What is differencing in time series, and why is it used?

Differencing in time series is a technique used to transform a non-stationary time series into a stationary one by computing the differences between consecutive observations. A stationary time series has statistical properties—like mean and variance—that remain constant over time, making it easier to model and analyze. Differencing works by subtracting the value of the series at a previous time step from the current value. For example, if you have a time series ( y_t ), the first difference is ( y’t = y_t - y{t-1} ). This helps remove trends or seasonality that might dominate the data, allowing underlying patterns to become more apparent.

The primary reason differencing is used is to address non-stationarity, which is common in real-world time series data. Many statistical models, such as ARIMA (Autoregressive Integrated Moving Average), assume stationarity. If a series has a trend (e.g., steadily increasing sales over years) or seasonal effects (e.g., higher ice cream sales every summer), models may struggle to capture meaningful relationships. Differencing helps “de-trend” the data. For instance, if monthly sales data shows an upward trend, first-order differencing would convert the absolute sales numbers into month-to-month changes, which could stabilize the mean. Seasonal differencing (e.g., subtracting values from 12 months prior for yearly seasonality) can address recurring patterns.

When implementing differencing, developers often start with first-order differencing and test for stationarity using methods like the Augmented Dickey-Fuller (ADF) test. Over-differencing—applying the technique too many times—can introduce unnecessary noise or distort the data. For example, differencing twice on a series that only needed one transformation might create artificial patterns. A practical example in code might involve using pandas in Python: df['diff'] = df['value'].diff(1) computes the first difference. If the original data has 100 points, differencing reduces it to 99, so handling the reduced dataset size is important in forecasting. Differencing is a foundational step in time series preprocessing, enabling models to focus on the relationships between observations rather than being misled by trends or seasonality.