This paper looks at the strong consistency of the ordinary least squares (OLS) estimator in a stereotypical macroeconomic model with adaptive learning. It is a companion to Christopeit & Massmann (2017, Econometric Theory) which considers the estimator’s convergence in distribution and its...

This paper looks at the strong consistency of the ordinary least squares (OLS) estimator in a stereotypical macroeconomic model with adaptive learning. It is a companion to Christopeit & Massmann (2017, Econometric Theory) which considers the estimator's convergence in distribution and its weak...

In this correspondence, we prove that if X is a random variable with P(X=0)=0 and E|X|=∞, then there exists a continuous function G on (0,∞) with 0G(x)↑∞ and xG(x)↑∞ as 0x↑∞ such that E(|X|/G(|X|))=∞. An application of this result pertaining to the Kolmogorov strong law of...

In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of metric entropy arguments and discrete approximations; we then exploit the Borell–TIS inequality to establish...