(This article was originally published at Hyndsight on Rob J Hyndman, and syndicated at StatsBlogs.)
The official guidelines for the M4 competition have now been published, and there have been several developments since my last post on this.
There is now a prize for prediction interval accuracy using a scaled version of the Mean Interval Score. If the $100(1-\alpha)$% prediction interval for time $t$ is given by $[L_{t},U_{t}]$, for $t=1,\dots,h$, then the MIS is defined as $$\frac{1}{h}\sum_{t=1}^{h} \left[ (U_t-L_t) + \frac{2}{\alpha}(L_t-Y_t)1(Y_t < L_t) + \frac{2}{\alpha}(Y_t-L_t)1(Y_t > U_t) \right] $$ where $Y_t$ is the observation at time $t$.
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