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Robust econometric inference with mixed integrated and mildly explosive regressors

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  • Phillips, Peter C.B.
  • Lee, Ji Hyung

Abstract

This paper explores in several prototypical models a convenient inference procedure for nonstationary variable regression that enables robust chi-square testing for a wide class of persistent and endogenous regressors. The approach uses the mechanism of self-generated instruments called IVX instrumentation developed by Magdalinos and Phillips (2009b). We first show that these methods remain valid for regressors with local unit roots in the explosive direction and mildly explosive roots, where the roots are further from unity in the explosive direction than O(n−1). It is also shown that Wald testing procedures remain robust for multivariate regressors with certain forms of mixed degrees of persistence. These robustifications are useful in econometric inference, for example, when there are periods of mildly explosive trends in some or all of time series employed in the analysis but the exact knowledge on the regressor persistence is unavailable. Some aspects of the choice of the IVX instruments are investigated and practical guidance is provided but the issue of optimal IVX instrument choice remains unresolved. The methods are straightforward to apply in practical work such as predictive regression applications in finance.

Suggested Citation

  • Phillips, Peter C.B. & Lee, Ji Hyung, 2016. "Robust econometric inference with mixed integrated and mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 192(2), pages 433-450.
  • Handle: RePEc:eee:econom:v:192:y:2016:i:2:p:433-450
    DOI: 10.1016/j.jeconom.2016.02.009
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    References listed on IDEAS

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    1. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Historical Episodes Of Exuberance And Collapse In The S&P 500," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1043-1078, November.
    2. Ioannis Kasparis & Peter C. B. Phillips & Tassos Magdalinos, 2014. "Nonlinearity Induced Weak Instrumentation," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 676-712, August.
    3. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    4. 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.
    5. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    6. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.
    7. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    8. Lee, Ji Hyung, 2016. "Predictive quantile regression with persistent covariates: IVX-QR approach," Journal of Econometrics, Elsevier, vol. 192(1), pages 105-118.
    9. Magdalinos, Tassos & Phillips, Peter C.B., 2009. "Limit Theory For Cointegrated Systems With Moderately Integrated And Moderately Explosive Regressors," Econometric Theory, Cambridge University Press, vol. 25(2), pages 482-526, April.
    10. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    11. Peter C. B. Phillips & Shuping Shi & Jun Yu, 2015. "Testing For Multiple Bubbles: Limit Theory Of Real‐Time Detectors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 1079-1134, November.
    12. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    13. Phillips, Peter C.B. & Lee, Ji Hyung, 2013. "Predictive regression under various degrees of persistence and robust long-horizon regression," Journal of Econometrics, Elsevier, vol. 177(2), pages 250-264.
    14. Campbell, John Y. & Yogo, Motohiro, 2006. "Efficient tests of stock return predictability," Journal of Financial Economics, Elsevier, vol. 81(1), pages 27-60, July.
    15. Miller, J. Isaac & Park, Joon Y., 2010. "Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory," Journal of Econometrics, Elsevier, vol. 155(1), pages 83-89, March.
    16. Donald W. K. Andrews & Patrik Guggenberger, 2014. "A Conditional-Heteroskedasticity-Robust Confidence Interval for the Autoregressive Parameter," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 376-381, May.
    17. Peter C. B. Phillips & Ji Hyung Lee, 2015. "Limit Theory for VARs with Mixed Roots Near Unity," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1035-1056, December.
    18. Phillips, Peter C.B. & Magdalinos, Tassos, 2009. "Unit Root And Cointegrating Limit Theory When Initialization Is In The Infinite Past," Econometric Theory, Cambridge University Press, vol. 25(6), pages 1682-1715, December.
    19. repec:taf:jnlbes:v:30:y:2012:i:2:p:229-241 is not listed on IDEAS
    20. Stock, James H., 1991. "Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series," Journal of Monetary Economics, Elsevier, vol. 28(3), pages 435-459, December.
    21. Phillips, Peter C.B., 2007. "Unit root log periodogram regression," Journal of Econometrics, Elsevier, vol. 138(1), pages 104-124, May.
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    Cited by:

    1. Zongwu Cai & Haiqiang Chen & Xiaosai Liao, 2020. "A New Robust Inference for Predictive Quantile Regression," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202002, University of Kansas, Department of Economics, revised Feb 2020.
    2. Rustam Ibragimov & Jihyun Kim & Anton Skrobotov, 2020. "New robust inference for predictive regressions," Papers 2006.01191, arXiv.org, revised Aug 2020.
    3. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    4. Stauskas, Ovidijus, 2019. "On the Limit Theory of Mixed to Unity VARs: Panel Setting With Weakly Dependent Errors," Working Papers 2019:2, Lund University, Department of Economics.
    5. Yan, Cheng & Wang, Xichen, 2018. "The non-persistent relationship between foreign equity flows and emerging stock market returns across quantiles," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 56(C), pages 38-54.
    6. Shuping Shi & Peter C B Phillips, 2020. "Diagnosing housing fever with an econometric thermometer," CAMA Working Papers 2020-43, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    7. Torben G. Andersen & Rasmus T. Varneskov, 2018. "Consistent Inference for Predictive Regressions in Persistent VAR Economies," CREATES Research Papers 2018-09, Department of Economics and Business Economics, Aarhus University.
    8. Ovidijus Stauskas, 2020. "On the limit theory of mixed to unity VARs: Panel setting with weakly dependent errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 892-898, November.
    9. Ji Hyung Lee & Zhentao Shi & Zhan Gao, 2018. "On LASSO for Predictive Regression," Papers 1810.03140, arXiv.org, revised Feb 2021.
    10. Fan, Rui & Lee, Ji Hyung, 2019. "Predictive quantile regressions under persistence and conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(1), pages 261-280.

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    More about this item

    Keywords

    Chi-square; Instrumentation; IVX methods; Local to unity; Mild integration; Mild explosiveness; Predictive regression; Robustness;
    All these keywords.

    JEL classification:

    • 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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