This paper empirically testes the Time-Varying Rational Expectations Hypothesis in US, UK, Japan and China stock markets based on asymmetric nonlinear smooth transition generalized autoregressive conditional heteroskedasticity(ANST—GARCH)models.The results illustrate that the asymmetric pattern of return reversals is directly associated with the unequal pricing behavior on the part of investors, which supports the Overreaction Hypothesis.Even though the risk premium is time-varying except in Nikkei, a bad information shock leads a positive relationship between expectation returns an d risk call not be held, which could not support the Time—Varying Rational Expectations Hypothesis.