A general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation. The asymptotic properties of the estimate are derived under the assumption of possible model misspecification. For autoregressive processes with time varying coefficients, the estimate is compared to the least squares estimate. Furthermore, the behavior of estimates is explained when a stationary model is fitted to a nonstationary process.
"Fitting time series models to nonstationary processes." Ann. Statist. 25 (1) 1 - 37, February 1997. https://doi.org/10.1214/aos/1034276620