Folds That Only Look Back

A daily electricity-demand forecaster is tested with walk-forward validation: train on everything before a cut-off, test on the block right after it, then move the cut-off forward and do it again. The training window only ever grows.

There's one more constraint. The forecasts are needed horizon days ahead. With a horizon of $h$, the newest value you have sits $h$ steps before the target, so in every fold the first test day sits $h$ steps after the fold's last training day. Any days in between are left out of that fold: neither trained on nor tested.

Days are numbered 0 to n - 1.

• Fold 1 trains on days 0 to first_cutoff - 1.
• Each fold's test block is test_size consecutive days, starting horizon steps after that fold's last training day.
• The next fold's cut-off is test_size days later, and it trains on every day before its cut-off.
• Keep adding folds while the whole test block fits inside the series. A partial block is not a fold.

Task: write walk_forward_splits(n, first_cutoff, test_size, horizon=1) returning a list of tuples (train, test), where train and test are lists of day indices in increasing order. If not even one fold fits, return [].

Testing with a smaller gap than the real horizon lets each fold use fresher data than the deployed model will ever have, so the score comes out better than the model's real performance.