We propose a continuous-time heterogeneous agent model consisting of fundamental, momentum, and contrarian traders to explain the significant time series momentum. We show that the market under-reacts in short-run and overreacts in long-run when momentum traders dominate the market, which provides profit opportunity for time series momentum strategies with short-time horizons and reversal with long-time horizons. We find momentum strategies with short horizons stabilise the market while the

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... ct becomes opposite with longer horizons. The results provide an insight into the profitability of time series momentum documented in recent empirical studies.