  In this paper we forecast daily returns of crypto-currencies using a wide
variety of different econometric models. To capture salient features commonly
observed in financial time series like rapid changes in the conditional
variance, non-normality of the measurement errors and sharply increasing
trends, we develop a time-varying parameter VAR with t-distributed measurement
errors and stochastic volatility. To control for overparameterization, we rely
on the Bayesian literature on shrinkage priors that enables us to shrink
coefficients associated with irrelevant predictors and/or perform model
specification in a flexible manner. Using around one year of daily data we
perform a real-time forecasting exercise and investigate whether any of the
proposed models is able to outperform the naive random walk benchmark. To
assess the economic relevance of the forecasting gains produced by the proposed
models we moreover run a simple trading exercise.
