Time series: theory and methods
Time series: theory and methods
The statistical theory of linear systems
The statistical theory of linear systems
Time series: data analysis and theory
Time series: data analysis and theory
HAC estimation and strong linearity testing in weak ARMA models
Journal of Multivariate Analysis
HAC estimation and strong linearity testing in weak ARMA models
Journal of Multivariate Analysis
Estimating structural VARMA models with uncorrelated but non-independent error terms
Journal of Multivariate Analysis
Computing and estimating information matrices of weak ARMA models
Computational Statistics & Data Analysis
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In the framework of ARMA models, we consider testing the reliability of the standard asymptotic covariance matrix (ACM) of the least-squares estimator. The standard formula for this ACM is derived under the assumption that the errors are independent and identically distributed, and is in general invalid when the errors are only uncorrelated. The test statistic is based on the difference between a conventional estimator of the ACM of the least-squares estimator of the ARMA coefficients and its robust HAC-type version. The asymptotic distribution of the HAC estimator is established under the null hypothesis of independence, and under a large class of alternatives. The asymptotic distribution of the proposed statistic is shown to be a standard χ2 under the null, and a noncentral χ2 under the alternatives. The choice of the HAC estimator is discussed through asymptotic power comparisons. The finite sample properties of the test are analyzed via Monte Carlo simulation.