Adding seasonality to demand forecasting


Seasonal products are common in many industries and can involve a large number of factors such as the influence of seasonal weather changes for example. By definition, it is any change at all that consistently influences your demand during the same periods. This places some complexity into demand forecasting models and limits the use of some of them. Simple and double exponential smoothing forecast models (discussed in previous articles) do not recognize these seasonal patterns and so cannot extrapolate any future seasonal behavior.

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Going through the concept to improve your demand planning process

Let’s first recapitulate. The Forecast (f) in double exponential smoothing is calculated by two layers, the Level (a) plus the Trend (b).


By inserting the seasonality into the model, Seasonal Factor (s),a new layer of exponential smoothing is added. It is estimated based on the most recent observation and its previous estimation.
A learning rate, gamma (\gamma), is applied to the Seasonal Factor (s) metric, so the model will use an exponential weighting method in order to determine how much weight percentage is given to the most recent observation compared to the previous estimation. In other words, \gamma will determine if the forecast should respond quickly or not to a certain demand variation. Considering that seasonality in general doesn´t have significant changes from one year to another, keeping the learning rate low, lower than 0.3 for example, will avoid unnecessary adapting to fit exceptional situations and outliers, and will keep this method a more regularized forecast model.

Still, it may require some degree of understanding of your market demand, but knowing if your seasonality is monthly, quarterly or yearly based, should give you a good hint as to the best degree of learning rate to use.

Choosing the right method for accurate demand forecasting

The triple exponential smoothing technique has two different approaches, and you should know the nature of your seasonality, in order to know which one to use.

  • Multiplicative Smoothing

If you sell 20% more of your product in December than in November, you probably have a multiplicative seasonal nature. In this case the Seasonal Factor (s) is simply multiplied into the forecast:


This predicts with reliable accuracy, responding in a very effective way to variations of seasonality and following the general trend of the demand, as shown on the example below comparing it with the forecast.

However, this method can result in mathematical errors if volumes or the seasonality factors are too close to 0. Also a small absolute demand variation can result in a great difference. Unfortunately, this means that this model is not suited for all products, and reinforces the importance of knowing the seasonal nature of your products.
In order to solve this issue a second demand forecasting approach is preferred:

  • Additive Smoothing

If you sell 20,000 more of your products in December than in November you have an additive seasonal nature. With this approach a season factor is added to the level predicted by the forecast model, so that the forecast responds with more adherence even at low volumes. Now we add the Seasonal Factor (s) into the forecast: f_{t+1}=a_{t}+b_{t}+s_{t}

Putting both approaches into a visual graphic perspective, gives us a clearer idea of how they will react over the demand variation, showing a best fit for the additive model.

But the additive method also has its demand forecasting limitations, such as an inability to deal with any external input (marketing budget or pricing impact for example). Besides that, there is the issue for items with a significant trend. The way the triple exponential smoothing model is defined, does not allow for the seasonality to quickly evolve through time nor to extrapolate changes. This new additive model is actually best suited for items with a stable demand or low demand.

Going deeper into demand forecasting methods

As you can see our two seasonal models are complementary and should allow you to forecast any seasonal product. However, achieving reliable results requires sensitive understanding of the behavior of your product demand variation over time. The best way of knowing which one you should use, is of course by experimenting.
The concept of the triple model is not that complex, but delving deeply into the equations, may be a little complicated without the proper tools. For more information on this model and other exponential smoothing models, you can check the freely available, online reference book “Forecasting: Principles and Practice", by Rob J Hyndman and George Athanasopoulos, two world-class leaders in the field of forecasting, and “Data Science for Supply Chain Forecast” by Nicolas Vandeput.
SKU Science has all these models and tools and can provide all the support you need to apply these demand forecasting methods reliably and effectively to your demand planning process.

You can also see a more detailed analysis of both models on supchains.com


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