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.     

Effects of vitamin B12 on plasma melatonin rhythm in humans: increased light sensitivity phase-advances the circadian clock?

Vitamin B12 (methylcobalamin) was administered orally (3 mg/day) to 9 healthy subjects for 4 weeks. Nocturnal melatonin levels after exposure to bright light (ca. 2500 lx) were determined, as well as the levels of plasma melatonin over 24 h. The timing of sleep was also recorded. Vitamin B12 was given blind to the subjects and crossed over with placebo. We found that the 24-h melatonin rhythm was significantly phase-advanced (1.1 h) in the vitamin B12 trial as compared with that in the placebo trial. In addition, the 24-h mean of plasma melatonin level was much lower in the vitamin B12 trial than with the placebo. Furthermore, the nocturnal melatonin levels during bright light exposure were significantly lower in the vitamin B12 trial than with the placebo. On the other hand, vitamin B12 did not affect the timing of sleep. These findings raise the possibility that vitamin B12 phase-advances the human circadian rhythm by increasing the light sensitivity of the circadian clock.