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## 13.5 Intermittent demand challenges

Intermittent demand is complicated and is difficult to work with. As a result, several challenges are related to the ADAM specifically and to the intermittent demand at large are worth discussing.

First, given the presence of zeroes, the decomposition (Section 3.2) of intermittent time series does not make sense. The classical time series model assumes that the demand happens on every observation, while the intermittent demand happens irregularly. This makes all the conventional models inapplicable to the problem, although some of them might still work well in some cases (for example, SES from Section 3.4 in case of mildly intermittent data).

The second follows directly from the first point. While, in theory, it is possible to use any ETS/ARIMA model for both demand occurrence and demand sizes of the ADAM, some of the specific model types are either impossible or very difficult to estimate. For example, seasonality on intermittent data is not very well pronounced, so estimating the initial values of components of seasonal models (such as ETS(M,N,M)) is not a trivial task. In some cases, if we have several products in a group that exhibit similar seasonal patterns, we can aggregate them to the group level to get a better estimate of seasonal indices, and then use them on the lower level. The adam() function allows doing that via initial=list(seasonal=seasonalIndices). But in all the other cases, the estimation of seasonal models might fail.

Third, in some cases, you might know when specifically demand will happen (for example, kiwis stop growing in New Zealand from May till September, so the crop will go down around that time). In this case, you do not need a proper intermittent demand model, you just need to deal with the demand sizes via ADAM ETS/ARIMA and provide zeroes and ones in the demand occurrence part for the variable $$o_t$$. We have discussed this type of model in Section 13.3. Practically speaking, this can be done in adam() via occurrence=ot, where ot would contain zeroes and ones for the sample. This can also be done for the holdout sample in the forecast() function in a similar manner:

forecast(ourModel, occurrence=otFuture, h=h)

where otFuture should contain the values of the occurrence variable in the future.

Fourth, more specialised models, such as iETS, will produce positively biased estimates of the smoothing parameters, whatever the estimator is used (see explanation in Svetunkov and Boylan, 2023a). This is caused by the assumption that the potential demand might change between the observed sales. In this situation, the components would evolve slowly, while we would only see their values before the set of zeroes and afterwards, which will make the applied model catch up to the data, thus inflating the estimates of smoothing parameters. This also implies that such forecasting methods as Croston and TSB would also result in positively biased estimates of parameters if we assume that demand might change between the non-zero observations. Practically speaking, this means that the smoothing parameters will be higher than needed, implying more rapid changes in components and thus higher uncertainty in final forecasts. There is currently no solution to this problem.

Finally, summarising this chapter, intermittent demand forecasting is a complex problem. Differences between various forecasting models and methods on such data might be insignificant, and it would be challenging to select the appropriate one. Furthermore, point forecasts on intermittent demand are difficult to grasp and make actionable (unless you are interested in lead time forecasts, to get an idea about the expected demand over a period of time). All of this means that intermittent demand should be avoided if possible. Yes, you can have fancy models for it, but do you need to? For example, do you need to look at daily demand on products if decisions are made on a weekly basis (e.g. how many units of pasta should a supermarket order for the next week)? In many cases thinking about the problem carefully would allow avoiding intermittent demand, making the life of the analyst easier. But if it is not possible, then ADAM iETS and iARIMA models can be considered potential solutions in some situations.

### References

• Croston, J.D., 1972. Forecasting and Stock Control for Intermittent Demands. Operational Research Quarterly (1970-1977). 23, 289. https://doi.org/10.2307/3007885
• Svetunkov, I., Boylan, J.E., 2023a. iETS: State Space Model for Intermittent Demand Forecastings. International Journal of Production Economics. 109013. https://doi.org/10.1016/j.ijpe.2023.109013
• Teunter, R.H., Syntetos, A.A., Babai, M.Z., 2011. Intermittent Demand: Linking Forecasting to Inventory Obsolescence. European Journal of Operational Research. 214, 606–615. https://doi.org/10.1016/j.ejor.2011.05.018