A concept of asymptotically efficient estimation is presented when a misspecified parametric time series model is fitted to a stationary process. Efficiency of several minimum distance estimates is proved and the behavior of the Gaussian maximum likelihood estimate is studied. Furthermore, the behavior of estimates that minimize the h-step prediction error is discussed briefly. The paper answers to some extent the question what happens when a misspecified model is fitted to time series data and one acts as if the model were true.
"Asymptotically optimal estimation in misspecified time series models." Ann. Statist. 24 (3) 952 - 974, June 1996. https://doi.org/10.1214/aos/1032526951