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1 results

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

  • from Part I - Trend Determination, Asset Price Bubbles, and Factor-Augmented Regressions
  • Edited by Shuping Shi, Macquarie University, Sydney, Xiaohu Wang, Fudan University, Shanghai, Tao Zeng, Zhejiang University, China
  • Book:
    Financial Econometrics
    Published online:
    20 February 2025
    Print publication:
    27 February 2025, pp 3-29

  • Summary

    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 chapter is largely pedagogical but contains new results, notational innovations, and procedures for dealing with rank deficiency that are useful in cases of wider applicability.