A nonlinear Bayesian filtering approach to estimating adaptive market efficiency

Russian Journal of Numerical Analysis and Mathematical Modelling, 34(1) (2019), 31-42
https://doi.org/10.1515/rnam-2019-0001

The adaptive market hypothesis (AMH) supplies a convincing motivation for why market efficiency should not be regarded as a stable property in time. This paper explores a Bayesian methodology for estimating weak-form market efficiency under the AMH using a test of evolving efficiency (TEE). More precisely, a generalized TEE (GTEE) approach is proposed in which the conditional first moment of a time series is assumed to be a nonlinear function of its conditional second moment, i.e. a nonlinear feedback term is present in the conditional mean equation. We then discuss a maximum likelihood estimation procedure for the resulting nonlinear model using the state-space approach and extended Kalman filtering. This methodology is used to estimate time-varying, weak-form market efficiency in four, specifically chosen, markets over a time-period that includes the global financial crisis of 2007/2008.