $\theta^f$, (forecast) and backward, $\theta^b$, (backcast). Blocks are organized into stacks using doubly residual stacking principle. A stack may have layers with shared $g^b$ and $g^f$. Forecasts are aggregated in hierarchical fashion. This enables building a very deep neural network with interpretable outputs.
• Figure 2: The outputs of generic and the interpretable configurations, M4 dataset. Each row is one time series example per data frequency, top to bottom (Yearly: id Y3974, Quarterly: id Q11588, Monthly: id M19006, Weekly: id W246, Daily: id D404, Hourly: id H344). The magnitudes in a row are normalized by the maximal value of the actual time series for convenience. Column (a) shows the actual values (ACTUAL), the generic model forecast (FORECAST-G) and the interpretable model forecast (FORECAST-I). Columns (b) and (c) show the outputs of stacks 1 and 2 of the generic model, respectively; FORECAST-G is their summation. Columns (d) and (e) show the output of the Trend and the Seasonality stacks of the interpretable model, respectively; FORECAST-I is their summation.
• Figure 3: M4 test performance ($\mathop{\mathrm{\textsc{owa}}}\nolimits$) as a function of ensemble size, based on N-BEATS-G. This figure shows that N-BEATS loses less than 0.5% in terms of $\mathop{\mathrm{\textsc{owa}}}\nolimits$ performance even if 10 times smaller ensemble size is used.
• Figure 4: The architectural configurations used in the ablation study of the doubly residual stack. Symbol $\diamond$ denotes unconnected output.
• Figure 5: The outputs of generic and the interpretable configurations, M4 dataset. Each row is one time series example per data frequency, top to bottom (Yearly: id Y3974, Quarterly: id Q11588, Monthly: id M19006, Weekly: id W246, Daily: id D404, Hourly: id H344). The magnitudes in a row are normalized by the maximal value of the actual time series for convenience. Column (a) shows the actual values (ACTUAL), the generic model forecast (FORECAST-G) and the interpretable model forecast (FORECAST-I). Columns (b) and (c) show the outputs of stacks 1 and 2 of the generic model, respectively; FORECAST-G is their summation. Columns (d) and (e) show the output of the Trend and the Seasonality stacks of the interpretable model, respectively; FORECAST-I is their summation.