Extension of the Wald statistic to models with dependent observations

A generalization of the Wald statistic for testing composite hypotheses is suggested for dependent data from exponential models which include Lévy processes and diffusion fields. The generalized statistic is proved to be asymptotically chi-squared distributed under regular composite hypotheses. It is simpler and more easily available than the generalized likelihood ratio statistic. Simulations in an example where the latter statistic is available show that the generalized Wald test achieves higher average power than the generalized likelihood ratio test. Received: February 29, 2000