IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v209y2019i2p338-352.html
   My bibliography  Save this article

Testing for randomness in a random coefficient autoregression model

Author

Listed:
  • Horváth, Lajos
  • Trapani, Lorenzo

Abstract

We propose a test to discern between an ordinary autoregressive model, and a random coefficient one. To this end, we develop a full-fledged estimation theory for the variances of the idiosyncratic innovation and of the random coefficient, based on a two-stage WLS approach. Our results hold irrespective of whether the series is stationary or nonstationary, and, as an immediate result, they afford the construction of a test for ”relevant” randomness. Further, building on these results, we develop a randomised test statistic for the null that the coefficient is non-random, as opposed to the alternative of a standard RCA(1) model. Monte Carlo evidence shows that the test has the correct size and very good power for all cases considered.

Suggested Citation

  • Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    • Handle: RePEc:eee:econom:v:209:y:2019:i:2:p:338-352
    DOI: 10.1016/j.jeconom.2019.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407619300090
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2019.01.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Daisuke Nagakura, 2009. "Inconsistency of a Unit Root Test against Stochastic Unit Root Processes," IMES Discussion Paper Series 09-E-23, Institute for Monetary and Economic Studies, Bank of Japan.
    3. 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.
    4. Anurag Narayan Banerjee & Guillaume Chevillon & Marie Kratz, 2013. "Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Coefficient Model," Working Papers hal-00870795, HAL.
    5. Wang, Xiaohu & Yu, Jun, 2015. "Limit theory for an explosive autoregressive process," Economics Letters, Elsevier, vol. 126(C), pages 176-180.
    6. Lieberman, Offer & Phillips, Peter C.B., 2017. "A multivariate stochastic unit root model with an application to derivative pricing," Journal of Econometrics, Elsevier, vol. 196(1), pages 99-110.
    7. Marine Carrasco & Liang Hu & Werner Ploberger, 2014. "Optimal Test for Markov Switching Parameters," Econometrica, Econometric Society, vol. 82(2), pages 765-784, March.
    8. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    9. Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
    10. Alexander Aue & Lajos Horváth & Josef Steinebach, 2006. "Estimation in Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 61-76, January.
    11. Corradi, Valentina & Swanson, Norman R., 2006. "The effect of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo results and a simple test," Journal of Econometrics, Elsevier, vol. 132(1), pages 195-229, May.
    12. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    13. Marc Hallin & Abdelhadi Akharif, 2003. "Efficient detection of random coefficients in AR(p) models," ULB Institutional Repository 2013/2121, ULB -- Universite Libre de Bruxelles.
    14. Abdelhadi Akharif & Marc Hallin, 2003. "Efficient detection of random coefficients in autoregressive models," ULB Institutional Repository 2013/127956, ULB -- Universite Libre de Bruxelles.
    15. Holger Dette & Dominik Wied, 2016. "Detecting relevant changes in time series models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 371-394, March.
    16. Christian Francq & Jean‐Michel Zakoïan, 2012. "Strict Stationarity Testing and Estimation of Explosive and Stationary Generalized Autoregressive Conditional Heteroscedasticity Models," Econometrica, Econometric Society, vol. 80(2), pages 821-861, March.
    17. Distaso, Walter, 2008. "Testing for unit root processes in random coefficient autoregressive models," Journal of Econometrics, Elsevier, vol. 142(1), pages 581-609, January.
    18. Lieberman, Offer & Phillips, Peter C.B., 2020. "Hybrid stochastic local unit roots," Journal of Econometrics, Elsevier, vol. 215(1), pages 257-285.
    19. Leybourne, S J & McCabe, B P M & Tremayne, A R, 1996. "Can Economic Time Series Be Differenced to Stationarity?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 435-446, October.
    20. Ramanathan, R. V. & Rajarshi, M. B., 1994. "Rank tests for testing the randomness of autoregressive coefficients," Statistics & Probability Letters, Elsevier, vol. 21(2), pages 115-120, September.
    21. Nagakura, Daisuke, 2009. "Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2476-2483, December.
    22. McCabe,B.P.M. & Tremayne,A.R., 1995. "Testing a Time-Series for Difference Stationarity," Cambridge Working Papers in Economics 9420, Faculty of Economics, University of Cambridge.
    23. 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.
    24. Offer Lieberman & Peter C. B. Phillips, 2014. "Norming Rates And Limit Theory For Some Time-Varying Coefficient Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 592-623, November.
    25. S. Y. Hwang & I. V. Basawa, 2005. "Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 807-824, November.
    26. repec:hal:journl:hal-00870795 is not listed on IDEAS
    27. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    28. Jonathan Hill & Liang Peng, 2014. "Unified Interval Estimation For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 282-297, May.
    29. Aue, Alexander, 2008. "Near-Integrated Random Coefficient Autoregressive Time Series," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1343-1372, October.
    30. W Distaso, "undated". "Testing for a random walk in random coefficient autoregressive models," Discussion Papers 05/14, Department of Economics, University of York.
    31. István Berkes & Lajos Horváth & Shiqing Ling, 2009. "Estimation in nonstationary random coefficient autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 395-416, July.
    32. Davidson, James, 1993. "The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case," Econometric Theory, Cambridge University Press, vol. 9(3), pages 402-412, June.
    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. Chi Yao & Wei Yu & Xuejun Wang, 2023. "Strong Consistency for the Conditional Self-weighted M Estimator of GRCA(p) Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-21, March.
    2. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2021. "Inference in heavy-tailed non-stationary multivariate time series," Papers 2107.13894, arXiv.org.
    3. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2022. "Tests for Random Coefficient Variation in Vector Autoregressive Models," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 1-35, Emerald Group Publishing Limited.
    4. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    5. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    6. Lorenzo Trapani & Emily Whitehouse, 2020. "Sequential monitoring for cointegrating regressions," Papers 2003.12182, arXiv.org.
    7. Marica Valente & Timm Gries & Lorenzo Trapani, 2023. "Informal employment from migration shocks," Working Papers 2023-09, Faculty of Economics and Statistics, Universität Innsbruck.
    8. Mikihito Nishi, 2023. "Testing for Coefficient Randomness in Local-to-Unity Autoregressions," Papers 2301.04853, arXiv.org, revised Jan 2023.
    9. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2020. "Determining the rank of cointegration with infinite variance," Discussion Papers 20/01, University of Nottingham, Granger Centre for Time Series Econometrics.

