Removing a slow trend before analysing the variability that rides on it.Detrending is the process of removing a slow, underlying trend from a time series so that the faster fluctuations or oscillations become visible. Many physical measurements contain both a long-term drift (e.g., gradual warming, sensor offset) and short-term variability of interest. By subtracting the trend, you isolate the deviations that might reveal periodicities, correlations, or anomalies. It is a common preprocessing step in data analysis across physics, finance, and climate science.
The practice dates back to early time-series analysis in the 19th century, with statisticians like Francis Galton and later Udny Yule using regression to remove trends before studying cycles. The term 'detrending' became standard in the 20th century with the rise of digital signal processing.
The trend is typically estimated by fitting a smooth function to the data, such as a polynomial, a moving average, or a low-pass filter. The fitted curve represents the slow component. Subtracting this curve from the original data leaves the residuals, which are the detrended signal. The choice of method depends on the nature of the trend: linear detrending removes a straight-line drift, while more flexible methods (e.g., LOESS) handle nonlinear trends. The goal is to remove only the slow variations, not the features of interest.
Used in climate studies to analyze temperature anomalies, in cardiology to examine heart rate variability, and in physics to remove instrumental drift from sensor data.
Detrended fluctuation analysis (DFA) is a method that uses detrending at multiple scales to detect long-range correlations in time series, and it is widely used in DNA sequence analysis.
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