IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/2332.html
   My bibliography  Save this paper

Asymptotics of Polynomial Time Trend Estimation and Hypothesis Testing under Rank Deficiency

Author

Abstract

Limit theory is developed for least squares regression estimation of a model involving time trend polynomials and a moving average error process with a unit root. Models with these features can arise from data manipulation such as overdifferencing and model features such as the presence of multicointegration. The impact of such features on the asymptotic equivalence of least squares and generalized least squares is considered. Problems of rank deficiency that are induced asymptotically by the presence of time polynomials in the regression are also studied, focusing on the impact that singularities have on hypothesis testing using Wald statistics and matrix normalization. The paper is largely pedagogical but contains new results, notational innovations, and procedures for dealing with rank deficiency that are useful in cases of wider applicability.

Suggested Citation

  • Peter C. B. Phillips, 2022. "Asymptotics of Polynomial Time Trend Estimation and Hypothesis Testing under Rank Deficiency," Cowles Foundation Discussion Papers 2332, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2332
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d23/d2332.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, vol. 3(3), pages 348-358, June.
    2. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    3. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    4. Phillips, Peter C.B. & Magdalinos, Tassos, 2013. "Inconsistent Var Regression With Common Explosive Roots," Econometric Theory, Cambridge University Press, vol. 29(4), pages 808-837, August.
    5. Vuong, Quang H., 1987. "Generalized inverses and asymptotic properties of Wald tests," Economics Letters, Elsevier, vol. 24(4), pages 343-347.
    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. Phillips, Peter C.B. & Kheifets, Igor L., 2024. "High-dimensional IV cointegration estimation and inference," Journal of Econometrics, Elsevier, vol. 238(2).

    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. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    2. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI), Brussels.
    3. Harald Badinger & Peter Egger, 2015. "Fixed Effects and Random Effects Estimation of Higher-order Spatial Autoregressive Models with Spatial Autoregressive and Heteroscedastic Disturbances," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(1), pages 11-35, March.
    4. Li, Degui & Phillips, Peter C.B. & Gao, Jiti, 2020. "Kernel-based Inference in Time-Varying Coefficient Cointegrating Regression," Journal of Econometrics, Elsevier, vol. 215(2), pages 607-632.
    5. Kunpeng Li & Degui Li & Zhongwen Liang & Cheng Hsiao, 2017. "Estimation of semi-varying coefficient models with nonstationary regressors," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 354-369, March.
    6. Yang, Minxian & Bewley, Ronald, 1996. "On cointegration tests for VAR models with drift," Economics Letters, Elsevier, vol. 51(1), pages 45-50, April.
    7. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, University Library of Munich, Germany.
    8. Ekaterini Panopoulou, 2005. "A Resolution of the Fisher Effect Puzzle: A Comparison of Estimators," The Institute for International Integration Studies Discussion Paper Series iiisdp067, IIIS.
    9. Arai, Yoichi, 2016. "Testing For Linearity In Regressions With I(1) Processes," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
    10. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    11. 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.
    12. Entorf, Horst, 1997. "Random walks with drifts: Nonsense regression and spurious fixed-effect estimation," Journal of Econometrics, Elsevier, vol. 80(2), pages 287-296, October.
    13. Pierre Perron & Gabriel Rodríguez, "undated". "Residuals-based Tests for Cointegration with GLS Detrended Data," Boston University - Department of Economics - Working Papers Series wp2015-017, Boston University - Department of Economics, revised 19 Oct 2015.
    14. Satorra, Albert & Neudecker, Heinz, 1997. "Compact Matrix Expressions for Generalized Wald Tests of Equality of Moment Vectors, ," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 259-276, November.
    15. Caner, Mehmet & Yıldız, Neşe, 2012. "CUE with many weak instruments and nearly singular design," Journal of Econometrics, Elsevier, vol. 170(2), pages 422-441.
    16. Husted, Steven & MacDonald, Ronald, 1998. "Monetary-based models of the exchange rate: a panel perspective," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 8(1), pages 1-19, January.
    17. José Roberto López, 1993. "Market efficiency, purchasing power parity and cointegration in Central American black foreing exchange markets," Estudios Económicos, El Colegio de México, Centro de Estudios Económicos, vol. 8(1), pages 111-153.
    18. Smaga, Łukasz, 2015. "Wald-type statistics using {2}-inverses for hypothesis testing in general factorial designs," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 215-220.
    19. Winkelried, Diego & Gutiérrez, José, 2012. "Dinámica inflacionaria regional y el esquema de metas de inflación en el Perú," Revista Estudios Económicos, Banco Central de Reserva del Perú, issue 24, pages 79-98.
    20. Otto, Glenn & Voss, Graham, 1996. "Public Capital and Private Production in Australia," MPRA Paper 52110, University Library of Munich, Germany.

    More about this item

    Keywords

    Asymptotic deficiency; Asymptotic equivalence; Hypothesis testing; Least squares regression; MA unit root; Trend regression; Wald statistic;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

    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:cwl:cwldpp:2332. 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: Brittany Ladd (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    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.