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A WILD BOOTSTRAP FOR DEPENDENT DATA

Published online by Cambridge University Press:  17 November 2021

Ulrich Hounyo
Ulrich Hounyo*
Affiliation:
University at Albany, SUNY and CREATES
*
Address correspondence to Ulrich Hounyo, Department of Economics, University at Albany, SUNY, Hudson Building (bldg. 25), room 103, 1400 Washington Ave, Albany, New York, NY 12222, USA; e-mail: khounyo@albany.edu.
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Abstract

This paper introduces a novel wild bootstrap for dependent data (WBDD) as a means of calculating standard errors of estimators and constructing confidence regions for parameters based on dependent heterogeneous data. The consistency of the bootstrap variance estimator for smooth function of the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first-order asymptotic validity of the WBDD in distribution approximation is established when data are assumed to satisfy a near epoch dependent condition and under the framework of the smooth function model. The WBDD offers a viable alternative to the existing non parametric bootstrap methods for dependent data. It preserves the second-order correctness property of blockwise bootstrap (provided we choose the external random variables appropriately), for stationary time series and smooth functions of the mean. This desirable property of any bootstrap method is not known for extant wild-based bootstrap methods for dependent data. Simulation studies illustrate the finite-sample performance of the WBDD.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 2 , April 2023 , pp. 264 - 289
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

I wish to thank editor Peter C. B. Phillips, co-editor Giuseppe Cavaliere and four anonymous referees for helpful comments and suggestions. This manuscript subsumes a previous working paper entitled “The wild tapered block bootstrap”. Financial support from CREATES, Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation, is gratefully acknowledged.

