ASYMPTOTICALLY OPTIMAL ESTIMATION IN MISSPECIFIED TIME-SERIES MODELS

A concept of asymptotically efficient estimation is presented when a m isspecified parametric time series model is fitted to a stationary pro cess. Efficiency of several minimum distance estimates is proved and t he behavior of the Gaussian maximum likelihood estimate is studied. Fu rthermore, the behavior of estimates that minimize the h-step predicti on enter is discussed briefly. The paper answers to some extent the qu estion what happens when a misspecified model is fitted to time series data and one acts as if the model were true.