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

Peter Phillips

No 2332, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Keywords: Asymptotic deficiency; Asymptotic equivalence; Hypothesis testing; Least squares regression; MA unit root; Trend regression; Wald statistic (search for similar items in EconPapers)
JEL-codes: C23 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2022-05
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sea
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Citations: View citations in EconPapers (1)

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