Estimating Adaptive Market Efficiency Using the Kalman Filter

This paper addresses the adaptive market hypothesis (AMH), which suggests that market efficiency is not a stable property, but rather that it evolves with time. The test of evolving efficiency (TEE) investigates the efficiency of a particular market by using a multi-factor model with time-varying coefficients and GARCH errors. The model is a variant of the stochastic GARCH in Mean (GARCH-M) proposed in 1990, which tests for market efficiency in an absolute sense, i.e. by assuming that market efficiency is unchanged over time. To resolve this problem, the TEE extends all previous tests and provides a mechanism for observing the market learning process by estimating the changes in market efficiency over time. Both stochastic GARCH-M and TEE models are estimated using Kalman filtering techniques. The contribution of this paper is two-fold:

1. we explain in detail the quasi-maximum likelihood estimation (QMLE) procedure based on the standard Kalman filter applied to the stochastic GARCH-M and TEE models;
2. we estimate the changes in the level of market efficiency in three markets over a period that includes the financial markets crisis of 2007/2008.

The three markets are specifically chosen to reflect a developed (London LSE), mature emerging (Johannesburg JSE) and immature emerging market (Nairobi NSE) perspective. Our empirical study suggests that, in spite of the financial crisis, all three markets maintained their pre-crisis level of weak-form efficiency.