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

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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.

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  • 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
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    References listed on IDEAS

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    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.
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    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).

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    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

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