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The available information for invariant tests of a unit root

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JournalEconometric Theory
DatePublished - Aug 2007
Issue number4
Volume23
Number of pages25
Pages (from-to)686-710
Original languageEnglish

Abstract

This paper considers the information available to invariant unit root tests at and near the unit root. Because all invariant tests will be functions of the maximal invariant, the Fisher information in this statistic will be the available information. The main finding of the paper is that the available information for all tests invariant to a linear trend is zero at the unit root. This result applies for any sample size, over a variety of distributions and correlation structures, and is robust to the inclusion of any other deterministic component. In addition, an explicit upper bound upon the power of all invariant unit root tests is shown to depend solely upon the information. This bound is illustrated via a brief simulation study that also examines the impact that different invariance requirements have on power.

    Research areas

  • LEAST-SQUARES REGRESSION, OIL-PRICE SHOCK, TIME-SERIES, ROBUST-TESTS, GREAT CRASH, HYPOTHESIS

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