Making Time Series Stationary – So Employers Understand the Insights

Business Challenges with Time Series Data Chart

In many businesses, time series data—such as daily sales, website traffic, or stock prices—holds critical insights. However, extracting meaningful information can be challenging because the data often contains trends, seasonal patterns, and random fluctuations all mixed together.

How do employers spot anomalies in such time series charts?
Imagine a sudden spike or drop in sales. Is this an anomaly, or just part of the usual seasonal cycle? Without accounting for seasonality, unusual but expected patterns may be mistaken for problems, or real anomalies might go unnoticed.

How do you compare data in charts when seasonality exists?
If sales always rise during holidays, comparing December to January directly can be misleading. Seasonality masks the true performance changes, making it difficult to tell if a campaign improved sales or if the change is just a normal seasonal effect.

How do you separate the effects of trend, seasonality, and other factors like marketing campaigns?
To accurately measure the impact of a marketing campaign or any external event, you need to isolate these effects. Otherwise, you might attribute an increase in sales to a campaign, when in reality it’s due to a long-term trend or seasonal pattern.

Understanding and addressing these challenges is crucial for businesses to make confident, data-driven decisions.

What Are Time Series and Stationary?

Before diving into solutions, let’s clarify two key concepts: time series data and stationary.

Time series data is a sequence of observations recorded at regular time intervals, such as hourly website visits, daily stock prices, or monthly revenue figures. The unique characteristic of time series data is that its values are ordered in time, and often influenced by past values.

Stationary is a property of a time series where its statistical characteristics—mean, variance, and auto-correlation—remain constant over time. In other words, a stationary time series doesn’t have trends or seasonality, and its behavior is stable throughout the observation period.

Why does stationary matter? Many statistical models and forecasting methods assume stationary because it makes the data predictable and easier to analyze. Non-stationary data can lead to misleading conclusions and poor predictions. But in our case, we're not focusing on forecasting—our goal is to make the data more understandable and visually clear for employers. By transforming the data into a stationary form, patterns, anomalies, and campaign impacts become easier to detect and explain.

Examples of Non-Stationary Time Series and Challenges in Understanding Them

As we see in the time series below, the mean does not remain constant over time, and there is clear seasonality. This makes it difficult to compare values from different time periods. For example, we might expect website traffic to increase after raising the marketing budget—but how much of that increase is actually due to the campaign, and how much is simply because it's summer and traffic naturally rises during that season? Without making the data stationary, it's hard to separate these effects and draw accurate conclusions and show it to the employer.

Technique to Make Time Series Stationary

One of the most common techniques to make a time series stationary is differencing, which involves subtracting the current value from a previous value (a “lagged” version of the series).

• Lag 1 differencing is used when the time series has a trend. It removes the trend by focusing on the change between consecutive data points:

  Y^′_t = Y_t − Y_t−1

  (This transformation highlights short-term changes and stabilizes the mean over time.)

• Lag 12 differencing is useful when the series has seasonality, such as monthly data with annual cycles. It subtracts each value from the same month in the previous year:

  Y^′_t = Y_t − Y_t−12

  (This removes repeating seasonal effects and helps reveal the underlying structure.)

If a time series contains both trend and seasonality, we often apply both techniques: first lag-1 differencing to remove the trend, followed by lag-12 differencing to remove seasonality. This prepares the data for clearer interpretation and more effective analysis.

Understanding Time Series Decomposition

A time series can be broken down into three main components:

time series = Trend + Seasonality + Residual

When trend and seasonality are removed from a time series, any anomaly point in the residual is more likely to reflect a real event—such as a business decision, marketing campaign, or unexpected external factor—rather than something caused by predictable seasonal patterns (like higher traffic in summer) or long-term trends (such as steady company growth). This process results in a stationary series, where what remains is the residual variation—short-term fluctuations around a stable mean. In this form, unusual data points stand out more clearly, as they are no longer hidden by regular patterns. This clarity makes it easier to detect meaningful changes in behavior or performance that deserve attention or deeper analysis, enabling more accurate interpretation and better business decision-making.

Time Series and Stationary Examples