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#m249 #mathematics #open-university #statistics #time-series

If a time series X_{t} 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

\(\hat{x}_{n+1}\)= αx_{n} + (1 − α)\(\hat{x}_n\)

where:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\)= αx

where:

- x
_{n}is the observed value at time n, - \(\hat{x}_n\)and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X
_{n}and X_{n+1}, - and α is a smoothing parameter, 0 ≤ α ≤ 1.

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