Functional Analysis of Intraday and Daily Dynamics of Cryptocurrency

Abstract

Cryptocurrencies have become one of the fastest-growing asset classes with significant investment potential. This research examines the dynamics of cryptocurrency returns and prices, and introduces new methods of functional time series analysis. It reveals the existence of common periodic effects, which are recurrent intraday and intraweek patterns in hourly and daily prices, returns, volumes, and volatility of different types of cryptocurrency. The empirical results show that the common intraday periodicity in native cryptocurrencies and tokens is driven by the operating hours of the NYSE, LSE, and Han Seng stock exchange markets. Moreover, the intraday and daily cross-sectional correlation matrices of cryptocurrency returns indicate high correlation among native cryptocurrencies and tokens, while stablecoins exhibit distinct dynamics and are uncorrelated with other cryptocurrencies. A functional CAPM is introduced to accommodate these periodic patterns, and it is estimated by regressing the functions of intraday and intraweek cryptocurrency returns on the market portfolio. A PCA-based principal eigenportfolio of the correlation matrix is used as a proxy of the cryptocurrency market portfolio. The major native cryptocurrencies and tokens satisfy affine relationships with the return functions of the market portfolio, and their functional betas display periodic intraday and intraweek patterns.

To bridge the functional and discrete-time approaches, the Karhunen-Loeve (KL) Dynamic Factor model is introduced. It offers a convenient framework for analyzing conditionally heteroscedastic functional time series. Improved interval forecasts of 15-minute and hourly Bitcoin future return functions are obtained when the conditional heteroscedasticity of return functions is accounted for. A "Rolling" FPCA-based algorithm is introduced for forecasting intraday incomplete functions. The proposed algorithm improves the intraday hourly forecast of Bitcoin returns.