    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. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.
    2. 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.
    3. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    4. Jonathan Hill & Liang Peng, 2014. "Unified Interval Estimation For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 282-297, May.
    5. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    6. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2017. "Random Coefficient Continuous Systems: Testing for Extreme Sample Path Behaviour," Economics and Statistics Working Papers 18-2017, Singapore Management University, School of Economics.
    7. Yoon, Gawon, 2016. "Stochastic unit root processes: Maximum likelihood estimation, and new Lagrange multiplier and likelihood ratio tests," Economic Modelling, Elsevier, vol. 52(PB), pages 725-732.
    8. Chi Yao & Wei Yu & Xuejun Wang, 2023. "Strong Consistency for the Conditional Self-weighted M Estimator of GRCA(p) Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-21, March.
    9. Lingjie Du & Tianxiao Pang, 2021. "Asymptotic Theory for a Stochastic Unit Root Model with Intercept and Under Mis-Specification of Intercept," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 767-799, September.
    10. Lajos Horvath & Lorenzo Trapani, 2021. "Changepoint detection in random coefficient autoregressive models," Papers 2104.13440, arXiv.org.
    11. Lieberman, Offer & Phillips, Peter C.B., 2022. "Understanding temporal aggregation effects on kurtosis in financial indices," Journal of Econometrics, Elsevier, vol. 227(1), pages 25-46.
    12. Mikihito Nishi, 2023. "Testing for Coefficient Randomness in Local-to-Unity Autoregressions," Papers 2301.04853, arXiv.org, revised Jan 2023.
    13. Muriel, Nelson & González-Farías, Graciela, 2018. "Testing the null of difference stationarity against the alternative of a stochastic unit root: A new test based on multivariate STUR," Econometrics and Statistics, Elsevier, vol. 7(C), pages 46-62.
    14. Daisuke Nagakura, 2007. "Testing for Coefficient Stability of AR(1) Model When the Null is an Integrated or a Stationary Process," IMES Discussion Paper Series 07-E-20, Institute for Monetary and Economic Studies, Bank of Japan.
    15. Nagakura, Daisuke, 2009. "Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2476-2483, December.
    16. Lieberman, Offer & Phillips, Peter C.B., 2020. "Hybrid stochastic local unit roots," Journal of Econometrics, Elsevier, vol. 215(1), pages 257-285.
    17. Bykhovskaya, Anna & Phillips, Peter C.B., 2020. "Point optimal testing with roots that are functionally local to unity," Journal of Econometrics, Elsevier, vol. 219(2), pages 231-259.
    18. Offer Lieberman & Peter C. B. Phillips, 2014. "Norming Rates And Limit Theory For Some Time-Varying Coefficient Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 592-623, November.
    19. Andreas Hetland, 2018. "The Stochastic Stationary Root Model," Econometrics, MDPI, vol. 6(3), pages 1-33, August.
    20. Westerlund, Joakim & Larsson, Rolf, 2012. "Testing for a unit root in a random coefficient panel data model," Journal of Econometrics, Elsevier, vol. 167(1), pages 254-273.

    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:eee:econom:v:209:y:2019:i:2:p:338-352. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.