If a time series X
t is described by an [...] model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula
\(\hat{x}_{n+1}\) = αx
n + (1 − α)
\(\hat{x}_n\)
where:
- xn is the observed value at time n,
- \(\hat{x}_n\) and \(\hat{x}_{n+1}\) are the 1-step ahead forecasts of Xn and Xn+1,
- and α is a smoothing parameter, 0 ≤ α ≤ 1.
The method requires an initial value
\(\hat{x}_1\), which is often chosen to be x
1 :
\(\hat{x}_1\) = x
1.