CFDP 2332

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


Publication Date: May 2022

Pages: 25


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

Keywords: Asymptotic deficiency, Asymptotic equivalence, Hypothesis testing, Least squares regression, MA unit root, Trend regression, Wald statistic

JEL Classification Codes: C23

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