Bubble regime identification in an attention-based model for Bitcoin and Ethereum price dynamics

In this paper we extend the model in Cretarola, Figà-Talamanca, ‘‘Detecting bubbles in Bitcoin price dynamics via market exuberance’’, Annals of Operations Research (2019), by allowing for a state- dependent correlation parameter between asset returns and market attention. We assume that the change of state is described by a continuous time latent Markov chain and we propose an estimation procedure based on the conditional maximum likelihood and on the Hamilton filter. Finally, model parameters, as well as Markov chain transition probabilities, are estimated on Bitcoin and Ethereum returns in case market attention is measured via the Google Search Volume Index for the keywords ‘‘bitcoin’’ and ‘‘ethereum’’, respectively; up to four regimes are considered in the empirical application. The empirical outcomes show that the model is not only capable of identifying bubble and non-bubble regimes but also enables the interpretation of the correlation between cryptocurrencies and their market attention as a tuning to define the speed at which a bubble boosts.