The paper presents a general minimum distance estimation procedure for nonstationary time series models with 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. The behavior of the estimates when a stationary model is fitted to a nonstationary process is also explained. The introduction highlights the importance of stationarity in time series analysis and the challenges posed by nonstationary processes. The Whittle method, a generalization of which is used in this paper, is based on minimizing a function that approximates the Gaussian likelihood function. The method is extended to locally stationary processes, where the periodogram is replaced by a local version integrated over time. The paper proves asymptotic normality of the estimate even in the misspecified case. The fitting of parametric models to locally stationary processes is discussed, with the estimate derived by minimizing a generalized Whittle function using local periodograms. The asymptotic properties of the estimate are established, including convergence and asymptotic distribution. The paper also explores autoregressive models with time-varying coefficients, providing estimation equations and comparing the minimum distance estimate to the least squares estimate. Finally, the paper examines the situation where a stationary model is fitted to a nonstationary process, discussing the behavior of the estimates in this scenario. The paper concludes with practical considerations and a simulation example.The paper presents a general minimum distance estimation procedure for nonstationary time series models with 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. The behavior of the estimates when a stationary model is fitted to a nonstationary process is also explained. The introduction highlights the importance of stationarity in time series analysis and the challenges posed by nonstationary processes. The Whittle method, a generalization of which is used in this paper, is based on minimizing a function that approximates the Gaussian likelihood function. The method is extended to locally stationary processes, where the periodogram is replaced by a local version integrated over time. The paper proves asymptotic normality of the estimate even in the misspecified case. The fitting of parametric models to locally stationary processes is discussed, with the estimate derived by minimizing a generalized Whittle function using local periodograms. The asymptotic properties of the estimate are established, including convergence and asymptotic distribution. The paper also explores autoregressive models with time-varying coefficients, providing estimation equations and comparing the minimum distance estimate to the least squares estimate. Finally, the paper examines the situation where a stationary model is fitted to a nonstationary process, discussing the behavior of the estimates in this scenario. The paper concludes with practical considerations and a simulation example.