  We estimate the parameter of a stationary time series process by minimizing
the integrated weighted mean squared error between the empirical and simulated
characteristic function, when the true characteristic functions cannot be
explicitly computed. Motivated by Indirect Inference, we use a Monte Carlo
approximation of the characteristic function based on iid simulated blocks. As
a classical variance reduction technique, we propose the use of control
variates for reducing the variance of this Monte Carlo approximation. These two
approximations yield two new estimators that are applicable to a large class of
time series processes. We show consistency and asymptotic normality of the
parameter estimators under strong mixing, moment conditions, and smoothness of
the simulated blocks with respect to its parameter. In a simulation study we
show the good performance of these new simulation based estimators, and the
superiority of the control variates based estimator for Poisson driven time
series of counts.
