Cryptocurrencies lack clear measures of fundamental values and are often associated with speculative bubbles. This paper introduces a new way of testing for speculative bubbles based on StockTwits sentiment, which is used as the transition variable in a smooth transition autoregression. The model allows for conditional heteroskedasticity and fat tails of the conditional distribution of the error term, and volatility may depend on the constructed sentiment index. We apply the model to the CRIX index, for which several bubble periods are identified. The detected locally explosive price dynamics, given the specified bubble regime controlled by a smooth transition function, are more akin to the notion of speculative bubble that is driven by exuberant sentiment. Furthermore, we find that volatility increases as the sentiment index decreases, which is analogous to the commonly called leverage effect.
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