References

REFERENCES

Bhattacharya, R. N. & Ghosh, J. K. (1978) On the validity of the formal Edgeworth expansion. Annals of Statistics 6, 434–451.CrossRefGoogle Scholar
Carlstein, E. (1986) The use of subseries values for estimating the variance of a general statistic from a stationary time series. The Annals of Statistics 14, 1171–1179.CrossRefGoogle Scholar
Cavaliere, G. (2004) Unit root tests under time-varying variances. Econometric Reviews 23, 259–292.CrossRefGoogle Scholar
Cavaliere, G. & Taylor, A. M. R. (2007) Testing for unit roots in time series models with non-stationary volatility. Journal of Econometrics 140, 919–947.CrossRefGoogle Scholar
Cavaliere, G. & Taylor, A. M. R. (2009) Heteroskedastic time series with a unit root. Econometric Theory 25, 1228–1276.CrossRefGoogle Scholar
Christensen, K., Hounyo, U., & Podolskij, M. (2018) Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment. Journal of Econometrics 205, 336–362.CrossRefGoogle Scholar
Davidson, R. & Flachaire, E. (2007) Asymptotic and bootstrap inference for inequality and poverty measures. Journal of Econometrics 141, 141–166.CrossRefGoogle Scholar
Efron, B. (1979) Bootstrap methods: another look at the jackknife. The Annals of Statistics 7, 1–26.CrossRefGoogle Scholar
Gonçalves, S., Hounyo, U., Patton, A. J., & Sheppard, K. (2019) Bootstrapping Two-Stage Quasi-Maximum Likelihood Estimators of Time Series Models. Working paper, McGill University.Google Scholar
Gonçalves, S. & White, H. (2002) The bootstrap of the mean for dependent heterogeneous arrays. Econometric Theory 18, 1367–1384.CrossRefGoogle Scholar
Gonçalves, S. & White, H. (2004) Maximum likelihood and the bootstrap for nonlinear dynamic models. Journal of Econometrics 119, 199–219.CrossRefGoogle Scholar
Götze, F. & Künsch, H. (1996) Second order correctness of the blockwise bootstrap for stationary observations. Annals of Statistics 24, 1914–33.CrossRefGoogle Scholar
Hall, P. (1992) The Bootstrap and Edgeworth Expansion. Springer-Verlag.CrossRefGoogle Scholar
Hounyo, U. (2017) Bootstrapping integrated covariance matrix estimators in noisy jump-diffusion models with non-synchronous trading. Journal of Econometrics 197, 130–152.CrossRefGoogle Scholar
Hounyo, U., Gonçalves, S., & Meddahi, N. (2017) Bootstrapping pre-averaged realized volatility under market microstructure noise. Econometric Theory 33, 791–838.CrossRefGoogle Scholar
Inoue, A. (2001) Testing for distributional changes in time series. Econometric Theory 17, 156–187.CrossRefGoogle Scholar
Kline, P. & Santos, A. (2012) Higher order properties of the wild bootstrap under missspecification. Journal of Econometrics 171, 54–70.CrossRefGoogle Scholar
Künsch, H. R. (1989) The jackknife and the bootstrap for general stationary observations. Annals of Statistics 17, 1217–1241.CrossRefGoogle Scholar
Lahiri, S. N. (2003) Resampling Methods for Dependent Data. Springer.CrossRefGoogle Scholar
Liu, R. Y. (1988) Bootstrap procedure under some non-i.i.d. models. Annals of Statistics 16, 1696–1708.CrossRefGoogle Scholar
Liu, R. Y. & Singh, K. (1992) Moving blocks Jackknife and bootstrap capture weak dependence. In LePage, R. & Billard, L. (eds.), Exploring the Limits of Bootstrap, pp. 225–248. Wiley.Google Scholar
Mammen, E. (1993) Bootstrap and wild bootstrap for high dimensional linear models. Annals of Statistics 21, 255–285.CrossRefGoogle Scholar
Paparoditis, E. & Politis, D. N. (2001) Tapered block bootstrap. Biometrika 88, 1105–1119.CrossRefGoogle Scholar
Paparoditis, E. & Politis, D. N. (2002) The tapered block bootstrap for general statistics from stationary sequences. Econometrics Journal 5, 131–148.CrossRefGoogle Scholar
Patton, A., Politis, D. N., & White, H. (2009). CORRECTION TO “Automatic block-length selection for the dependent bootstrap” by D. Politis and H. White. Econometric Reviews 28, 372–375.CrossRefGoogle Scholar
Politis, D. N. & Romano, J. P. (1994) The stationary bootstrap. Journal of the American Statistical Association 89, 1303–1313.CrossRefGoogle Scholar
Politis, D. N., Romano, J. P., & Wolf, M. (1997) Subsampling for heteroscedastic time series. Journal of Econometrics 81, 281–317.CrossRefGoogle Scholar
Politis, D. N. & White, H. (2004) Automatic block-length selection for the dependent bootstrap. Econometric Reviews 23, 53–70.CrossRefGoogle Scholar
Priestley, M. B. (1981) Spectral Analysis and Time Series. Academic Press.Google Scholar
Phillips, P. C. B. & Xu, K. L. (2006) Inference in autoregression under heteroskedasticity. Journal of Time Series Analysis 27, 289–308.CrossRefGoogle Scholar
Shao, X. (2010) The dependent wild bootstrap. Journal of the American Statistical Association 105, 218–235.CrossRefGoogle Scholar
Shao, X. (2011) A bootstrap-assisted spectral test of white noise under unknown dependence. Journal of Econometrics 162, 213–224.CrossRefGoogle Scholar
Wu, C. F. J. (1986) Jackknife, bootstrap and other resampling methods in regression analysis. Annals of Statistics 14, 1261–1295.Google Scholar
Xu, K. L. & Phillips, P. C. B. (2008) Inference in autoregression under heteroskedasticity. Journal of Econometrics 142, 265–280.CrossRefGoogle Scholar
Yeh, A. B. (1998) A bootstrap procedure in linear regression with nonstationary errors. The Canadian Journal of Statistics Association 26, 149–160.CrossRefGoogle Scholar
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