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Autoregressive wild bootstrap inference for nonparametric trends

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  • Friedrich, Marina
  • Smeekes, Stephan
  • Urbain, Jean-Pierre

Abstract

In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions.

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  • Friedrich, Marina & Smeekes, Stephan & Urbain, Jean-Pierre, 2020. "Autoregressive wild bootstrap inference for nonparametric trends," Journal of Econometrics, Elsevier, vol. 214(1), pages 81-109.
    • Handle: RePEc:eee:econom:v:214:y:2020:i:1:p:81-109
    DOI: 10.1016/j.jeconom.2019.05.006
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    1. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
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    7. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2011. "Cross-sectional dependence robust block bootstrap panel unit root tests," Journal of Econometrics, Elsevier, vol. 163(1), pages 85-104, July.
    8. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
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    10. Smeekes, S. & Urbain, J.R.Y.J., 2014. "A multivariate invariance principle for modified wild bootstrap methods with an application to unit root testing," Research Memorandum 008, Maastricht University, Graduate School of Business and Economics (GSBE).
    11. Ross R. McKitrick & Timothy J. Vogelsang, 2014. "HAC robust trend comparisons among climate series with possible level shifts," Environmetrics, John Wiley & Sons, Ltd., vol. 25(7), pages 528-547, November.
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    13. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
    15. Joel R. Norris & Robert J. Allen & Amato T. Evan & Mark D. Zelinka & Christopher W. O’Dell & Stephen A. Klein, 2016. "Evidence for climate change in the satellite cloud record," Nature, Nature, vol. 536(7614), pages 72-75, August.
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    Citations

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    Cited by:

    1. C. Vladimir Rodr'iguez-Caballero & Esther Ruiz, 2024. "Temperature in the Iberian Peninsula: Trend, seasonality, and heterogeneity," Papers 2406.14145, arXiv.org.
    2. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    3. Marina Friedrich & Eric Beutner & Hanno Reuvers & Stephan Smeekes & Jean-Pierre Urbain & Whitney Bader & Bruno Franco & Bernard Lejeune & Emmanuel Mahieu, 2020. "A statistical analysis of time trends in atmospheric ethane," Climatic Change, Springer, vol. 162(1), pages 105-125, September.
    4. Friedrich, Marina & Lin, Yicong, 2024. "Sieve bootstrap inference for linear time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 239(1).
    5. Marina Friedrich & Luca Margaritella & Stephan Smeekes, 2023. "High-Dimensional Granger Causality for Climatic Attribution," Papers 2302.03996, arXiv.org, revised Jun 2024.
    6. Yayi Yan & Jiti Gao & Bin peng, 2020. "A Class of Time-Varying Vector Moving Average (infinity) Models," Monash Econometrics and Business Statistics Working Papers 39/20, Monash University, Department of Econometrics and Business Statistics.
    7. González-Rivera, Gloria & Rodríguez Caballero, Carlos Vladimir, 2023. "Modelling intervals of minimum/maximum temperatures in the Iberian Peninsula," DES - Working Papers. Statistics and Econometrics. WS 37968, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Marina Friedrich & S'ebastien Fries & Michael Pahle & Ottmar Edenhofer, 2019. "Understanding the explosive trend in EU ETS prices -- fundamentals or speculation?," Papers 1906.10572, arXiv.org, revised Mar 2020.
    9. Yayi Yan & Jiti Gao & Bin Peng, 2020. "A Class of Time-Varying Vector Moving Average Models: Nonparametric Kernel Estimation and Application," Papers 2010.01492, arXiv.org.
    10. Marina Friedrich & Sébastien Fries & Michael Pahle & Ottmar Edenhofer, 2020. "Rules vs. Discretion in Cap-and-Trade Programs: Evidence from the EU Emission Trading System," CESifo Working Paper Series 8637, CESifo.
    11. Yicong Lin & Mingxuan Song, 2023. "Robust bootstrap inference for linear time-varying coefficient models: Some Monte Carlo evidence," Tinbergen Institute Discussion Papers 23-049/III, Tinbergen Institute.
    12. Giannerini, Simone & Goracci, Greta & Rahbek, Anders, 2024. "The validity of bootstrap testing for threshold autoregression," Journal of Econometrics, Elsevier, vol. 239(1).
    13. Yayi Yan & Jiti Gao & Bin Peng, 2021. "Asymptotics for Time-Varying Vector MA(∞) Processes," Monash Econometrics and Business Statistics Working Papers 22/21, Monash University, Department of Econometrics and Business Statistics.

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    More about this item

    Keywords

    Autoregressive wild bootstrap; Nonparametric estimation; Time series; Simultaneous confidence bands; Trend estimation;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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