Efficient Wald Tests for Fractional Unit Roots

Ignacio N. Lobato · Carlos Velasco

123 citations0/0 files storedEconometrica

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Monetary Policy and Economic Impact Complex Systems and Time Series Analysis Diverse Scientific and Economic Studies

Abstract

In this article we introduce efficient Wald tests for testing the null hypothesis of the unit root against the alternative of the fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson Lagrange multiplier tests. Our results contrast with the tests for fractional unit roots, introduced by Dolado, Gonzalo, and Mayoral, which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first-order asymptotic properties of the proposed tests are not affected by the preestimation of short or long memory parameters.

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References

2001Econometric Analysis of Cross Section and Panel Data 1979Distribution of the Estimators for Autoregressive Time Series with a Unit Root 1979Distribution of the Estimators for Autoregressive Time Series With a Unit Root 1995Gaussian Semiparametric Estimation of Long Range Dependence 1994Efficient Tests of Nonstationary Hypotheses 1991Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression 1994Efficient Tests of Nonstationary Hypotheses 1999THE NONSTATIONARY FRACTIONAL UNIT ROOT

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