Abstract
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.
Highlights
The current literature on bubble tests is confronted with the difficulty to conclude that a price bubble is not caused by time-varying or regime switching fundamentals (Gürkaynak 2008)
Our model allows to test for speculative bubbles in cryptocurrencies using a sentiment index, which drives the transition in a regime switching autoregression
Volatility is specified as a score-driven EGARCH-type model augmented with the daily changes of the sentiment index
Summary
The current literature on bubble tests is confronted with the difficulty to conclude that a price bubble is not caused by time-varying or regime switching fundamentals (Gürkaynak 2008). We postulate that a bubble-like behavior of prices is characterized by a smooth transition function that dynamically assigns the probability (loading) to the explosive regime and the random walk regime, given the exogenous sentiment information. Due to the limited knowledge of a fundamental value in this new digital asset class, the mispricing caused by sentiments cannot be promptly corrected or revert to its fundamental value This is the reason why sentiment entails a short-run predictability because of an inefficient crypto market that defers a price correction process.
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