Introducing N-BEATS: Neural basis expansion analysis for interpretable time series forecasting for after-work quants

Takeaway. You do not need Holt–Winters inside the net. N-BEATS is a deep stack of ReLU MLPs. Each block emits a backcast (subtract from the look-back) and a forecast (summed). Generic blocks learn the basis; interpretable stacks force polynomial trend + Fourier seasonality. Pure DL beat the M4 statistical/hybrid field.

N-BEATS: Neural basis expansion analysis for interpretable time series forecasting (Boris N. Oreshkin, Dmitri Carpov, Nicolas Chapados, Yoshua Bengio, 2019; ICLR 2020; arXiv:1905.10437). Element AI / Mila.

Fit for learners: Pure deep residual stacks that won M4 — clean baseline before you add finance-specific features.

This Hub note is a plain-language intro. Not investment advice.

The problem

M4 (100k series) crowned Smyl’s hybrid (dilated LSTM + Holt–Winters). Makridakis et al. read that as “hybrids are the way forward.” This paper asks whether residual FC stacks with no TS gadgets can win anyway — and whether you can still read trend vs season.

The idea / core intuition

• Look-back (\mathbf{x}) of length (2H)–(7H). Block (\ell): four FC-ReLU layers → (\theta^b,\theta^f) → (\hat{\mathbf{x}}\ell = g^b(\theta^b)), (\hat{\mathbf{y}}\ell = g^f(\theta^f)).
• Doubly residual: (\mathbf{x}{\ell} = \mathbf{x}{\ell-1} - \hat{\mathbf{x}}{\ell-1}) (peel what this block explained); (\hat{\mathbf{y}} = \sum\ell \hat{\mathbf{y}}_\ell).
• Generic: (g) is a learned linear basis (V\theta + b) — waveforms have no human name.
• Interpretable: trend stack (g(\theta) = T\theta) with (T = [1,t,\ldots,t^p]), (p\in{2,3}); seasonality stack (g(\theta) = S\theta) with sines/cosines up to (\lfloor H/2\rfloor). Trend stack first, so seasonality sees a detrended residual. Weights shared inside a stack.
• Univariate point forecasts. Shared architecture across yearly/quarterly/monthly/… ; one model per horizon. Batch 1024, Adam, early stop on a held-out last horizon.
• Ensemble (needed to match M4 entries): mix SMAPE/MASE/MAPE losses, look-backs (2H\ldots7H), bagged inits; median. Ensembling beat dropout/L2 for them.
• M4: N-BEATS-G OWA 0.797 / SMAPE 11.168 vs Smyl 0.821 / 11.374 (~ 3% better than the winner, ~  vs statistical benchmark). I+G . Same architecture SOTA on M3 and tourism MAPE.