Intraday Functional PCA Forecasting of Cryptocurrency Returns

We study the functional PCA (FPCA) forecasting method in application to functions of intraday returns on Bitcoin. We show that improved interval forecasts of future return functions are obtained when the conditional heteroscedasticity of return functions is taken into account. The Karhunen–Loeve (KL) dynamic factor model is introduced to bridge the functional and discrete‐time approaches. It offers a convenient framework for the analysis of conditionally heteroscedastic functional time series. For intraday forecasting of incomplete functions, we introduce a new algorithm based on the FPCA applied by rolling, which can be used for any data observed continuously 24/7. The proposed forecasting methods are applied to return functions computed from data sampled hourly and at 15‐min intervals. The proposed pointwise forecast intervals for complete functions show improved accuracy compared to the literature. Our intraday pointwise hourly forecasts of Bitcoin returns compare favorably with competitors in the recent literature, in terms of directional (sign) and accuracy.