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Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications

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  • Choi, In

Abstract

Using the asymptotic normality of the least-squares estimates for the autoregressive (AR) process with real, positive unit roots and at least one stable root, we consider the asymptotic distributions of the Wald and t ratio tests on AR coefficients. In addition, we propose a method of constructing confidence intervals for the sum of AR coefficients possibly in the presence of a unit root. Using simulation methods, we compare the finite-sample cumulative distributions of the t ratios for individual autoregressive coefficients with those of standard normal distributions, and investigate the finite-sample performance of our confidence intervals and t ratios. Our simulation results show that the t ratios for nonstationary processes converge to a standard normal distribution more slowly than those for stationary processes. Further, the confidence intervals are shown to work reasonably well in moderately large samples, but they display unsatisfactory performance at small sample sizes.

Suggested Citation

  • Choi, In, 1993. "Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications," Econometric Theory, Cambridge University Press, vol. 9(2), pages 263-282, April.
  • Handle: RePEc:cup:etheor:v:9:y:1993:i:02:p:263-282_00
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    Cited by:

    1. Tae‐Hwan Kim & Stephen J. Leybourne & Paul Newbold, 2004. "Asymptotic mean‐squared forecast error when an autoregression with linear trend is fitted to data generated by an I(0) or I(1) process," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 583-602, July.
    2. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 2005-12, Universite de Montreal, Departement de sciences economiques.
    3. Hadri, Kaddour & Kurozumi, Eiji, 2012. "A simple panel stationarity test in the presence of serial correlation and a common factor," Economics Letters, Elsevier, vol. 115(1), pages 31-34.
    4. Ismet GOCER & Sedat ALATAS & Osman PEKER, 2016. "Effects of R&D and innovation on income in EU countries: new generation panel cointegration and causality analysis," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(4(609), W), pages 153-164, Winter.
    5. Judith A. Clarke & Mukesh Ralhan, 2005. "Direct and Indirect Causality Between Exports and Economic Output for Bangladesh and Sri Lanka: Horizon Matters," Econometrics Working Papers 0512, Department of Economics, University of Victoria.
    6. Dufour, Jean-Marie & Pelletier, Denis & Renault, Eric, 2006. "Short run and long run causality in time series: inference," Journal of Econometrics, Elsevier, vol. 132(2), pages 337-362, June.
    7. Dietmar Bauer & Alex Maynard, 2010. "Persistence-robust Granger causality testing," Working Papers 1011, University of Guelph, Department of Economics and Finance.
    8. Castro, Tomás del Barrio & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2013. "The Impact Of Persistent Cycles On Zero Frequency Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1289-1313, December.
    9. Lin, Yingqian & Tu, Yundong, 2020. "Robust inference for spurious regressions and cointegrations involving processes moderately deviated from a unit root," Journal of Econometrics, Elsevier, vol. 219(1), pages 52-65.
    10. Hadri, Kaddour & Kurozumi, Eiji, 2008. "A Simple Panel Stationarity Test in the Presence of Cross-Sectional Dependence," CCES Discussion Paper Series 7, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    11. Breitung, Jörg & Demetrescu, Matei, 2015. "Instrumental variable and variable addition based inference in predictive regressions," Journal of Econometrics, Elsevier, vol. 187(1), pages 358-375.
    12. Zeren, Feyyaz & Öztürk, Erkan, 2015. "Testing For Profit Persistence Of Listed Manufacturing Companies In Istanbul Stock Exchange," Ekonomika, Journal for Economic Theory and Practice and Social Issues, Society of Economists Ekonomika, Nis, Serbia, vol. 61(2), pages 1-10, June.
    13. Bauer, Dietmar & Maynard, Alex, 2012. "Persistence-robust surplus-lag Granger causality testing," Journal of Econometrics, Elsevier, vol. 169(2), pages 293-300.
    14. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 229-254.
    15. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    16. Lutkepohl, Helmut & Saikkonen, Pentti, 1999. "A lag augmentation test for the cointegrating rank of a VAR process," Economics Letters, Elsevier, vol. 63(1), pages 23-27, April.
    17. Ismet GOCER & Sedat ALATAS & Osman PEKER, 2016. "Effects of R&D and innovation on income in EU countries: new generation panel cointegration and causality analysis," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(4(609), W), pages 153-164, Winter.
    18. Kurozumi, Eiji & Aono, Kohei, 2013. "Estimation And Inference In Predictive Regressions," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 54(2), pages 231-250, December.
    19. Vishal Jaunky, 2013. "Democracy and economic growth in Sub-Saharan Africa: a panel data approach," Empirical Economics, Springer, vol. 45(2), pages 987-1008, October.
    20. In Choi & Sun Ho Hwang, 2016. "Optimal Autoregressive Predictions," Working Papers 1607, Research Institute for Market Economy, Sogang University.

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