Forecasting Bitcoin realized volatility by exploiting measurement error under model uncertainty

Modeling Bitcoin realized volatility by the heterogeneous autoregressive model is subject to substantial model specification uncertainty in practice. To circumvent the lag specification uncertainty, we introduce a new model averaging coefficient estimator with the mean squared error of the coefficient to be minimized. We show that the averaged coefficient vector has a root-n consistency with n being the sample size and propose using a double bootstrap to provide inference. Monte Carlo simulation results demonstrate reliability of the proposed method. The in-sample application shows that adjustment for measurement errors by HARQ-type models is necessary. The model averaging estimator has higher in-sample explanatory power with more significant predictors. The out-of-sample outcomes reveal that the forecast horizon plays a key role at determining the effectiveness of signed realized variance for predicting the Bitcoin volatility. Finally, the model averaging HARQ-type models demonstrate superior out-of-sample performance for both short and long forecast horizons.