Statistical Inferences for Price Staleness

60 Pages Posted: 13 Nov 2018

See all articles by Aleksey Kolokolov

Aleksey Kolokolov

University of Manchester - Manchester Business School

Giulia Livieri

Scuola Normale Superiore

Davide Pirino

Department of Economics and Finance, University of Rome "Tor Vergata"

Date Written: November 6, 2018

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. In this paper, we propose a theoretical framework for formalizing this phenomenon. It hinges on the existence of a latent continuous-time stochastic process pt valued in the open interval (0; 1), which represents at any point in time the probability of the occurrence of a zero return. Using a standard infill asymptotic design, we develop an inferential theory for nonparametrically testing, the null hypothesis that pt is constant over one day. Under the alternative, which encompasses a semimartingale model for pt, we develop non-parametric inferential theory for the probability of staleness that includes the estimation of various integrated functionals of pt and its quadratic variation. Using a large dataset of stocks, we provide empirical evidence that the null of the constant probability of staleness is fairly rejected. We then show that the variability of pt is mainly driven by transaction volume and is almost unaffected by bid-ask spread and realized volatility.

Keywords: staleness, idle time, liquidity, zero returns, stable convergence

Suggested Citation

Kolokolov, Aleksey and Livieri, Giulia and Pirino, Davide, Statistical Inferences for Price Staleness (November 6, 2018). SAFE Working Paper No. 236. Available at SSRN: https://ssrn.com/abstract=3283628 or http://dx.doi.org/10.2139/ssrn.3283628

Aleksey Kolokolov (Contact Author)

University of Manchester - Manchester Business School ( email )

Booth Street West
Manchester, M15 6PB
United Kingdom

Giulia Livieri

Scuola Normale Superiore ( email )

Piazza dei Cavalieri, 7
Pisa, 56126
Italy

Davide Pirino

Department of Economics and Finance, University of Rome "Tor Vergata" ( email )

Via Columbia 2
Rome, Lazio 00133
Italy

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