Indirect inference for time series using the empirical characteristic function and control variates

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