Introducing DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks for after-work quants

Takeaway. One global LSTM is trained on all related series. At each step it emits parameters of a likelihood (Gaussian or negative binomial), not a point. At test time you feed sampled (\tilde z_t) back in and draw paths. Quantiles of sums over a horizon stay coherent.

DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks (David Salinas, Valentin Flunkert, Jan Gasthaus, 2017; International Journal of Forecasting 2020; arXiv:1704.04110). Amazon Research.

Fit for learners: Classic probabilistic RNN forecaster — learn predictive distributions before you size positions.

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

The problem

Classical ETS/ARIMA fit one series. Retail / energy / traffic give you thousands to millions of related series with a power-law of scales (few SKUs sell a lot; most sell almost none). You need distributions for inventory risk, not a pretty median. Shared seasonality should be learned once.

The idea / core intuition

• Conditioning range vs prediction range. Shared-weight encoder = decoder LSTM: (h_t = h(h_{t-1}, z_{t-1}, x_t, \Theta)). (\theta_t = \theta(h_t)) parametrizes (\ell(z_t \mid \theta_t)).
• Gaussian: (\mu = w_\mu^\top h + b_\mu), (\sigma = \mathrm{softplus}(w_\sigma^\top h + b_\sigma)). Negative binomial (counts): softplus (\mu, \alpha) with (\mathrm{Var} = \mu + \mu^2\alpha).
• Training: teacher-forced log-likelihood (they also score the history). Sliding windows; pad “new” items with zeros so cold-start is learned.
• Inference: ancestral sampling — 200 paths in their setup. Shuffle-across-time breaks calibration of multi-step sums → the model does learn path dependence.
• Scale: divide autoregressive (z) by (\nu_i \approx 1 + \mathrm{mean}(z)) in the condition window; multiply (\mu) back. Weighted sampling (\propto \nu_i) so whales are not ignored.
• Covariates: age, calendar, item embedding (category or identity).
• Empirics: parts, electricity, traffic vs MatFact; Amazon ec / ec-sub vs ISSM/Croston/ETS — roughly ~15% better (\rho)-risk vs then-SOTA on the retail sets. Uncertainty not forced to grow linearly (Q4 bump on ec).

Still the mental model inside GluonTS / SageMaker DeepAR. Chronos (paper 89) is the 2024 “tokenize it” cousin.