Data-driven smooth tests for the martingale difference hypothesis

A general method for testing the martingale difference hypothesis is proposed. The new tests are data-driven smooth tests based on the principal components of certain marked empirical processes that are asymptotically distributionfree, with critical values that are already tabulated. The data-driven smooth tests are optimal in a semiparametric sense discussed in the paper, and they are robust to conditional heteroskedasticity of unknown form. A simulation study shows that the smooth tests perform very well for a wide range of realistic alternatives and have more power than the omnibus and other competing tests. Finally, an application to the S&P 500 stock index and some of its components highlights the merits of our approach. Juan Carlos Escanciano Department of Economics, Indiana University, 100 S. Woodlawn, Wylie Hall, Bloomington, IN 47405-7104, USA. [email protected] Silvia Mayoral Universidad de Navarra Depto. Métodos Cuantitativos Campus Universitario 31080 Pamplona [email protected]