We introduce a wild multiplicative bootstrap for M and GMM estimators in nonlinear models when autocorrelation structures of moment functions are unknown. The implementation of the bootstrap algorithm does not require any parametric assumptions on the data generating process. After proving its validity, we also investigate the accuracy of our procedure through Monte Carlo simulations. The wild bootstrap algorithm always outperforms inference based on standard first-order asymptotic theory. Moreover, in most cases the accuracy of our procedure is also better and more stable than that of block bootstrap methods. Finally, we apply the wild bootstrap approach to study the forecast ability of variance risk premia to predict future stock returns. We consider US equity from 1990 to 2010. For the period under investigation, our procedure provides significance in favor of predictability. By contrast, the block bootstrap implies ambiguous conclusions that heavily depend on the selection of the block size.

中文翻译：

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时间序列中M和GMM估计量的野生乘法引导程序

当矩函数的自相关结构未知时，我们为非线性模型中的M和GMM估计量引入了一个野生的乘法引导程序。引导算法的实现不需要对数据生成过程进行任何参数假设。在证明其有效性之后，我们还将通过蒙特卡洛模拟研究该程序的准确性。基于标准的一阶渐近理论，野生引导算法总是胜过推理。而且，在大多数情况下，我们的程序的准确性也比块自举法的准确性更好，更稳定。最后，我们采用野生自举法研究方差风险溢价的预测能力，以预测未来的股票收益。我们考虑了1990年至2010年的美国权益。在本调查期间，我们的程序具有可预测性的意义。相比之下，块引导程序暗示了模棱两可的结论，该结论很大程度上取决于块大小的选择。