WHEN THERE IS NOTHING TO PREDICT: DIRECTIONAL BIAS IN TIME SERIES FOUNDATION MODELS

Time series foundation models forecast a new series from its context alone. We ask what they forecast when there is nothing to predict. On a martingale the last observed value is the best point forecast under squared loss, and any other forecast adds risk equal to the mean square of its departure from that value, so what a model adds can be measured against a known optimum. The part of a departure that stays the same when the history is negated cannot come from the direction of the history; removing it is the mirror correction. We find that several released models carry a directional bias that, on rising markets, looks like skill. On random walks five of the eleven models, none of them decoder-only, forecast a rise on up to 85 percent of contexts. A corpus with positive trends suffices to cause such a bias, in a decoder-only model as well. On daily prices every model loses to the last value once the return signs are randomised, and on equity windows from a rising market the mirror correction lowers 128-day skill for ten of the eleven models. On 1996–2014 windows several models time the market far better than trend rules read from the same contexts, which points to memory: public training data contain those years. The mirror correction, already built into TimesFM-2.5, lowers risk whenever past and future are symmetric under negation, and an exact identity gives its cost elsewhere; mirror augmentation during fine-tuning removes most of Chronos-Bolt's bias.