## Detrending Time Series

Detrending time series 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:

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

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

### Detrending Time Series (Stationary Time Series)

The detrending time series is a process of removing the trend from a non-stationary time series. A detrended time series is known as a stationary time series, while a time series with a trend is a non-stationary time series. A stationary time series oscillates about the horizontal line. If a series does not have a trend or we remove the trend successfully, the series is said to be trend stationary.

Eliminating the trend component may be thought of as rotating the trend line to a horizontal position. The trend component can be eliminated from the observed time series by computing either the ratios to the trend if the multiplicative model is assumed or the deviations from the trend if the additive model is assumed.