## Detrending of time Series

Detrending is a process of eliminating the trend component from a time series, where a trend refers to a change in the mean over time (a continuous decrease or increase over time). It means when data is detrended, an aspect from that data has been removed that you think is causing some kind of distortion.

Assuming the multiplicative model:

$$Detrended\, value = \frac{Y}{T} = \frac{TSCI}{T}=SCI$$

$$Detrended\, value = Y-T=T+S+C+I-T = S+C+I$$