# Exponential smoothing

The raw data sequence is often represented by ${\displaystyle \{x_{t}\}}$ beginning at time ${\displaystyle t=0}$, and the output of the exponential smoothing algorithm is commonly written as ${\displaystyle \{s_{t}\}}$, which may be regarded as a best estimate of what the next value of ${\displaystyle x}$ will be. When the sequence of observations begins at time ${\displaystyle t=0}$, the simplest form of exponential smoothing is given by the formulas:[1]
{\displaystyle {\begin{aligned}s_{0}&=x_{0}\\s_{t}&=\alpha x_{t}+(1-\alpha )s_{t-1},\quad t>0\end{aligned}}}
where ${\displaystyle \alpha }$ is the smoothing factor, and ${\displaystyle 0<\alpha <1}$.