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International Conference on Computational Science and Its Applications

ICCSA 2019: Computational Science and Its Applications – ICCSA 2019 pp 12–22Cite as

Asymtotic Distribution of the Bootstrap Parameter Estimator for the AR(p) Model

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11620))

Abstract

This paper is the generalization of our two previous researches about asymptotic distribution of the bootstrap parameter estimator for the AR(1) and AR(2) models. We investigate the asymptotic distribution of the bootstrap parameter estimator of pth order autoregressive or AR(p) model by applying the delta method. The asymptotic distribution is the crucial property in inference of statistics. We conclude that the bootstrap parameter estimator of the AR(p) model is asymptotically converges in distribution to the p–variate normal distribution.

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References

  1. Bibi, A., Aknounche, A.: Yule-Walker type estimators in periodic bilinear model: strong consistency and asymptotic normality. J. Stat. Methods Appl. 19, 1–30 (2010)

    Article  MathSciNet  Google Scholar 

  2. Bose, A.: Edgeworth correction by bootstrap in autoregressions. Ann. Statist. 16, 1709–1722 (1988)

    Article  MathSciNet  Google Scholar 

  3. Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer, New York (1991)

    Book  Google Scholar 

  4. Brouste, A., Cai, C., Kleptsyna, M.: Asymptotic properties of the MLE for the autoregressive process coefficients under stationary Gaussian noise. Math. Methods Statist. 23, 103–115 (2014)

    Article  MathSciNet  Google Scholar 

  5. Efron, B., Tibshirani, R.: An Introduction to the Bootstrap. Chapman & Hall, New York (1993)

    Book  Google Scholar 

  6. Freedman, D.A.: On bootstrapping two-stage least-squares estimates in stationary linear models. Ann. Statist. 12, 827–842 (1984)

    Article  MathSciNet  Google Scholar 

  7. Hardle, W., Horowitz, J., Kreiss, J.P.: Bootstrap methods for time series. Int. Stat. Rev. 71, 435–459 (2003)

    Article  Google Scholar 

  8. Politis, D.N.: The impact of bootstrap methods on time series analysis. Stat. Sci. 18, 219–230 (2003)

    Article  MathSciNet  Google Scholar 

  9. Sahinler, S., Topuz, D.: Bootstrap and jackknife resampling algorithms for estimation of regression parameters. J. Appl. Quant. Methods 2, 188–199 (2007)

    Google Scholar 

  10. Singh, K.: On the asymptotic accuracy of Efron’s bootstrap. Ann. Statist. 9, 1187–1195 (1981)

    Article  MathSciNet  Google Scholar 

  11. Suprihatin, B., Guritno, S., Haryatmi, S.: Asymptotic distribution of the bootstrap parameter estimator for AR(1) process. Model Assist. Statist. Appl. 10, 53–61 (2015)

    Article  Google Scholar 

  12. Van der Vaart, A.W.: Asymptotic Statistics. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  13. Van der Vaart, A.W.: Lecture Notes on Time Series. Vrije Universiteit, Amsterdam (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Sriwijaya University, Indralaya, Indonesia

    Bambang Suprihatin, Endro Setyo Cahyono & Novi Rustiana Dewi

Authors
  1. Bambang Suprihatin
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  2. Endro Setyo Cahyono
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  3. Novi Rustiana Dewi
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Corresponding author

Correspondence to Bambang Suprihatin .

Editor information

Editors and Affiliations

  1. Covenant University, Ota, Nigeria

    Sanjay Misra

  2. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  3. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir Korkhov

  6. Polytechnic University of Bari, Bari, Italy

    Carmelo Torre

  7. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  8. Monash University, Clayton, VIC, Australia

    David Taniar

  9. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  10. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

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Suprihatin, B., Cahyono, E.S., Dewi, N.R. (2019). Asymtotic Distribution of the Bootstrap Parameter Estimator for the AR(p) Model. In: Misra, S., et al. Computational Science and Its Applications – ICCSA 2019. ICCSA 2019. Lecture Notes in Computer Science(), vol 11620. Springer, Cham. https://doi.org/10.1007/978-3-030-24296-1_2

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  • DOI: https://doi.org/10.1007/978-3-030-24296-1_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-24295-4

  • Online ISBN: 978-3-030-24296-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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