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LM TESTS FOR A UNIT ROOT IN THE PRESENCE OF DETERMINISTIC TRENDS *

LM TESTS FOR A UNIT ROOT IN THE PRESENCE OF DETERMINISTIC TRENDS * Peter Schmidt and Peter C. B. Phillips INTRODUCTION The most commonly used tests of the null hypothesis of a unit root in an observed time series are derivatives of the Dickey-Fuller tests (Dickey(1976), Fuller (1976), Dickey and Fuller (1979)). The Dickey-Fuller tests were developed for simple Gaussian random walks and the derivative procedures (notably Said and Dickey (1984), Phillips (1987) and Phillips and Perron (1988)) are intended to detect the presence of a unit root in a general integrated process of order one (I( 1) process). The Dickey-Fuller tests are based on the regression of the observed variable (say, y ) on its one-period lagged value, with the regression sometimes including an intercept and time trend; that is, they are based on regressions of the form: Yl =BY,- + &I I + El (1) Y, = a + BY, y,=a+/?y,-,+dt+E,, (3) for t = 1,2,...,T.The 6, ,hp,and ,ijr tests are based on the statistic T(B - l), where B is the OLS estimator of B in (l), and (3)respectively, while the i, (2) i ,and irtests are based on the t-statistics for the hypothesis /3 = 1 in the same , three regressions. The former are coefficient tests, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Oxford Bulletin of Economics & Statistics Wiley

LM TESTS FOR A UNIT ROOT IN THE PRESENCE OF DETERMINISTIC TRENDS *

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References (25)

Publisher
Wiley
Copyright
1992 Blackwell Publishers Ltd
ISSN
0305-9049
eISSN
1468-0084
DOI
10.1111/j.1468-0084.1992.tb00002.x
Publisher site
See Article on Publisher Site

Abstract

Peter Schmidt and Peter C. B. Phillips INTRODUCTION The most commonly used tests of the null hypothesis of a unit root in an observed time series are derivatives of the Dickey-Fuller tests (Dickey(1976), Fuller (1976), Dickey and Fuller (1979)). The Dickey-Fuller tests were developed for simple Gaussian random walks and the derivative procedures (notably Said and Dickey (1984), Phillips (1987) and Phillips and Perron (1988)) are intended to detect the presence of a unit root in a general integrated process of order one (I( 1) process). The Dickey-Fuller tests are based on the regression of the observed variable (say, y ) on its one-period lagged value, with the regression sometimes including an intercept and time trend; that is, they are based on regressions of the form: Yl =BY,- + &I I + El (1) Y, = a + BY, y,=a+/?y,-,+dt+E,, (3) for t = 1,2,...,T.The 6, ,hp,and ,ijr tests are based on the statistic T(B - l), where B is the OLS estimator of B in (l), and (3)respectively, while the i, (2) i ,and irtests are based on the t-statistics for the hypothesis /3 = 1 in the same , three regressions. The former are coefficient tests,

Journal

Oxford Bulletin of Economics & StatisticsWiley

Published: Aug 1, 1992

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