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#m249 #mathematics #open-university #statistics #time-series
The 1-step ahead forecast error at time t, which is denoted et, is the difference between the observed value and the 1-step ahead forecast of Xt:
et = xt - \(\hat{x}_t\)
The sum of squared errors, or SSE, is given by

SSE = \(\large \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2\)

Given observed values x1 ,x2 ,...,xn ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.
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