IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v40y2021i3p220-256.html
   My bibliography  Save this article

Testing for strict stationarity in a random coefficient autoregressive model

Author

Listed:
  • Lorenzo Trapani

Abstract

We propose a procedure to decide between the null hypothesis of (strict) stationarity and the alternative of nonstationarity, in the context of a random coefficient autoregression (RCAR). The procedure is based on randomizing a diagnostic which diverges to positive infinity under the null, and drifts to zero under the alternative. Thence, we propose a randomized test which can be used directly and—building on it—a decision rule to discern between the null and the alternative. The procedure can be applied under very general circumstances: albeit developed for an RCAR model, it can be used in the case of a standard AR(1) model, without requiring any modifications or prior knowledge. Also, the test works (again with no modification or prior knowledge being required) in the presence of infinite variance, and in general requires minimal assumptions on the existence of moments.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:emetrv:v:40:y:2021:i:3:p:220-256
    DOI: 10.1080/07474938.2020.1773667
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2020.1773667
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2020.1773667?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. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    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. Kapetanios, George & Shin, Yongcheol & Snell, Andy, 2003. "Testing for a unit root in the nonlinear STAR framework," Journal of Econometrics, Elsevier, vol. 112(2), pages 359-379, February.
    4. Gawon Yoon, 2006. "A Note on Some Properties of STUR Processes," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(2), pages 253-260, April.
    5. Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
    6. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    7. Wang, Xiaohu & Yu, Jun, 2015. "Limit theory for an explosive autoregressive process," Economics Letters, Elsevier, vol. 126(C), pages 176-180.
    8. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    9. 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.
    10. Giraitis, Liudas & Leipus, Remigijus & Philippe, Anne, 2006. "A Test For Stationarity Versus Trends And Unit Roots For A Wide Class Of Dependent Errors," Econometric Theory, Cambridge University Press, vol. 22(6), pages 989-1029, December.
    11. Phillips, P.C.B., 1990. "Time Series Regression With a Unit Root and Infinite-Variance Errors," Econometric Theory, Cambridge University Press, vol. 6(1), pages 44-62, March.
    12. Stock, James H., 1994. "Deciding between I(1) and I(0)," Journal of Econometrics, Elsevier, vol. 63(1), pages 105-131, July.
    13. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.
    14. Murray, Christian J. & Nelson, Charles R., 2000. "The uncertain trend in U.S. GDP," Journal of Monetary Economics, Elsevier, vol. 46(1), pages 79-95, August.
    15. Corradi, Valentina, 1999. "Deciding Between I(0) And I(1) Via Flil-Based Bounds," Econometric Theory, Cambridge University Press, vol. 15(5), pages 643-663, October.
    16. 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.
    17. Peng, Liang & Yao, Qiwei, 2004. "Nonparametric regression under dependent errors with infinite variance," LSE Research Online Documents on Economics 22874, London School of Economics and Political Science, LSE Library.
    18. Shiqing Ling, 2004. "Estimation and testing stationarity for double‐autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78, February.
    19. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.
    20. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    21. 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.
    22. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    23. Cavaliere, Giuseppe & Georgiev, Iliyan & Taylor, A.M.Robert, 2018. "Unit Root Inference For Non-Stationary Linear Processes Driven By Infinite Variance Innovations," Econometric Theory, Cambridge University Press, vol. 34(2), pages 302-348, April.
    24. W Distaso, "undated". "Testing for a random walk in random coefficient autoregressive models," Discussion Papers 05/14, Department of Economics, University of York.
    25. 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.
    26. B. G. Quinn, 1982. "A Note On The Existence Of Strictly Stationary Solutions To Bilinear Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(4), pages 249-252, July.
    27. Bandi, Federico M. & Corradi, Valentina, 2014. "Nonparametric Nonstationarity Tests," Econometric Theory, Cambridge University Press, vol. 30(1), pages 127-149, February.
    28. Cai, Ye & Shintani, Mototsugu, 2006. "On The Alternative Long-Run Variance Ratio Test For A Unit Root," Econometric Theory, Cambridge University Press, vol. 22(3), pages 347-372, June.
    29. Beechey, Meredith & Österholm, Pär, 2008. "Revisiting the uncertain unit root in GDP and CPI: Testing for non-linear trend reversion," Economics Letters, Elsevier, vol. 100(2), pages 221-223, August.
    30. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    31. 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.
    32. 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.
    33. Rudebusch, Glenn D, 1993. "The Uncertain Unit Root in Real GNP," American Economic Review, American Economic Association, vol. 83(1), pages 264-272, March.
    34. Nielsen, Heino Bohn & Rahbek, Anders, 2014. "Unit root vector autoregression with volatility induced stationarity," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 144-167.
    35. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    36. Fabio Busetti & Andrew Harvey, 2010. "Tests of strict stationarity based on quantile indicators," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(6), pages 435-450, November.
    37. Thorsten Fink & Jens-Peter Kreiss, 2013. "Bootstrap For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(6), pages 646-667, November.
    38. Liang Peng & Qiwei Yao, 2004. "Nonparametric regression under dependent errors with infinite variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 73-86, March.
    39. 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.
    40. Enders, Walter & Lee, Junsoo, 2012. "The flexible Fourier form and Dickey–Fuller type unit root tests," Economics Letters, Elsevier, vol. 117(1), pages 196-199.
    41. Distaso, Walter, 2008. "Testing for unit root processes in random coefficient autoregressive models," Journal of Econometrics, Elsevier, vol. 142(1), pages 581-609, January.
    42. 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.
    43. 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.
    44. Giraitis, L. & Kapetanios, G. & Yates, T., 2014. "Inference on stochastic time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 179(1), pages 46-65.
    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. Palandri, Alessandro, 2024. "Reconciling interest rates evidence with theory: Rejecting unit roots when the HD(1) is a competing alternative," Journal of Banking & Finance, Elsevier, vol. 161(C).
    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. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    5. Marie Badreau & Frédéric Proïa, 2023. "Consistency and asymptotic normality in a class of nearly unstable processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 619-641, October.

