The estimation of parameters of time series whose marginal distribution is exponential with parameter $\mu$, $\mu>0$ is somewhat more complicated than the estimation of parameters of Gaussian time series. One possible approach using the method of least squares is given. Namely, the method of least squares is applied in two steps for estimating the parameters of generalized first order autoregressive time series with exponential marginals. A special case of estimating parameters of the model FAREX (1) is also given.