#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)$$\hat{x}_n$$
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 x1 : $$\hat{x}_1$$ = x1.
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