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A nonlinear Bayesian filtering approach to estimating adaptive market effciency. (English) Zbl 1422.91805

Summary: 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.

MSC:

91G99 Actuarial science and mathematical finance
62C10 Bayesian problems; characterization of Bayes procedures
62P05 Applications of statistics to actuarial sciences and financial mathematics
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