Estimation of the Probability of Informed Trading Models Via an Expectation-Conditional Maximization Algorithm

Abstract

The estimation of the PIN model and its extensions has posed significant challenges due to various computational problems. To address these issues, we propose a novel estimation method called the Expectation-Conditional Maximization (ECM) algorithm, which can serve as an alternative to existing methods for estimating various PIN models.Our method provides optimal estimates for the original PIN model of Easley et al. (1996), as well as two of its extensions:the MPIN model introduced by Ersan (2016), and the adjusted PIN model of Duarte and Young (2009), along with its restricted versions. Our results indicate that the estimation using the ECM algorithm is, by and large, faster, more accurate, and uses less memory than standard methods used in the literature, making it a robust alternative. Importantly, the ECM algorithm is not limited to the discussed extensions and can be easily adapted to estimate other PIN-related models.

Keywords: Expectation-conditional maximization algorithm, ECM, PIN model, MPIN, Multilayer probability of informed trading, Adjusted PIN model, Maximum-likelihood estimation, Private information, Information asymmetry