    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. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    2. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    3. 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.
    4. 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.
    5. 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.
    6. Phiri, Andrew, 2018. "Robust analysis of convergence in per capita GDP in BRICS economies," MPRA Paper 86936, University Library of Munich, Germany.
    7. Palandri, Alessandro, 2024. "Reconciling interest rates evidence with theory: Rejecting unit roots when the HD(1) is a competing alternative," Journal of Banking & Finance, Elsevier, vol. 161(C).
    8. Laura Mayoral, 2006. "Further Evidence on the Statistical Properties of Real GNP," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 901-920, December.
    9. Mikihito Nishi, 2023. "Testing for Coefficient Randomness in Local-to-Unity Autoregressions," Papers 2301.04853, arXiv.org, revised Jan 2023.
    10. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    11. Noriega Antonio E. & Ventosa-Santaulària Daniel, 2010. "Spurious Long-Horizon Regression in Econometrics," Working Papers 2010-06, Banco de México.
    12. Omay, Tolga & Shahbaz, Muhammad & Stewart, Chris, 2021. "Is There Really Hysteresis in OECD Countries’ Unemployment Rates? New Evidence Using a Fourier Panel Unit Root Test," MPRA Paper 107691, University Library of Munich, Germany, revised 10 May 2021.
    13. Cheng, Ka Ming, 2022. "Doubts on natural rate of unemployment: Evidence and policy implications," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 230-239.
    14. 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.
    15. Murray, Christian J. & Nelson, Charles R., 2000. "The uncertain trend in U.S. GDP," Journal of Monetary Economics, Elsevier, vol. 46(1), pages 79-95, August.
    16. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    17. Shyh-Wei Chen & Chi-Sheng Hsu & Cyun-Jhen Pen, 2016. "Are Inflation Rates Mean-reverting Processes? Evidence from Six Asian Countries," Journal of Economics and Management, College of Business, Feng Chia University, Taiwan, vol. 12(1), pages 119-155, February.
    18. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Tolga Omay, 2019. "Does U.K.’s Real GDP have a Unit Root? Evidence from a Multi-Century Perspective," Working Papers 201926, University of Pretoria, Department of Economics.
    19. Hwa-Taek Lee & Gawon Yoon, 2013. "Does purchasing power parity hold sometimes? Regime switching in real exchange rates," Applied Economics, Taylor & Francis Journals, vol. 45(16), pages 2279-2294, June.
    20. Razvan Pascalau, 2010. "Unit root tests with smooth breaks: an application to the Nelson-Plosser data set," Applied Economics Letters, Taylor & Francis Journals, vol. 17(6), pages 565-570.

    More about this item

    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:taf:emetrv:v:40:y:2021:i:3:p:220-256. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.