Generalized Information Criteria for Sparse Statistical Jump Models

We extend the generalized information criteria for high-dimensional penalized models to sparse statistical jump models, a new class of statistically robust and computationally efficient alternatives to hidden Markov models. In a simulation study, we demonstrate that the new generalized information criteria selects the correct hyperparameters with high probability. Finally, providing an empirical application, we infer the key features that drive the return dynamics of the largest cryptocurrencies. We find that a four-state model best describes the dynamics of cryptocurrency returns. The states have natural market-based interpretations as they correspond to bull, bull-neutral, bear-neutral, and bear market regimes, respectively.