Testing for Linear and Nonlinear Predictability of Stock Returns

We develop tests for predictability in a first-order ARMA model often suggested for stock returns. Instead of the conventional ARMA model, we consider its non-Gaussian and noninvertible counterpart that has identical autocorrelation properties but allows for conditional heteroskedasticity prevalent in stock returns. In addition to autocorrelation, the tests can also be used to test for nonlinear predictability, in contrast to previously proposed predictability tests based on invertible ARMA models. Simulation results attest to improved power. We apply our tests to postwar U.S. stock returns. All return series considered are found serially uncorrelated but dependent and, hence, nonlinearly predictable.