Chapter 18 What’s next?

Having discussed the main aspects of ADAM and how to use it in different circumstances, I want to pause to look back at what we have covered and what is left behind.

The reason why I did not call this textbook “Forecasting with ETS” or “Forecasting with State space models” is because the framework proposed here is not the same as for ETS, and it does not rely on the standard state space model. The combination of ETS, ARIMA and Regression in one unified model has not been discussed in the literature before. This is then extended by introducing a variety of distributions: typically, dynamic models rely on Normality, which is not realistic in real life, but ADAM supports several real-valued and several positive distributions. Furthermore, the model that can be applied to both regular and intermittent demand has been developed only by Svetunkov and Boylan (2019) but has not been published yet (and god knows when it will be). This is included in ADAM. In addition, the model then can be extended with multiple seasonal components, making it applicable to high-frequency data. All of the aspects mentioned above are united in one approach, giving immense flexibility to the analyst.

But what’s next? While we have discussed the important aspects of ADAM, there are still several things left that I did not have time to make work yet.

The first one is the scale model for ADAM. This is already implemented for the alm() function in the greybox package and will be discussed in Svetunkov (2021b) in one of the subsequent online editions. For ADAM, this would mean that the scale parameter (e.g. variance in Normal distribution) can be modelled explicitly using the combination of ETS, ARIMA and regression models. This would have some similarities with GARCH and/or GAMLSS, but (again) would be united in one framework.

The second one is the ADAM with asymmetric Laplace and similar distributions with the non-zero mean (the related to this is the estimation of ADAM with non-standard loss functions, such as pinball). While it is possible to use such distributions, in theory, they do not work as intended in the ADAM framework. They work perfectly in the case of the regression model (e.g. see how the alm() from the greybox works with the Asymmetric Laplace) but fail when a model has MA-related terms. This is because the model becomes more adaptive to the changes, pulls to the centre and cannot maintain the desired quantile. An introduction of such distributions would imply changing the architecture of the state space model.

Third, model combination and selection literature has seen several bright additions to the field, such as a stellar paper by Kourentzes et al. (2019a) on pooling. This is neither implemented in the adam() function nor discussed in the textbook. Yes, one can use ADAM to do pooling, but it would make sense to introduce it as a part of the ADAM approach.

Fourth, we have not discussed multiple frequency models in detail that they deserve. For example, we have not mentioned how to diagnose such models when the sample includes thousands of observations. The classical statistical approaches discussed in Section 14 typically fail in this situation, and other tools can be used in this context.

Fifth, adam() has a built-in missing values approach that relies on interpolation and intermittent state space model (from Section 13). While this already works in practice, there are some aspects of this that are worth discussing that have been left outside this textbook.

Finally, while I tried to introduce examples of application of ADAM, case studies for several contexts would be helpful. This would show how ADAM can be used for decisions in inventory management (we have touched the topic in Subsection 17.3.4), scheduling, staff allocation etc.

All of this will hopefully come in the next editions of this textbook.

References

• Kourentzes, N., Barrow, D., Petropoulos, F., 2019a. Another look at forecast selection and combination: Evidence from forecast pooling. International Journal of Production Economics. 209, 226–235. https://doi.org/10.1016/j.ijpe.2018.05.019
• Svetunkov, I., 2021b. Statistics for business analytics. https://openforecast.org/sba/ (version: 01.10.2021)
• Svetunkov, I., Boylan, J.E., 2019. Multiplicative state-space models for intermittent time series. https://doi.org/10.13140/RG.2.2.35897.06242