In this paper we compare ways of computing stationarity tests. We show that whereas some of the p... more In this paper we compare ways of computing stationarity tests. We show that whereas some of the procedures recommended lead to inconsistency of the tests, it is still possible to compute a test with good properties in finite sample in terms of empirical size and power. The guidance suggested in the paper is illustrated by testing for the purchasing power parity hypothesis in some developed countries.
We propose a Lagrange Multiplier-type statistic to test the null hypothesis of cointegration allo... more We propose a Lagrange Multiplier-type statistic to test the null hypothesis of cointegration allowing for the possibility of a structural break, in both the deterministic and the cointegration vectors. Our proposal focuses on the presence of endogenous regressors. The test complements the usual non-cointegration tests so as to obtain stronger evidence of cointegration. We consider the cases of known and unknown dates of the break. In the latter case, we show that minimizing the Sum of Squared Residuals results in a super-consistent estimator of the break fraction. Finally, the behaviour of the tests is studied through Monte Carlo experiments.
Summary Several tests based on a t-ratio have been proposed in the literature to decide the orde... more Summary Several tests based on a t-ratio have been proposed in the literature to decide the order of integration of a time series allowing for a structural break. However, another approach based on testing a joint hypothesis of unit root and the irrelevance of some nuisance parameters is also feasible. This paper proposes new unit root tests consistent with the presence of a structural break applying this second perspective. Our approach deals both with the case where the break is not allowed under the null hypothesis, and where it is allowed. Simulations investigate the performance of this proposal compared to the existing tests and show important gains in terms of power.
In this note the nonparametric unit root test of Burridge and Guerre (1996, Econometric Theory, 1... more In this note the nonparametric unit root test of Burridge and Guerre (1996, Econometric Theory, 12, 705 723), which is based on the standardized number of crossings of a level of a random walk, is extended in two ways, allowing for a deterministic trend in the process and more general innovations. The test has a well-known standard limit distribution. Monte
We discuss the effects of temporal aggregation on the estimation of cointegrating vectors and on ... more We discuss the effects of temporal aggregation on the estimation of cointegrating vectors and on testing linear restrictions on this vector. We adopt a discrete time approach and demonstrate, in contrast with the findings of Chambers (2003, Econometric Theory 19, 49 77), who adopts a continuous time approach, that in some situations, when the regressand must be aggregated, systematic sampling is preferable to average sampling for estimation purposes. Like Chambers, we show that the best aggregation scheme for regressors, in terms of asymptotic estimation efficiency, is always average sampling. We also show that different types of aggregation have no influence on the relative size of tests of linear restrictions on the cointegration vector.We thank Soren Johansen, Niels Haldrup, Raquel Waters, the associate editor, and two anonymous referees for their helpful comments. Of course, any remaining error is the responsibility of the authors. The first author gratefully acknowledges the financial support of a Marie Curie Fellowship of the European Community Programme Improving the Human Research Potential and the Socio-Economic Knowledge Base under contract HPMF-CT-2002-01662 and the Danish Research Council. The second author gratefully acknowledges the financial support of the Spanish Ministry of Science and Technology SEC2002-01512.
In this paper we compare ways of computing stationarity tests. We show that whereas some of the p... more In this paper we compare ways of computing stationarity tests. We show that whereas some of the procedures recommended lead to inconsistency of the tests, it is still possible to compute a test with good properties in finite sample in terms of empirical size and power. The guidance suggested in the paper is illustrated by testing for the purchasing power parity hypothesis in some developed countries.
We propose a Lagrange Multiplier-type statistic to test the null hypothesis of cointegration allo... more We propose a Lagrange Multiplier-type statistic to test the null hypothesis of cointegration allowing for the possibility of a structural break, in both the deterministic and the cointegration vectors. Our proposal focuses on the presence of endogenous regressors. The test complements the usual non-cointegration tests so as to obtain stronger evidence of cointegration. We consider the cases of known and unknown dates of the break. In the latter case, we show that minimizing the Sum of Squared Residuals results in a super-consistent estimator of the break fraction. Finally, the behaviour of the tests is studied through Monte Carlo experiments.
Summary Several tests based on a t-ratio have been proposed in the literature to decide the orde... more Summary Several tests based on a t-ratio have been proposed in the literature to decide the order of integration of a time series allowing for a structural break. However, another approach based on testing a joint hypothesis of unit root and the irrelevance of some nuisance parameters is also feasible. This paper proposes new unit root tests consistent with the presence of a structural break applying this second perspective. Our approach deals both with the case where the break is not allowed under the null hypothesis, and where it is allowed. Simulations investigate the performance of this proposal compared to the existing tests and show important gains in terms of power.
In this note the nonparametric unit root test of Burridge and Guerre (1996, Econometric Theory, 1... more In this note the nonparametric unit root test of Burridge and Guerre (1996, Econometric Theory, 12, 705 723), which is based on the standardized number of crossings of a level of a random walk, is extended in two ways, allowing for a deterministic trend in the process and more general innovations. The test has a well-known standard limit distribution. Monte
We discuss the effects of temporal aggregation on the estimation of cointegrating vectors and on ... more We discuss the effects of temporal aggregation on the estimation of cointegrating vectors and on testing linear restrictions on this vector. We adopt a discrete time approach and demonstrate, in contrast with the findings of Chambers (2003, Econometric Theory 19, 49 77), who adopts a continuous time approach, that in some situations, when the regressand must be aggregated, systematic sampling is preferable to average sampling for estimation purposes. Like Chambers, we show that the best aggregation scheme for regressors, in terms of asymptotic estimation efficiency, is always average sampling. We also show that different types of aggregation have no influence on the relative size of tests of linear restrictions on the cointegration vector.We thank Soren Johansen, Niels Haldrup, Raquel Waters, the associate editor, and two anonymous referees for their helpful comments. Of course, any remaining error is the responsibility of the authors. The first author gratefully acknowledges the financial support of a Marie Curie Fellowship of the European Community Programme Improving the Human Research Potential and the Socio-Economic Knowledge Base under contract HPMF-CT-2002-01662 and the Danish Research Council. The second author gratefully acknowledges the financial support of the Spanish Ministry of Science and Technology SEC2002-01512.
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Papers by Andreu Sansó