We consider the Breitung (2002, <italic>Journal of Econometrics</italic> 108, 343–363) statistic ξ_null, which provides a nonparametric test of the I(1) hypothesis. If ξ denotes the limit in distribution of ξ_null as <italic>n</italic> → ∞, we prove (Theorem 1) that 0 ≤ ξ ≤ 1/π², a result that holds under any...

In this article we aim to establish intuitively appealing and verifiable conditions for the first-order efficiency and asymptotic normality of ML estimators in a multi-parameter framework, assuming joint normality but neither the independence nor the identical distribution of the observations....

In this paper we bring together those properties of the Kronecker product, the vec operator, and 0-1 matrices which in our view are of interest to researchers and students in econometrics and statistics. The treatment of Kronecker products and the vec operator is fairly exhaustive; the treatment...

Let <italic>X</italic>₀ be a square matrix (complex or otherwise) and <italic>u</italic>₀ a (normalized) eigenvector associated with an eigenvalue λ^o of <italic>X</italic>₀, so that the triple (<italic>X</italic>₀, <italic>u</italic>₀, λ₀) satisfies the equations <italic>Xu</italic> = λ<italic>u</italic>, null. We investigate the conditions under which unique differentiable functions λ(<italic>X</italic>) and <italic>u</italic>(<italic>X</italic>) exist in a...

Many regression models have two dimensions, say time (<italic>t</italic> = 1,…,<italic>T</italic>) and households (<italic>i</italic> = 1,…,<italic>N</italic>), as in panel data, error components, or spatial econometrics. In estimating such models we need to specify the structure of the error variance matrix <italic>Ω</italic>, which is of dimension <italic>T N</italic> × <italic>T N</italic>. If <italic>T N</italic> is...