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.