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Title: Statistical inferences for price staleness Authors:  Davide Pirino - University of Rome Tor Vergata (Italy)
Giulia Livieri - Scuola Normale Superiore (Italy)
Aleksey Kolokolov - Alliance Manchester Business School (United Kingdom) [presenting]
Abstract: Asset transaction prices sampled at high frequency are much staler than one might expect, in the sense that they frequently lack new updates showing zero returns. We propose a theoretical framework that hinges on the existence of a latent continuous-time stochastic process $p_t$ valued in the open interval (0,1), which represents, at any point in time, the probability of occurrence of a zero return. Using a standard infill asymptotics design, we develop an inferential theory for testing, non-parametrically, the null hypothesis that $p_t$ is constant over one day. Under the alternative, which encompasses a semimartingale model for $p_t$, we prove that the integrated volatility of the probability of staleness can be consistently estimated. Empirically, on a large dataset of NYSE stocks, we provide evidence that the null of constant probability of staleness is fairly rejected and that the integrated volatility of $p_t$ is mainly determined by transaction volume, bid-ask spread and realized volatility.