midTime Series
What is differencing in time series and how does it help in making a series stationary?
Updated May 15, 2026
Short answer
Differencing removes trend and stabilizes the mean by subtracting consecutive observations.
Deep explanation
Differencing is a transformation technique used to make a non-stationary time series stationary. It computes the difference between consecutive observations: y'(t) = y(t) - y(t-1). This removes trends and reduces autocorrelation structure, making the series more suitable for models like ARIMA. Higher-order differencing can remove more complex trends but may introduce noise if overused.
Real-world example
Stock price levels are often differenced to analyze daily returns instead of raw prices.
Common mistakes
- Applying excessive differencing, which destroys meaningful signal structure.
Follow-up questions
- What is first-order vs second-order differencing?
- How do you know if differencing is enough?