Modelling cryptocurrency high–low prices using fractional cointegrating VAR

Abstract

This paper empirically provides support for fractional cointegration of high and low cryptocurrency price series, using particularly, Bitcoin, Ethereum, Litecoin and Ripple; synchronized at different high time frequencies. The difference of high and low price gives the price range, and the range-based estimator of volatility is more efficient than the return-based estimator of realized volatility. A more general fractional cointegration technique applied is the Fractional Cointegrating Vector Autoregressive framework. The results show that high and low cryptocurrency prices are actually cointegrated in both stationary and non-stationary levels; that is, the range of high–low price. It is therefore quite interesting to note that the fractional cointegration approach presents a lower measure of the persistence for the range compared to the fractional integration approach, and the results are insensitive to different time frequencies. The main finding in this work serves as an alternative volatility estimation method in cryptocurrency and other assets' price modelling and forecasting.