Mean Removal
Mean removal is a fundamental preprocessing step in time series analysis and correlation studies. By removing the average value of the data, the resulting series will have a mean closer to zero. This process helps stabilize the baseline level of the series, making comparisons and correlations more straightforward.
Why Remove the Mean?
- Centering Around Zero: Data centered around zero often simplifies analytical methods and can improve the performance of correlation and regression analyses.
- Stationarity: Some time series models assume stationarity. Removing the mean often brings the series closer to a stationary process by stabilizing its level.
- Clarity in Correlation: When comparing two series, if both are mean-removed, their correlation reflects their joint fluctuations rather than differing average values.
How to Remove the Mean?
- Calculate the Mean: Compute the average value of the time series:
mean_value = np.mean(y). - Subtract the Mean: Produce a new series by subtracting this mean:
y_mean_removed = y - mean_value.
Example (Pseudo-Code):
y = [2.5, 3.0, 2.0, 4.5, 3.5] # Example data mean_value = np.mean(y) # e.g., 3.1 y_mean_removed = y - mean_value # e.g., [-0.6, -0.1, -1.1, 1.4, 0.4]
After mean removal, your data will fluctuate around zero, making subsequent normalization or correlation analysis more interpretable and less sensitive to initial scaling or offsets.