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Jackknife Estimation of Stationary Autoregressive Models

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  • Chambers, MJ

Abstract

This paper reports the results of an extensive investigation into the use of the jackknife as a method of estimation in stationary autoregressive models. In addition to providing some general theoretical results concerning jackknife methods it is shown that a method based on the use of non-overlapping sub-intervals is found to work particularly well and is capable of reducing bias and root mean squared error (RMSE) compared to ordinary least squares (OLS), subject to a suitable choice of the number of sub-samples, rules-of-thumb for which are provided. The jackknife estimators also outperform OLS when the distribution of the disturbances departs from normality and when it is subject to autoregressive conditional heteroskedasticity. Furthermore the jackknife estimators are much closer to being median-unbiased than their OLS counterparts.

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  • Chambers, MJ, 2010. "Jackknife Estimation of Stationary Autoregressive Models," Economics Discussion Papers 2786, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:2786
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    Cited by:

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    2. Kanchana Nadarajah & Gael M Martin & Donald S Poskitt, 2019. "Optimal Bias Correction of the Log-periodogram Estimator of the Fractional Parameter: A Jackknife Approach," Monash Econometrics and Business Statistics Working Papers 7/19, Monash University, Department of Econometrics and Business Statistics.
    3. Iglesias, Emma M., 2014. "Testing of the mean reversion parameter in continuous time models," Economics Letters, Elsevier, vol. 122(2), pages 187-189.
    4. Artūras Juodis & Yiannis Karavias & Vasilis Sarafidis, 2021. "A homogeneous approach to testing for Granger non-causality in heterogeneous panels," Empirical Economics, Springer, vol. 60(1), pages 93-112, January.
    5. Ye Chen & Jun Yu, 2011. "Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models," Working Papers 12-2011, Singapore Management University, School of Economics.
    6. Christian Weiß & Hee-Young Kim, 2013. "Parameter estimation for binomial AR(1) models with applications in finance and industry," Statistical Papers, Springer, vol. 54(3), pages 563-590, August.
    7. Chen, Ye & Yu, Jun, 2015. "Optimal jackknife for unit root models," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 135-142.
    8. Kyriacou, Maria, 2014. "Overlapping sub-sampling and invariance to initial conditions," Discussion Paper Series In Economics And Econometrics 1203, Economics Division, School of Social Sciences, University of Southampton.
    9. Gourieroux, Christian & Zakoïan, Jean-Michel, 2013. "Estimation-Adjusted Var," Econometric Theory, Cambridge University Press, vol. 29(4), pages 735-770, August.
    10. Aaron H. Anglin & Aaron F. McKenny & Jeremy C. Short, 2018. "The Impact of Collective Optimism on New Venture Creation and Growth: A Social Contagion Perspective," Entrepreneurship Theory and Practice, , vol. 42(3), pages 390-425, May.
    11. Kruse, Yves Robinson & Kaufmann, Hendrik, 2015. "Bias-corrected estimation in mildly explosive autoregressions," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112897, Verein für Socialpolitik / German Economic Association.
    12. Marian Vavra, 2023. "Bias-Correction in Time Series Quantile Regression Models," Working and Discussion Papers WP 3/2023, Research Department, National Bank of Slovakia.
    13. Kruse, Robinson & Kaufmann, Hendrik & Wegener, Christoph, 2018. "Bias-corrected estimation for speculative bubbles in stock prices," Economic Modelling, Elsevier, vol. 73(C), pages 354-364.
    14. Diana Escandon-Barbosa & David Urbano-Pulido & Andrea Hurtado-Ayala, 2019. "Exploring the Relationship between Formal and Informal Institutions, Social Capital, and Entrepreneurial Activity in Developing and Developed Countries," Sustainability, MDPI, vol. 11(2), pages 1-20, January.
    15. Hendrik Kaufmannz & Robinson Kruse, 2013. "Bias-corrected estimation in potentially mildly explosive autoregressive models," CREATES Research Papers 2013-10, Department of Economics and Business Economics, Aarhus University.
    16. Bork, Lasse & Kaltwasser, Pablo Rovira & Sercu, Piet, 2022. "Aggregation bias in tests of the commodity currency hypothesis," Journal of Banking & Finance, Elsevier, vol. 135(C).
    17. Arturas Juodis & Yiannis Karavias, 2019. "Partially heterogeneous tests for Granger non-causality in panel data," Bank of Lithuania Working Paper Series 59, Bank of Lithuania.
    18. Chambers, MJ & McCrorie, JR & Thornton, MA, 2017. "Continuous Time Modelling Based on an Exact Discrete Time Representation," Economics Discussion Papers 20497, University of Essex, Department of Economics.
    19. Marcus J. Chambers & Maria Kyriacou, 2018. "Jackknife Bias Reduction in the Presence of a Near-Unit Root," Econometrics, MDPI, vol. 6(1), pages 1-28, March.
    20. Marcus J. Chambers, 2015. "A Jackknife Correction to a Test for Cointegration Rank," Econometrics, MDPI, vol. 3(2), pages 1-21, May.
    21. Chambers, Marcus J. & Kyriacou, Maria, 2013. "Jackknife estimation with a unit root," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1677-1682.
    22. Chambers, MJ & Kyriacou, M, 2010. "Jackknife Bias Reduction in the Presence of a Unit Root," Economics Discussion Papers 2785, University of Essex, Department of Economics.
    23. Yong Bao, 2013. "On Sample Skewness and Kurtosis," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 415-448, December.

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    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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