Wild multiplicative bootstrap for M and GMM estimators in time series

Francesco Audrino; Lorenzo Camponovo; Constantin Roth; Francesco Audrino; Lorenzo Camponovo; Constantin Roth

doi:10.3934/QFE.2019.1.165

Quantitative Finance and Economics

2019, Volume 3, Issue 1: 165-186. doi: 10.3934/QFE.2019.1.165

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Research article

Wild multiplicative bootstrap for M and GMM estimators in time series

1.
Department of Economics, University of St.Gallen, St.Gallen, Switzerland
2.
Department of Innovative Technologies, SUPSI, University of Applied Sciences and Arts of Southern Switzerland, Manno, Switzerland

Received: 03 January 2019 Accepted: 01 April 2019 Published: 08 April 2019
JEL Codes: C12, C13, C15

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.
- M and GMM estimators,
- time series,
- wild bootstrap
Citation: Francesco Audrino, Lorenzo Camponovo, Constantin Roth. Wild multiplicative bootstrap for M and GMM estimators in time series[J]. Quantitative Finance and Economics, 2019, 3(1): 165-186. doi: 10.3934/QFE.2019.1.165

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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.

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