Wild multiplicative bootstrap for M and GMM estimators in time series

Abstract

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.

Keywords

• M and GMM estimators| time series| wild bootstrap