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#m249 #mathematics #open-university #statistics #time-series
If a time series Xt is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula
\(\hat{x}_{n+1}\)= αxn + (1 − α)\(\hat{x}_n\)
  • 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 x1 : \(\hat{x}_1\) = x1.
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