Modeling Holiday Seasonality Demand

There is no question that holidays are very critical for retailers. The National Retail Federation (NRF) even has a dedicated page for holiday trends covering occasions like Christmas, Easter, and St. Patrick’s Day. More broadly, it also tracks other important events such as Mother’s Day, Valentine’s Day, and the Super Bowl. Intuitively, we can guess that each holiday may impact different products to different degrees. One often overlooked aspect is that in certain cases, demand builds up before the holiday and then drops off suddenly afterward; the rate of decay can vary by product. In some applications, the demand model should capture this behavior, and we want to learn it from data.

One way to model this behavior is to use a negative exponential decay function, such as: \( \text{demand} \propto e^{-\alpha x} \) where \( \alpha \) is the decay parameter controlling how fast demand drops after the peak.

When using a linear regression model, we can include multiple features with different \( \alpha \) values representing different decay speeds. The model then learns from data which decay parameters best explain the observed demand.

Alternatively, we can build a custom optimization model that directly estimates the optimal decay parameters by minimizing forecasting errors, providing more tailored control.

A third approach is to approximate the decay by combining two exponential features with distinct α values and learn a weighted average between them. While this is an approximation, it can perform well in many practical scenarios and offers a good balance between complexity and accuracy.