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Limit theory for an explosive autoregressive process

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  • Wang, Xiaohu
  • Yu, Jun

Abstract

Large sample properties are studied for a first-order autoregression (AR(1)) with a root greater than unity. It is shown that, contrary to the AR coefficient, the least-squares (LS) estimator of the intercept and its t-statistic are asymptotically normal without requiring the Gaussian error distribution, and hence an invariance principle applies. The coefficient based test and the t test have better power for testing the hypothesis of zero intercept in the explosive process than in the stationary process.

Suggested Citation

  • Wang, Xiaohu & Yu, Jun, 2015. "Limit theory for an explosive autoregressive process," Economics Letters, Elsevier, vol. 126(C), pages 176-180.
    • Handle: RePEc:eee:ecolet:v:126:y:2015:i:c:p:176-180
    DOI: 10.1016/j.econlet.2014.12.004
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    1. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2014. "Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behaviour," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 315-333, June.
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    11. Peter C. B. Phillips & Shu-Ping Shi & Jun Yu, 2011. "Specification Sensitivity in Right-Tailed Unit Root Testing for Explosive Behavior," Working Papers 15-2011, Singapore Management University, School of Economics.
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    Cited by:

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    2. Fei, Yijie, 2018. "Limit theory for mildly integrated process with intercept," Economics Letters, Elsevier, vol. 163(C), pages 98-101.
    3. Gao, Min & Yang, Wenzhi & Wu, Shipeng & Yu, Wei, 2022. "Asymptotic normality of residual density estimator in stationary and explosive autoregressive models," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    4. 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.
    5. Andras Fulop & Jun Yu, 2017. "Bayesian Analysis of Bubbles in Asset Prices," Econometrics, MDPI, vol. 5(4), pages 1-23, October.
    6. Norbert Christopeit & Michael Massmann, 2013. "Estimating Structural Parameters in Regression Models with Adaptive Learning," Tinbergen Institute Discussion Papers 13-111/III, Tinbergen Institute.
    7. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    8. Wang, Xiaohu & Yu, Jun, 2016. "Double asymptotics for explosive continuous time models," Journal of Econometrics, Elsevier, vol. 193(1), pages 35-53.
    9. Christoph P. Kustosz & Anne Leucht & Christine H. MÜller, 2016. "Tests Based on Simplicial Depth for AR(1) Models With Explosion," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(6), pages 763-784, November.
    10. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    11. Katsuto Tanaka & Weilin Xiao & Jun Yu, 2020. "Maximum Likelihood Estimation for the Fractional Vasicek Model," Econometrics, MDPI, vol. 8(3), pages 1-28, August.
    12. Gangzheng Guo & Yixiao Sun & Shaoping Wang, 2019. "Testing for moderate explosiveness," The Econometrics Journal, Royal Economic Society, vol. 22(1), pages 73-95.
    13. Skrobotov Anton, 2023. "Testing for explosive bubbles: a review," Dependence Modeling, De Gruyter, vol. 11(1), pages 1-26, January.
    14. Xiao, Weilin & Yu, Jun, 2019. "Asymptotic theory for rough fractional Vasicek models," Economics Letters, Elsevier, vol. 177(C), pages 26-29.
    15. Jingjie Xiang & Gangzheng Guo & Qing Zhao, 2022. "Testing for a Moderately Explosive Process with Structural Change in Drift," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(2), pages 300-333, April.
    16. Guo, Gangzheng & Wang, Shaoping & Sun, Yixiao, 2018. "Testing for Moderate Explosiveness in the Presence of Drift," University of California at San Diego, Economics Working Paper Series qt2k26h10n, Department of Economics, UC San Diego.

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    More about this item

    Keywords

    Explosive model; Intercept; Invariance principle; Bubbles;
    All these keywords.

    JEL classification:

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