When Are Statistical Forecast Gains Economically Relevant? Evidence From Bitcoin Returns

ABSTRACT We study how statistical forecast gains for Bitcoin translate into trading profits. Using real‐time out‐of‐sample forecasts from daily bivariate VARs from October 2021 to February 2024, we show that Bitcoin returns are forecastable and that seven predictive indices yield significant gains in directional accuracy (DA). However, mean‐squared forecast error is largely uninformative, and mean DA alone is insufficient to explain trading profitability. To understand this puzzle, we introduce a conditional DA measure based on the magnitude of price movements and a threshold‐based trading strategy. Profits arise only when DA remains stable during large market swings. Mean DA obscures breakdowns precisely when accurate forecasts are most valuable. Under a formal excess‐profitability test, the USD index and the Shanghai Stock Exchange deliver statistically significant profits, challenging the efficient market hypothesis.