IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2307.14463.html
   My bibliography  Save this paper

Bootstrapping Nonstationary Autoregressive Processes with Predictive Regression Models

Author

Listed:
  • Christis Katsouris

Abstract

We establish the asymptotic validity of the bootstrap-based IVX estimator proposed by Phillips and Magdalinos (2009) for the predictive regression model parameter based on a local-to-unity specification of the autoregressive coefficient which covers both nearly nonstationary and nearly stationary processes. A mixed Gaussian limit distribution is obtained for the bootstrap-based IVX estimator. The statistical validity of the theoretical results are illustrated by Monte Carlo experiments for various statistical inference problems.

Suggested Citation

  • Christis Katsouris, 2023. "Bootstrapping Nonstationary Autoregressive Processes with Predictive Regression Models," Papers 2307.14463, arXiv.org.
    • Handle: RePEc:arx:papers:2307.14463
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2307.14463
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
    2. Marian Z. Stoykov, 2019. "Least Squares Bias in Time Series with Moderate Deviations from a Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(1), pages 23-42, January.
    3. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    4. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    5. Larsson, Rolf, 1995. "The Asymptotic Distributions Of Some Test Statistics in Near-Integrated AR Processes," Econometric Theory, Cambridge University Press, vol. 11(2), pages 306-330, February.
    6. Giuseppe Cavaliere & Iliyan Georgiev, 2020. "Inference Under Random Limit Bootstrap Measures," Econometrica, Econometric Society, vol. 88(6), pages 2547-2574, November.
    7. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    8. Christis Katsouris, 2023. "Structural Break Detection in Quantile Predictive Regression Models with Persistent Covariates," Papers 2302.05193, arXiv.org.
    9. Fukang Zhu & Zongwu Cai & Liang Peng, 2014. "Predictive regressions for macroeconomic data," Papers 1404.7642, arXiv.org.
    10. Perron, Pierre, 1991. "A Continuous Time Approximation to the Unstable First-Order Autoregressive Process: The Case without an Intercept," Econometrica, Econometric Society, vol. 59(1), pages 211-236, January.
    11. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    12. Psaradakis, Zacharias, 2001. "On bootstrap inference in cointegrating regressions," Economics Letters, Elsevier, vol. 72(1), pages 1-10, July.
    13. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    14. Willa W. Chen & Rohit S. Deo & Yanping Yi, 2013. "Uniform Inference in Predictive Regression Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 525-533, October.
    15. Georgiev, Iliyan & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2018. "Testing for parameter instability in predictive regression models," Journal of Econometrics, Elsevier, vol. 204(1), pages 101-118.
    16. 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.
    17. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
    18. 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.
    19. Berkes, István & Gombay, Edit & Horváth, Lajos & Kokoszka, Piotr, 2004. "SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1140-1167, December.
    20. Phillips, P.C.B., 1988. "Weak Convergence of Sample Covariance Matrices to Stochastic Integrals Via Martingale Approximations," Econometric Theory, Cambridge University Press, vol. 4(3), pages 528-533, December.
    21. Chenxue Li & Deyuan Li & Liang Peng, 2017. "Uniform Test for Predictive Regression With AR Errors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 29-39, January.
    22. Michael Jansson, 2004. "The Error in Rejection Probability of Simple Autocorrelation Robust Tests," Econometrica, Econometric Society, vol. 72(3), pages 937-946, May.
    23. Phillips, Peter C.B. & Magdalinos, Tassos & Giraitis, Liudas, 2010. "Smoothing local-to-moderate unit root theory," Journal of Econometrics, Elsevier, vol. 158(2), pages 274-279, October.
    24. Paparoditis, Efstathios & Politis, Dimitris N, 2001. "Unit Root Testing via the Continuous-Path Block Bootstrap," University of California at San Diego, Economics Working Paper Series qt9qb4r775, Department of Economics, UC San Diego.
    25. Hall, Alastair R & Rudebusch, Glenn D & Wilcox, David W, 1996. "Judging Instrument Relevance in Instrumental Variables Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 283-298, May.
    26. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1131-1147, October.
    27. Gonçalves, Sílvia & Kaffo, Maximilien, 2015. "Bootstrap inference for linear dynamic panel data models with individual fixed effects," Journal of Econometrics, Elsevier, vol. 186(2), pages 407-426.
    28. Hongyi Li & Zhijie Xiao, 2001. "Bootstrapping Time Series Regressions with Integrated Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 461-480, July.
    29. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    30. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    31. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    32. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
    33. Marta Moreno & Juan Romo, 2012. "Unit root bootstrap tests under infinite variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 32-47, January.
    34. Zacharias Psaradakis, 2001. "Bootstrap Tests for an Autoregressive Unit Root in the Presence of Weakly Dependent Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(5), pages 577-594, September.
