Properties and applications of a martingale hypothesis test

Abstract

In this thesis, I explore the properties of a martingale hypothesis test, and present three applications of the test that address empirical questions in asset-pricing finance. The martingale test exploits the lack of correlation between forecast error and the current information set. The test is designed to consider all alternatives, including linear and nonlinear relationships between the forecast error and a current information variable. When the current information variable is stationary, I follow the transformed empirical process approach of Koul and Stute (1999) to construct the appropriate test statistics for models with homoscedastic instantaneous variance and extend their results to models with conditional heteroscedasticity. When the current information variable is an integrated process, I follow the approach of Park and Whang (1999), and extend their results to account for estimated parameters, and derive the asymptotic properties. In the first application, I construct a test to determine if continuous-time affine diffusion models provide adequate approximations of observed discrete data, primarily with respect to the models' short-term forecastability. I apply the martingale hypothesis to test various parameteric specifications of the conditional means for the affine diffusion models. In the second application, I propose a unit-root type specification test for stochastic processes generated by linear functions of nonstationary integrated process, in order to test the random walk hypothesis in asset prices. In the third application, I construct a test of forward unbiasedness in order to relate the price of a futures contract to the future price of the underlying asset.