Statistical properties of volume in the Bitcoin/USD market

Abstract

It is widely known that the volumes of limit orders and market orders display non-trivial statistical properties. For example, the sizes of volumes can take on many different values across several orders of magnitude, with a marked preference for whole numbers like 5, 10, 100. These studies have been centered on the volume of incoming orders or of realized transactions. In the present work we analyze the statistical properties of volumes stored at the best ask and best bid. We measured both dynamical properties as well as properties that do not directly depend on time. Of the properties found some are also present in the time series of price returns while others turn out to be particularly idiosyncratic and distinguish the stochastic nature of volume time series from that of price returns time series