Testing adaptive market efficiency in the presence of non-Gaussian uncertainties

One of the central debates in finance concerns the Efficient Market Hypothesis (EMH)—wherein markets are assumed to be efficient in the absolute sense. However, the possibility of time-varying weak-form market efficiency has received increasing attention in recent years. Under the Adaptive Market Hypothesis (AMH) it is postulated that market efficiency is dynamic, which advocates using models with non-constant coefficients. The concept of evolving efficiency has yielded a Test for Evolving Efficiency (TEE) and following that, a Generalised Test for Evolving Efficiency (GTEE) – both with an associated Kalman filtering (KF) technique. Unfortunately, these methods assume that the inherent stochastic processes are Gaussian despite widespread evidence that many real financial time series are nonGaussian. Unlike the classical KF, modern filters such as the maximum correntropy Kalman filters (MCC-KF) have been shown to be less sensitive to non-Gaussian uncertainties. These filters utilise a similarity measure known as correntropy– which incorporates higher order information than the mean square criterion that is utilised in the classical KF. As a result, they have been shown to improve filter robustness against outliers or impulsive noises. In this paper, the South African and American stock markets are tested for adaptive market efficiency using both the standard KF and the MCC-KF. A simulation study shows that the MCC-KF is a more robust estimator of adaptive efficiency but it less accurately estimates unknown system parameters. The South African stock market is found to be inefficient prior to August 2004 but achieves efficiency thereafter. Testing the S&P500 does not provide evidence of inefficiency in the American stock markets. The GTEE, implemented with the MCC-KF, is selected as the bestperforming test for the S&P500