Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series

In this paper we modify the general hypothesis studied by Robinson (1989) for semi-/nonparametric time-series models, and present a consistent testing procedure for the modified hypothesis. As examples, we provide consistent tests for the portfolio conditional mean-variance efficiency hypothesis, for theomitted variables in a multivariate nonparametric time-series regression model, and for the two original examples in Robinson. The asymptotic distributions under the null and Pitman local alternatives are established by invoking central limit theorems for Hilbert-valued-dependent random arrays. To approximate the critical values of the general test, we modify the conditional Monte-Carlo approach of Hansen (1996) and the stationary bootstrap of Politis and Romano (1994a,b), and show that both work asymptotically.