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.