Statistical inferences for price staleness

Aleksey Kolokolov, Giulia Livieri, Davide Pirino

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This paper proposes a nonparametric theory for statistical inferences on zero returns of high-frequency asset prices. Using an infill asymptotic design, we derive limit theorems for the percentage of zero returns observed on a finite time interval and for other related quantities. Within this framework, we develop two nonparametric tests. First, we test whether intra-day zero returns are independent and identically distributed. Second, we test whether intra-day variation of the likelihood of occurrence of zero returns can be solely explained by a deterministic diurnal pattern. In an empirical application to ten representative stocks of the NYSE, we provide evidence that the null of independent and identically distributed intra-day zero returns can be conclusively rejected. We further find that a deterministic diurnal pattern is not sufficient to explain the intra-day variability of the distribution of zero returns.
Original languageEnglish
Pages (from-to)32-81
Number of pages50
JournalJournal of Econometrics
Issue number1
Early online date8 Feb 2020
Publication statusPublished - 1 Sept 2020


  • Average staleness
  • Instantaneous price staleness
  • Liquidity
  • Stable convergence
  • Zero returns


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