Functional PCA for Intraday Bitcoin Return Forecasting

Summary

This study applies functional principal component analysis (FPCA) to forecast intraday Bitcoin return functions. It introduces a Karhunen–Loève dynamic factor model as a link between functional observations and discrete-time dynamics, and proposes a rolling FPCA procedure designed for continuously operating markets. The forecasts use returns sampled at hourly and 15-minute intervals. The study also considers conditional heteroscedasticity, finding that accounting for changing variance improves interval forecasts of future return functions.

For evaluation, forecasts at specific times are compared with machine-learning approaches and a traditional ARMA model. The reported results indicate good forecast accuracy and stronger directional prediction at fixed time points for the FPCA-based methods. The description does not name the competing models, specify evaluation periods or metrics, or discuss transaction costs. The evidence therefore concerns forecast performance, not profitability of a trading strategy.

Key ideas

• Rolling FPCA is used to forecast functions of intraday Bitcoin returns.
• A Karhunen–Loève dynamic factor model connects functional and discrete-time analysis.
• Modeling conditional heteroscedasticity improves interval forecasts in the reported study.
• Evaluation uses hourly and 15-minute samples and compares forecasts with machine learning and ARMA methods.
• FPCA methods perform well on accuracy and directional forecasts, but profitability is not assessed in the description.

Tags

# Intraday Functional PCA Forecasting of Cryptocurrency Returns


# 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 dynamic models. It offers a convenient framework for functional time series analysis. For intraday forecasting, 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 FPCA forecasting methods are applied to return functions computed from data sampled hourly and at 15-minute intervals. Next, the functional forecasts evaluated at discrete points in time are compared with the forecasts based on other methods, including machine learning and a traditional ARMA model. The proposed FPCA-based methods perform well in terms of forecast accuracy and outperform competitors in terms of directional (sign) of return forecasts at fixed points in time.

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