    35. Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrapping Unit Root Tests for Autoregressive Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 545-553, June.
    36. 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.
    37. Demetrescu, Matei & Georgiev, Iliyan & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2023. "Extensions to IVX methods of inference for return predictability," Journal of Econometrics, Elsevier, vol. 237(2).
    38. 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.
    39. Christis Katsouris, 2023. "Testing for Structural Change under Nonstationarity," Papers 2302.02370, arXiv.org.
    40. Li, Hongyi & Maddala, G. S., 1997. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 80(2), pages 297-318, October.
    41. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, July.
    42. 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.
    43. Horváth, Lajos & Kokoszka, Piotr, 2003. "A bootstrap approximation to a unit root test statistic for heavy-tailed observations," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 163-173, April.
    44. Jayetileke, Harshanie L. & Wang, You-Gan & Zhu, Min, 2021. "Predictive regression with p-lags and order-q autoregressive predictors," Journal of Empirical Finance, Elsevier, vol. 62(C), pages 282-293.
    45. Efstathios Paparoditis & Dimitris N. Politis, 2003. "Residual-Based Block Bootstrap for Unit Root Testing," Econometrica, Econometric Society, vol. 71(3), pages 813-855, May.
    46. Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(3), pages 269-306, September.
    47. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    48. Christis Katsouris, 2022. "Partial Sum Processes of Residual-Based and Wald-type Break-Point Statistics in Time Series Regression Models," Papers 2202.00141, arXiv.org, revised Feb 2022.
    49. Alexandros Kostakis & Tassos Magdalinos & Michalis P. Stamatogiannis, 2015. "Robust Econometric Inference for Stock Return Predictability," The Review of Financial Studies, Society for Financial Studies, vol. 28(5), pages 1506-1553.
    50. Phillips, Peter C B & Ouliaris, S, 1990. "Asymptotic Properties of Residual Based Tests for Cointegration," Econometrica, Econometric Society, vol. 58(1), pages 165-193, January.
    51. Parker, Cameron & Paparoditis, Efstathios & Politis, Dimitris N., 2006. "Unit root testing via the stationary bootstrap," Journal of Econometrics, Elsevier, vol. 133(2), pages 601-638, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christis Katsouris, 2023. "Optimal Estimation Methodologies for Panel Data Regression Models," Papers 2311.03471, arXiv.org, revised Nov 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    2. Christis Katsouris, 2023. "Break-Point Date Estimation for Nonstationary Autoregressive and Predictive Regression Models," Papers 2308.13915, arXiv.org.
    3. Christis Katsouris, 2023. "Structural Break Detection in Quantile Predictive Regression Models with Persistent Covariates," Papers 2302.05193, arXiv.org.
    4. Christis Katsouris, 2023. "Predictability Tests Robust against Parameter Instability," Papers 2307.15151, arXiv.org.
    5. Christis Katsouris, 2023. "Unified Inference for Dynamic Quantile Predictive Regression," Papers 2309.14160, arXiv.org, revised Nov 2023.
    6. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    7. Christis Katsouris, 2024. "Robust Estimation in Network Vector Autoregression with Nonstationary Regressors," Papers 2401.04050, arXiv.org.
    8. Lee, Ji Hyung & Shi, Zhentao & Gao, Zhan, 2022. "On LASSO for predictive regression," Journal of Econometrics, Elsevier, vol. 229(2), pages 322-349.
    9. Bingduo Yang & Xiaohui Liu & Liang Peng & Zongwu Cai, 2018. "Unified Tests for a Dynamic Predictive Regression," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201808, University of Kansas, Department of Economics, revised Sep 2018.
    10. Christis Katsouris, 2022. "Partial Sum Processes of Residual-Based and Wald-type Break-Point Statistics in Time Series Regression Models," Papers 2202.00141, arXiv.org, revised Feb 2022.
    11. Gonzalo, Jesús & Pitarakis, Jean-Yves, 2019. "Predictive Regressions," UC3M Working papers. Economics 28554, Universidad Carlos III de Madrid. Departamento de Economía.
    12. Lee, Ji Hyung, 2016. "Predictive quantile regression with persistent covariates: IVX-QR approach," Journal of Econometrics, Elsevier, vol. 192(1), pages 105-118.
    13. Cai, Zongwu & Chen, Haiqiang & Liao, Xiaosai, 2023. "A new robust inference for predictive quantile regression," Journal of Econometrics, Elsevier, vol. 234(1), pages 227-250.
    14. Minxian, Yang, 1998. "System estimators of cointegrating matrix in absence of normalising information," Journal of Econometrics, Elsevier, vol. 85(2), pages 317-337, August.
    15. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    16. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
    17. Christis Katsouris, 2022. "Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions," Papers 2204.02073, arXiv.org, revised Aug 2023.
    18. Rustam Ibragimov & Jihyun Kim & Anton Skrobotov, 2020. "New robust inference for predictive regressions," Papers 2006.01191, arXiv.org, revised Mar 2023.
    19. Pesavento, Elena, 2004. "Analytical evaluation of the power of tests for the absence of cointegration," Journal of Econometrics, Elsevier, vol. 122(2), pages 349-384, October.
    20. Christis Katsouris, 2023. "Estimation and Inference in Threshold Predictive Regression Models with Locally Explosive Regressors," Papers 2305.00860, arXiv.org, revised May 2023.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2307.14463. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.