Efficient wald tests for fractional unit roots

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.Publicad

A simple and general test for white noise

This article considers testing that a time series is uncorrelated when it possibly exhibits some form of dependence. Contrary to the currently employed tests that require selecting arbitrary user-chosen numbers to compute the associated tests statistics, we consider a test statistic that is very simple to use because it does not require any user chosen number and because its asymptotic null distribution is standard under general weak dependent conditions, and hence, asymptotic critical values are readily available. We consider the case of testing that the raw data is white noise, and also consider the case of applying the test to the residuals of an ARMA model. Finally, we also study finite sample performance

Power comparison among tests for fractional unit roots

This article compares the asymptotic power properties of the Wald, the Lagrange Multiplier and the Likelihood Ratio test for fractional unit roots. The paper shows that there is an asymptotic inequality between the three tests that holds under fixed alternatives.Publicad

Efficient wald tests for fractional unit roots

In this article we introduce efficient Wald tests for testing the null hypothesis of unit root against the alternative of fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson (1991, 1994a) Lagrange Multiplier tests. Our results contrast with the tests for fractional unit roots introduced by Dolado, Gonzalo and Mayoral (2002) 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 pre-estimation of short or long memory parameter

A simple test for normality for time series

This paper considers testing for normality for correlated data. The proposed test procedure employs the skewness-kurtosis test statistic, but studentized by standard error estimators that are consistent under serial dependence of the observations. The standard error estimators are sample versions of the asymptotic quantities that do not incorporate any downweighting, and, hence, no smoothing parameter is needed. Therefore, the main feature of our proposed test is its simplicity, because it does not require the selection of any user-chosen parameter such as a smoothing number or the order of an approximating model.Publicad

EFFICIENT WALD TESTS FOR FRACTIONAL UNIT ROOTS

In this article we introduce efficient Wald tests for testing the null hypothesis of unit root against the alternative of fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson (1991, 1994a) Lagrange Multiplier tests. Our results contrast with the tests for fractional unit roots introduced by Dolado, Gonzalo and Mayoral (2002) 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 pre-estimation of short or long memory parameters

A simple and general test for white noise

This article considers testing that a time series is uncorrelated when it possibly exhibits some form of dependence. Contrary to the currently employed tests that require selecting arbitrary user-chosen numbers to compute the associated tests statistics, we consider a test statistic that is very simple to use because it does not require any user chosen number and because its asymptotic null distribution is standard under general weak dependent conditions, and hence, asymptotic critical values are readily available. We consider the case of testing that the raw data is white noise, and also consider the case of applying the test to the residuals of an ARMA model. Finally, we also study finite sample performanceautocorrelation, spectral analysis, nonlinear dependence

Optimal Fractional Dickey-Fuller Tests for Unit Roots

This article studies the fractional Dickey- Fuller (FDF) test for unit roots recently introduced by Dolado, Gonzalo and Mayoral (2002). Apart from the analogy with the Dickey-Fuller test, the main motivation for their method relies on simulations since these authors do not provide any justification for their particular implementation of the FDF test. In order to give additional rationale to the test, we frame the FDF test in a model where a nuisance or auxiliary parameter is not identified under the null hypothesis. Within this framework we investigate optimality aspects of the class of tests indexed by this auxiliary parameter and show that the test proposed by these authors is not optimal. In addition, we propose feasible FDF tests with good asymptotic and finite sample properties.