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native · entrylib:2026.000003 · 2026-11-11 · Statistics and Probability · corrected · v2

The observed-data likelihood of ADAM and iETS with unobserved periods

Ivan Svetunkov

For a model of intermittent demand $y_t=o_tz_t$ with Bernoulli occurrence $o_t\sim\text{Bernoulli}(p_t)$ independent of a positive continuous size $z_t$, the observed-data likelihood is $\sum_{O_t=1}\log f(z_t\mid Y_{t-1};\theta) + \sum_{O_t=1}\log p_t + \sum_{O_t=0}\log(1-p_t),$ in which the unobserved sizes do not appear and the size and occurrence parts separate.

11 principal claims · 37 claims · 20 pieces of evidence