A Transfer Learning Approach for Testing the Adaptive Market Hypothesis: Evidence from BWP/USD to Cryptocurrency Markets

The efficient market hypothesis, which holds that prices completely reflect available information, is commonly used in financial market analysis. However, emerging empirical evidence shows that market efficiency develops with time, as posited by the adaptive market hypothesis (AMH), with predictability varying across shifting economic and behavioural regimes. Despite the increasing use of deep learning in financial forecasting, there has been little systematic investigation into whether neural network topologies can successfully identify time-varying efficiency trends across diverse markets. Furthermore, the relevance of transfer learning in studying adaptive behaviour between foreign exchange markets and extremely volatile cryptocurrency markets has received little attention. Using these data, we investigate the AMH by comparing the forecasting performance of various deep learning architectures and determining whether knowledge transfer from a relatively stable fiat currency market, Botswana Pula/US Dollar (BWP/USD), improves the predictive accuracy in a highly volatile cryptocurrency market, Bitcoin/US Dollar (BTC/USD). We use daily data from 1 January 2015 to 11 January 2026 to develop deep neural networks (DNNs) and alpha-recurrent neural networks, and, for generalisation, we benchmark using a recurrent temporal neural network (RTNN), a domain-adversarial neural network (DANN), and KLIEP-based importance-weighted regression. A transfer learning technique is used, in which models are initially trained on BWP/USD and then re-estimated on BTC/USD without freezing any network layers, ensuring complete flexibility and enabling parameters to respond to changing market dynamics. Out-of-sample accuracy measures and rolling long-memory diagnostics are used to evaluate forecast performance in terms of time-varying efficiency. The findings reveal that the RTNN regularly outperforms other forecasting models across marketplaces. Predictive accuracy fluctuates with time, and rolling long-memory measurements show persistent departures from random walk behaviour, which supports the AMH. Transfer learning improves predictive stability in the cryptocurrency market by identifying the existence of transferable informational structures between fiat and digital asset markets. Overall, our results support the idea that market efficiency is dynamic rather than static, and they show that adaptive deep learning systems are an excellent way to test the AMH. The paper suggests that cross-market transfer mechanisms and adaptive modelling methodologies be investigated further in growing foreign exchange and cryptocurrency markets.