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Autoregressive Wild Bootstrap Inference for Nonparametric Trends

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  • Friedrich, Marina

    (QE Econometrics, RS: GSBE ETBC)

  • Smeekes, Stephan

    (QE Econometrics, RS: GSBE EFME)

  • Urbain, Jean-Pierre

    (RS: GSBE EFME)

Abstract

In this paper a modified wild bootstrap method is presented to construct pointwise confidence intervals around a nonparametric deterministic trend model. We derive the asymptotic distribution of a nonparametric kernel estimator of the trend function under general conditions, which allow for serial correlation and heteroskedasticity. Asymptotic validity of the bootstrap method is established and it is shown to work well in finite samples in an extensive simulation study. The bootstrap method has the potential of providing simultaneous confidence bands for the same models along the lines of Bühlmann (1998) and can be applied without further adjustments to missing data. We illustrate this by applying the proposed method to a time series of atmospheric ethane which can be used as an indicator of atmospheric pollution and transport.

Suggested Citation

  • Friedrich, Marina & Smeekes, Stephan & Urbain, Jean-Pierre, 2017. "Autoregressive Wild Bootstrap Inference for Nonparametric Trends," Research Memorandum 010, Maastricht University, Graduate School of Business and Economics (GSBE).
    • Handle: RePEc:unm:umagsb:2017010
    DOI: 10.26481/umagsb.2017010
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    References listed on IDEAS

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    10. 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.
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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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Friedrich, Marina & Lin, Yicong, 2024. "Sieve bootstrap inference for linear time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 239(1).
    9. Marina Friedrich & Luca Margaritella & Stephan Smeekes, 2023. "High-Dimensional Granger Causality for Climatic Attribution," Papers 2302.03996, arXiv.org, revised Jun 2024.
    10. 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.
    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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    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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