Estimation for conditional moment models based on martingale difference divergence
提出一种基于鞅差散度的条件矩模型估计方法，通过非可积权重函数捕捉更多无条件矩信息，提升估计效率，并解决截距参数不可识别问题，适用于含条件异方差的时间序列数据。
We provide a new estimation method for conditional moment models via the martingale difference divergence (MDD). Our MDD‐based estimation method is formed in the framework of a continuum of unconditional moment restrictions. Unlike the existing estimation methods in this framework, the MDD‐based estimation method adopts a non‐integrable weighting function, which could capture more information from unconditional moment restrictions than the integrable weighting function to enhance the estimation efficiency. Due to the nature of shift‐invariance in MDD, our MDD‐based estimation method can not identify the intercept parameters. To overcome this identification issue, we further provide a two‐step estimation procedure for the model with intercept parameters. Under regularity conditions, we establish the asymptotics of the proposed estimators, which are not only easy‐to‐implement with expectation‐based asymptotic variances, but also applicable to time series data with an unspecified form of conditional heteroskedasticity. Finally, we illustrate the usefulness of the proposed estimators by simulations and two real examples.