The available information for invariant tests of a unit root

Patrick Marsh

doi:10.1017/S0266466607070296

The available information for invariant tests of a unit root

Patrick Marsh

Economics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	686-710
Number of pages	25
Journal	Econometric Theory
Volume	23
Issue number	4
DOIs	https://doi.org/10.1017/S0266466607070296
Publication status	Published - Aug 2007

Keywords

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

Access to Document

10.1017/S0266466607070296

http://dx.doi.org/10.1017/S0266466607070296

Cite this

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title = "The available information for invariant tests of a unit root",

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.",

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AB - 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.

KW - LEAST-SQUARES REGRESSION

KW - OIL-PRICE SHOCK

KW - TIME-SERIES

KW - ROBUST-TESTS

KW - GREAT CRASH

KW - HYPOTHESIS

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