Probabilistic Forecasting: a notebook course (monthly data)

Repository: https://github.com/abhijeetkumar1/beyond-point-forecasts

Fifteen self-contained Jupyter notebooks. Each one explains the theory of one type of probabilistic forecast (with formulas), then implements it from scratch on monthly data and evaluates it with proper scoring rules. The notebooks are saved with outputs, so you can read them without running anything.

#	Notebook	Covers
00	00_foundations	point vs probabilistic, aleatoric/epistemic, calibration & sharpness, PIT, proper scoring rules, losses that elicit mean/median/quantiles, CRPS, rolling-origin backtests
01	01_full_predictive_distribution	SARIMA → log-normal predictive density, σ_h growth via ψ-weights, deriving any quantity from F, CRPS / log score (with Jacobian) / PIT
02	02_quantile_forecasts	pinball loss derivation, quantile regression & heteroscedasticity, parametric vs empirical quantiles, wQL, quantile calibration, crossing & rearrangement
03	03_prediction_intervals	PI vs CI, analytic / bootstrap / empirical-error / naive intervals, coverage by horizon, Winkler score, pointwise vs path coverage
04	04_conformal_prediction	split conformal & the (n+1) correction, per-horizon conformal for time series, ACI under regime change, CQR
05	05_ensembles_and_sample_paths	simulation, parameter-uncertainty and multi-model ensembles, path functionals (annual totals, peaks), linear pool vs quantile averaging, rank histograms, spread–skill, foundation models
06	06_event_probabilities	P(event) from distributions vs classifiers, Brier / log loss / Murphy decomposition, reliability diagrams, AUC caveat, isotonic recalibration, cost–loss value curves
07	07_categorical_and_binned	tercile outlooks, RPS vs Brier, multinomial logit, histogram (binned density) forecasts, randomised PIT
08	08_distribution_families_and_counts	choosing a family, Student-t tails, intermittent demand (ADI/CV²), Poisson vs Negative Binomial vs Gaussian, discrete CRPS & randomised PIT
09	09_multivariate_joint	Sklar / copulas, Gaussian copula, Schaake shuffle, energy & variogram scores, why marginal scores miss dependence
10	10_hierarchical_reconciliation	summing matrix, bottom-up / OLS / WLS / MinT-shrink, probabilistic reconciliation of joint samples
11	11_bayesian_forecasting	posterior predictive, epistemic vs aleatoric decomposition, conjugate regression (and prior traps), AR posterior simulation, Gaussian process in NumPy, PyMC sketch
12	12_evaluation_and_decisions	full backtest scoreboard, skill scores, Diebold–Mariano, newsvendor / critical-ratio decisions, choosing the forecast type
13	13_temporal_convolutional_networks	causal & dilated convolutions, receptive field, residual blocks, global models on a 300-SKU panel, non-crossing multi-horizon quantile head, integer quantiles for counts, conformal calibration (needs PyTorch)
14	14_deepar	autoregressive LSTM + NegBin / Gaussian likelihood, scaling, teacher forcing, ancestral sampling of paths, P(zero sales), annual totals from paths (needs PyTorch)

Suggested order: 00 → 01 → 02 → 03 → 04 → 05, then any of 06–11, then 12. 13 → 14 are the deep-learning extension.

Data (all monthly, generated or embedded by pf_utils.py, so no downloads are needed)

• AirPassengers 1949–1960 (embedded): trend + multiplicative seasonality.
• Synthetic retail hierarchy 2015–2024: Total → North/South → 4 stores, with common + regional AR(1) shocks.
• Synthetic SKU demand 2012–2024: lumpy, over-dispersed count data (Gamma–Poisson).
• Synthetic SKU panel 2015–2024 (nb 13–14): 300 related count series with four seasonal families, scales from <1 to hundreds of units, latent demand shocks, and staggered product launches. The true rates are returned too, so the notebooks can show an oracle benchmark.

pf_utils.py also holds every scoring rule (pinball, wQL, CRPS, interval score, Brier, RPS, energy, variogram, PIT) and the Plotly helpers: one shared template (a colour-blind-safe palette in a fixed order, so the same method or series keeps the same colour) plus fan charts, PIT histograms, reliability diagrams, step histograms and sample-path plots. All charts are interactive: hover a fan chart to read every interval for that month.

Setup

Only numpy, pandas, scipy, plotly (+ nbformat, which Plotly needs to display figures in notebooks) and statsmodels are needed for notebooks 00–12. No scikit-learn. Notebooks 13–14 also need PyTorch (pip install torch; the CPU build is enough, and each runs in 1–2 minutes). The saved outputs are Plotly figures, so open the notebooks in JupyterLab, Jupyter Notebook or VS Code to see them (GitHub's notebook preview does not render Plotly).

git clone https://github.com/abhijeetkumar1/beyond-point-forecasts.git
cd beyond-point-forecasts
uv venv --python 3.12 .venv
uv pip install --python .venv/bin/python -r requirements.txt
.venv/bin/jupyter lab

To export a chart as PNG/SVG, pip install kaleido and call fig.write_image("chart.png").

Optional extras mentioned in the notebooks: chronos-forecasting (nb 05), pymc (nb 11), hierarchicalforecast (nb 10), lightgbm (nb 02).