Introducing N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting for after-work quants

Takeaway. Long horizons make a vanilla MLP quadratic and noisy. N-HiTS keeps N-BEATS’ doubly residual stacks, then (1) MaxPool the look-back so each block sees a coarser sampling rate, and (2) predict only ceil(r_ell * H) knots and interpolate them to length H. Low-frequency blocks fire first. Univariate, global weights.

N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting (Cristian Challu, Kin G. Olivares, Boris N. Oreshkin, Federico Garza, Max Mergenthaler-Canseco, Artur Dubrawski, 2022; AAAI 2023; arXiv:2201.12886). CMU Auton Lab / Unity / Nixtla.

Fit for learners: Fast hierarchical interpolation heir of N-BEATS — great NeuralForecast library companion for long horizons.

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

The problem

N-BEATS already beats hybrids on M4 with ReLU stacks. Push the horizon to 720 and two things explode: memory (the last linear map is width H) and wiggle (every step is a free parameter). Transformer LTSF papers (Informer, Autoformer, FEDformer) attack the same pain with sparse attention. This paper asks whether pooling + interpolation on an MLP is enough — and cheaper.

The idea / core intuition

• Same residual fork as N-BEATS: block ell emits a backcast (subtract from the look-back) and a forecast (summed). Stacks S=3, one block per stack in the main recipe.
• Multi-rate sampling: MaxPool kernel k_ell on the input of block ell. Larger k kills high-frequency junk so that block can only talk about slow scale. MaxPool beat AveragePool in their ablation.
• Hierarchical interpolation: the MLP does not output H numbers. Expressiveness ratio r_ell sets |theta^f| = ceil(r_ell * H). Linear (or nearest / cubic) interpolator g fills the rest. Typical schedules: coarse then fine, e.g. inverse-r = [24, 12, 1] or calendar-aligned [168, 24, 1].
• Top-down order matters: synthesize low frequency first, subtract, then let later blocks fit the leftover. Reversing the schedule cost them about 7.5% MSE.
• Univariate: each series is forecast from its own history; weights are shared across the panel. Train MAE, Adam 1e-3, batch 256, Hyperopt 20 trials on val MAE.
• Table 1 (multivariate LTSF protocol, eight seeds): vs best Transformer baseline, average . Longest horizon (720/60): . ETTm2 H=96: MSE vs FEDformer 0.203 / Autoformer 0.255. Exchange H=96: . ILI H=24: .