Time as a Model? Real‐Time Forecasting With Trend‐Based Intrinsic Time

ABSTRACT We define trend‐based intrinsic time (TBIT) as a path‐dependent sampling rule that aggregates consecutive same‐sign returns into directional runs and tests its real‐time implementability. A run‐terminal day becomes identifiable only when the first opposite‐sign return arrives. This timing feature implies that a forecasting design must use the reversal‐confirmation date, rather than the preceding run‐terminal date, as the information date. At each reversal‐confirmation date, we summarize the completed run by its signed average return and ask whether this TBIT state adds predictive information for a common future calendar‐return target. We conduct expanding‐window walk‐forward forecasts on actual S&P 500 and Bitcoin returns using zero, sign‐only, event‐calendar, full‐history calendar, and direct multi‐day benchmarks. At the 1‐day horizon, TBIT does not improve S&P 500 forecasts and is also inferior for Bitcoin. At the 5‐day horizon, TBIT lowers S&P 500 MSFE by only 0.08% relative to the event‐calendar benchmark; a Clark–West statistic of 0.84 (one‐sided p = 0.20) and stationary‐bootstrap inference provide no evidence of a reliable improvement. In a Bitcoin replication, TBIT raises MSFE by 0.58% relative to the event‐calendar benchmark and the Clark–West statistic is negative ( p = 0.81). The evidence therefore does not support a robust forecasting advantage for TBIT. More broadly, the study shows that endogenous event clocks should be defined through real‐time‐observable stopping rules, evaluated on common forecast targets, and benchmarked against mechanical features such as sign alternation.