Price discovery and long-memory property: Simulation and empirical evidence from the bitcoin market

Price discovery studies of a single asset traded in multiple markets have traditionally focused on assessing the relative price discovery contribution of each market. However, in this paper, we demonstrate that the overall price discovery across all markets can undergo changes even when the relative price discovery of each market remains constant. We propose that this overall change in price discovery can be effectively captured by the fractional parameter in the fractionally cointegrated vector autoregressive (FCVAR) model. In contrast, the widely used cointegrated vector autoregressive (CVAR) model fails to account for this dynamic in overall price discovery. Through a combination of simulation exercises and empirical applications, we show that the FCVAR approach outperforms the CVAR model not only in evaluating the relative price discovery contributions but also, more importantly, in providing a comprehensive measurement of overall price discovery.