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Chapter 5 Pure additive ADAM ETS

Now that we are familiar with the conventional ETS, we can move to the discussion of ADAM implementation of it, which has several important differences from the classical one. We start the discussion with the pure additive models, which are much easier to work with than other ETS models. This chapter focuses on technical details of the model, discussing general formulation in algebraic form, then moving to recursive relations, that are needed in order to understand how to produce forecasts from the model and how to estimate it correctly (i.e. impose restrictions on the parameters). Finally, we discuss the distributional assumptions for ADAM ETS, introducing not only the Normal distribution, but also showing how to use Laplace, S, Generalised Normal, Log Normal, Gamma and Inverse Gaussian distributions in the context.