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

The 1-step ahead forecast error at time t, which is denoted e_{t}, is the diﬀerence between the observed value and the 1-step ahead forecast of X_{t}:

e_{t }= x_{t} - \(\hat{x}_t\)

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 x_{1} ,x_{2} ,...,x_{n} ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.

e

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 x

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