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Cauchy Estimators For Autoregressive Processes With Applications To Unit Root Tests And Confidence Intervals

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  • So, Beong Soo
  • Shin, Dong Wan
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    Abstract

    For autoregressive processes, we propose new estimators whose pivotal statistics have the standard normal limiting distribution for all ranges of the autoregressive parameters. The proposed estimators are approximately median unbiased. For seasonal time series, the new estimators give us unit root tests that have limiting normal distribution regardless of period of the seasonality. Using the estimators, confidence intervals of the autoregressive parameters are constructed. A Monte-Carlo simulation for first-order autoregressions shows that the proposed tests for unit roots are locally more powerful than the tests based on the ordinary least squares estimators. It also shows that the proposed confidence intervals have shorter average lengths than those of Andrews (1993, Econometrica 61, 139 165) based on the ordinary least squares estimators when the autoregressive coefficient is close to one.

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    Bibliographic Info

    Article provided by Cambridge University Press in its journal Econometric Theory.

    Volume (Year): 15 (1999)
    Issue (Month): 02 (April)
    Pages: 165-176

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    Handle: RePEc:cup:etheor:v:15:y:1999:i:02:p:165-176_15

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    Cited by:
    1. Demetrescu, Matei & Hanck, Christoph, 2012. "A simple nonstationary-volatility robust panel unit root test," Economics Letters, Elsevier, vol. 117(1), pages 10-13.
    2. Wan Shin, Dong & Soo So, Beong, 2001. "Confidence intervals for the largest root of autoregressive models based on instrumental variable estimators," Economics Letters, Elsevier, vol. 71(2), pages 181-189, May.
    3. Phillips, Peter C. B. & Park, Joon Y. & Chang, Yoosoon, 2004. "Nonlinear instrumental variable estimation of an autoregression," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 219-246.
    4. Eiji Kurozumi & Kohei Aono, 2011. "Estimation and Inference in Predictive Regressions," Global COE Hi-Stat Discussion Paper Series gd11-192, Institute of Economic Research, Hitotsubashi University.
    5. Shin, Dong Wan & So, Beong Soo, 2000. "Gaussian tests for seasonal unit roots based on Cauchy estimation and recursive mean adjustments," Journal of Econometrics, Elsevier, vol. 99(1), pages 107-137, November.
    6. Kuzin, Vladimir, 2005. "Recursive demeaning and deterministic seasonality," Statistics & Probability Letters, Elsevier, vol. 72(3), pages 195-204, May.
    7. Gorodnichenko, Yuriy & Mikusheva, Anna & Ng, Serena, 2012. "Estimators For Persistent And Possibly Nonstationary Data With Classical Properties," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1003-1036, October.
    8. Chang, Yoosoon, 2012. "Taking a new contour: A novel approach to panel unit root tests," Journal of Econometrics, Elsevier, vol. 169(1), pages 15-28.
    9. Choi, Chi-Young & Matsubara, Kiyoshi, 2007. "Heterogeneity in the persistence of relative prices: What do the Japanese cities tell us?," Journal of the Japanese and International Economies, Elsevier, vol. 21(2), pages 260-286, June.
    10. Wan Shin, Dong & Lee, Oesook, 2003. "An instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models," Journal of Econometrics, Elsevier, vol. 115(1), pages 29-52, July.
    11. Beong So, 2005. "A new instrumental variable estimation for diffusion processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(4), pages 733-745, December.
    12. Shin, Dong Wan & So, Beong Soo, 1999. "New tests for unit roots in autoregressive processes with possibly infinite variance errors," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 387-397, October.

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