3. Seasonality and Stationarity#
Real-world time series data is rarely a simple, straight line. Instead, it is often a complex weave of repeating patterns, evolving trends, and shifting statistical properties. To build reliable models and make accurate forecasts, we must be able to disentangle these components and understand the underlying stability of the data. This chapter explores the critical concepts of Seasonality and Stationarity, providing you with the tools to decode recurring cycles and evaluate the consistency of your time series over time.
In this chapter, you will learn the following topics:
Understanding Seasonality: Many time series exhibit regular, periodic fluctuations—such as the surge in retail sales during the holidays or the rise in temperature during summer months. This section defines seasonality, explores how it differs from cyclical patterns, and introduces the fundamental distinction between Additive and Multiplicative Decomposition. You will learn how to determine which model best fits your data based on whether the seasonal fluctuations remain constant or scale with the overall trend.
Seasonal-Trend Decomposition (STL): Beyond identifying patterns, we need robust methods to separate a time series into its constituent parts: trend, seasonality, and residuals. This section focuses on Seasonal-Trend Decomposition using LOESS (STL), a versatile and powerful technique for handling complex seasonal patterns. You will discover the advantages of Robust STL, which prevents outliers from distorting your decomposition, and learn how to implement these techniques to gain a clearer view of the underlying “signal” in your data.
Stationarity and Non-Stationarity: A cornerstone of time-series modeling is the concept of stationarity—the idea that a series’ statistical properties, like mean and variance, do not change over time. This section explains why stationarity is essential for most forecasting algorithms and how to identify Non-Stationarity in practice. You will learn about common causes of non-stationarity, such as unit roots and trends, and explore the mathematical transformations required to stabilize your data for more effective analysis.