Modeling Seasonality

Time-series data typically exhibit a seasonality component, which can be modeled in various ways. Assuming we are using a linear regression model, the simplest approach is to include indicator variables for each month. This method makes the coefficients easy to interpret, but the resulting pattern is not smooth. Alternatively, Fourier terms can produce a smooth seasonal curve, though their coefficients are harder to interpret. Periodic splines offer the best of both worlds; providing smoothness while retaining interpretability.

Seasonal patterns are very common in many business applications. They reflect recurring fluctuations in data that repeat over fixed periods, such as days, weeks, or years. Recognizing and modeling these patterns can significantly improve forecasting accuracy and interpretation.

To effectively incorporate seasonality into models, we can use: (1) Indicator (Dummy) Variables, (2) Fourier Terms or (3) Periodic Splines

Indicator (Dummy) Variables

Add binary flags for known periods like weekends, holidays, or specific months. Simple and interpretable, but limited to fixed, known cycles.

Fourier Terms

Approximate seasonal patterns with sine and cosine terms, capturing complex and smooth cycles. Especially useful for long-term or multiple overlapping seasonalities (e.g., daily and yearly).

Periodic Splines

Flexible, smooth curves that can adapt to non-linear seasonal patterns. Offer a good balance between flexibility and interpretability.