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 i.i.d. 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.

中文翻译：

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使用经验特征函数和控制变量对时间序列进行间接推断

当无法明确计算真实特征函数时，我们通过最小化经验特征函数和模拟特征函数之间的积分加权均方误差来估计平稳时间序列过程的参数。受间接推理的启发，我们使用基于 iid 模拟块的特征函数的蒙特卡罗近似。作为一种经典的方差减少技术，我们建议使用控制变量来减少这种蒙特卡罗近似的方差。这两个近似产生了两个适用于一大类时间序列过程的新估计量。我们展示了在强混合、矩条件和模拟块相对于其参数的平滑度下参数估计器的一致性和渐近正态性。