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2009•Applied mathematical sciencesRequires access

On Perron’s Unit Root Tests in the Presence of an Innovation Variance Break

Amit Sen

Open publisher page 3 citations

Abstract

The unit root tests of Perron (1989, Econometrica) were designed to have power against the stationary alternative characterized by a break in the trend function. We show that all versions of Perron’s (1989) tests can be over-sized when there is a break in the innovation variance. We propose modified Perron statistics based on the GLS transformation proposed by Kim, Leybourne, and Newbold (2002, Journal of Econometrics) that maintain size and have power against the trend-break stationary alternative. The modified Perron statistics weakens evidence against the unit root null for the Nelson-Plosser macroeconomic series. Mathematics Subject Classification: 62F03, 62M10, 62P20, 91B84

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What this paper is about

The unit root tests of Perron (1989, Econometrica) were designed to have power against the stationary alternative characterized by a break in the trend function. We show that all versions of Perron’s (1989) tests can be over-sized when there is a break in the innovation variance. We propose modified Perron statistics based on the GLS transformation proposed by Kim, Leybourne, and Newbold (2002, Journal of Econometrics) that maintain size and have power against the trend-break stationary alternative. The modified Perron statistics weakens evidence against the unit root null for the Nelson-Plosser macroeconomic series. Mathematics Subject Classification: 62F03, 62M10, 62P20, 91B84

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Available abstract

The unit root tests of Perron (1989, Econometrica) were designed to have power against the stationary alternative characterized by a break in the trend function. We show that all versions of Perron’s (1989) tests can be over-sized when there is a break in the innovation variance. We propose modified Perron statistics based on the GLS transformation proposed by Kim, Leybourne, and Newbold (2002, Journal of Econometrics) that maintain size and have power against the trend-break stationary alternative. The modified Perron statistics weakens evidence against the unit root null for the Nelson-Plosser macroeconomic series. Mathematics Subject Classification: 62F03, 62M10, 62P20, 91B84

Key concepts: Unit root, Mathematics, Econometrics, Variance (accounting), Structural break, Null hypothesis, Unit root test, Null (SQL)

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On Perron’s Unit Root Tests in the Presence of an Innovation Variance Break — Research Paper | ScholarLens