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.

中文翻译：

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价格发现和长记忆属性：比特币市场的模拟和经验证据

对在多个市场交易的单一资产的价格发现研究传统上侧重于评估每个市场的相对价格发现贡献。然而，在本文中，我们证明，即使每个市场的相对价格发现保持不变，所有市场的总体价格发现也可能发生变化。我们建议，价格发现的整体变化可以通过分数协整向量自回归（FCVAR）模型中的分数参数来有效捕获。相比之下，广泛使用的协整向量自回归（CVAR）模型无法解释整体价格发现中的这种动态。通过模拟练习和实证应用的结合，我们表明 FCVAR 方法不仅在评估相对价格发现贡献方面优于 CVAR 模型，更重要的是，在提供总体价格发现的综合衡量方面也优于 CVAR 模型。