Time-series momentum (TSMOM) is a well-documented finding that past returns predict next-period returns for many asset types. Is the relationship between past and future performance linear? In their December 2025 paper entitled "Nonlinear Time Series Momentum", Tobias Moskowitz, Riccardo Sabbatucci, Andrea Tamoni and Björn Uhl compare a TSMOM trading strategy with non-linear weights to: (1) theoretically optimal weights; (2) published alternative weighting schemes; and, (3) a machine learning (neural network) method. They consider:
- Time series for 8 equity index futures, 24 commodity futures and 21 interest rate and currency futures contracts. They roll futures contracts on the earlier of the last trade date or the first day of the futures contract month.
- Momentum measurement (lookback) intervals of 21, 62 or 260 trading days.
- Daily, weekly or monthly reweighting frequencies.
They seek to maximize out-of-sample gross Sharpe ratio based on TSMOM signals. They set asset position weights by dividing past return by most recent 260-day volatility and adjusting it to an arbitrary 12% annualized volatility target. Using front-month data for the selected futures contracts as available during January 1980 through October 2024, they find that:
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