On Multi-Dimensional Time-Varying Price Staleness

The price staleness is referred to as the extent of the presence of the zero returns in the price dynamics. The proportion of the zero returns could be high in the high-frequency data sets, as pointed by Bandi et al. (2020a). Considering the price staleness as a dynamic system too, in this paper, we extend the framework of Bandi et al. (2020b) and study the statistical inference of the idiosyncratic price staleness and systematic price staleness between assets, where the systematic price staleness characterizes the probability of the presence of com- mon zero returns. We propose consistent estimators for both the idiosyncratic and systematic price stalenesses under the new framework, and their distributional theory are established. Moreover, we develop a feasible nonparametric test for the constancy of the systematic price staleness. All of the methodologies are based on the high-frequency observations, namely, we require the observing intervals shrink to zero. Finally, we conduct simulation studies under various scenarios to assess the finite sample performance of the proposed approaches, and provide an empirical illustration for the proposed theory.