On the limitations of comparing mean square forecast errors

Linear models are invariant under non-singular, scale-preserving linear transformations, whereas mean square forecast errors (MSFEs) are not. Different rankings may result across models or methods from choosing alternative yet isomorphic representations of a process. One approach can dominate others for comparisons in levels, yet lose to another for differences, to a second for cointegrating vectors and to a third for combinations of variables. The potential for switches in ranking is related to criticisms of the inadequacy of MSFE against encompassing criteria, which are invariant under linear transforms and entail MSFE dominance. An invariant evaluation criterion which avoids misleading outcomes is examined in a Monte Carlo study of forecasting methods.     

Choroidal and iris angioarchitecture of the newt: A scanning electron-microscopic study of vascular corrosion casts

The corrosion cast technique provided for the first time an excellent three-dimensional visualization of the vascular pattern of the choroid and iris in the newt eye. The results show the presence of a single arterial afference to the choroidal and iris capillaries: the ophthalmic artery is the origin fo both ciliary arteries and the long posterior ciliary artery. Slightly behind the equatorial circumference of the eyeball the venous drainage consists of a single vessel on the dorsal side and two distinct vessels on the ventral one. It receives blood from both iris and choroid. The surface of the plastic endocasts shows some details of fine luminal structures of the endothelial cells. Shallow depressions may be regarded as imprints of endothelial cell nuclei, and they are distinctly different for arteries and capillaries. The angioarchitecture of the newt eye differs from that of brain in that hairpin-shaped capillary loops are not observed at all.