# Books or articles to study different forecasting techniques for lumpy and intermittent demand

I am doing a project to forecast demand for an automotive firm making spare parts. Using average demand interval (ADI) and square of the Coefficient of Variation (CV2), I have categorized product SKUs into smooth, erratic, lumpy and intermittent. There are ARIMA, exponential smoothing techniques for smooth demand. However, I am unable to find enough literature for lumpy and intermittent demand. There are 3 methods that have been mentioned in several blogs for intermittent -

1) Croston's method 2) Adjusted Croston's method 3) Bootstrap method

I am reading about these 3 methods. However, I haven't found any literature on lumpy demand forecasting.

Can some please suggest me some good books or articles to understand the different forecasting techniques for lumpy and intermittent demand (can have state space and neural networks also)? If that book or article explains the above 3 methods, it will be an added bonus for me. Thanks.

This article by Hyndman and Kostenko proposes the following schema for applying models based on the $$ADI$$ and $$CV2$$ coefficients that you have mentioned. Notice that CRO stands for the simple Croston Method and SBA for the bias adjusted version of the Croston Method.

For count data model there are three main approaches that you could consider:

• Ad-hoc models. Croston model and the modified versions.
• Statistical based models. Like an INARMA or GARMA models.
• Regression models. Zero Inflated, Hurdle or Poisson-Tweedie Regression

Ad-hoc models can account for reducing the bias (error in the prediction) in the forecast like the SBA, but if you update the forecast only in periods of positive demand it has a negative effect for periods of highly intermittent demand, in this case the TSB model is more suitable. The INARMA model is more adecuate if you would like to consider also the lead time for inventory replenishment. Now, Zero Inflated or Hurdle Regression is more useful when you have a great amount of zeros in your data. However, the Poisson-Tweedie regression can account for zeros present, extreme values and over dispersion (the variance is greater than the expected).

To get an insight about the theory of this models, I suggest you to consider

• Regression Analysis of Count Data by Colin Cameron and Pravin Trivedi.
• Managing Intermittent Demand by Torben Engelmeyer.

Regarding practical implementations in R

• Regression Models. This link explains how to implement them. It considers from the Poisson to the Hurdle model, also you could consider the ZIM package for Zero Inflated Models. Also tweeDESeq can be considered as an alternative for the Tweedie models.

• Ad-hoc models. tsintermittent implements the Croston, SBA and TSB model.

It is important also to consider an appropiate metric for evaluating the forecast, because traditional metrics like $$RMSE$$ or $$MAE$$ tend to bias forecast in favour of zero demand forecast. Hyndman and Koehler suggest to consider the MASE as metric.

Also, the current M5 forecasting competition in Kaggle considers sku's with lot of zeros, here is a link for an example of a Tree Based Model that considers Tweedie Regression. Finally, I have provided a brief explanation of count models on this repo, I would really appreciate your comments.