Resumen
We implement hidden Markov models (HMMs) and hidden semi-Markov models (HSMMs) on Bitcoin/US dollar (BTC/USD) with the aim of market phase detection. We make analogous comparisons to Standard and Poor?s 500 (S and P 500), a benchmark traditional stock index and a protagonist of several studies in finance. Popular labels given to market phases are ?bull?, ?bear?, ?correction?, and ?rally?. In the first part, we fit HMMs and HSMMs and look at the evolution of hidden state parameters and state persistence parameters over time to ensure that states are correctly classified in terms of market phase labels. We conclude that our modelling approaches yield positive results in both BTC/USD and the S and P 500, and both are best modelled via four-state HSMMs. However, the two assets show different regime volatility and persistence patterns?BTC/USD has volatile bull and bear states and generally weak state persistence, while the S and P 500 shows lower volatility on the bull states and stronger state persistence. In the second part, we put our models to the test of detecting different market phases by devising investment strategies that aim to be more profitable on unseen data in comparison to a buy-and-hold approach. In both cases, for select investment strategies, four-state HSMMs are also the most profitable and significantly outperform the buy-and-hold strategy.