on 18-May-2015 (Mon)

Flashcard 150891353

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
simple exponential smoothing: the term exponential refers to the fact that the weights [give formula] lie on an exponential curve.
α(1 − α)i

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simple exponential smoothing: the term exponential refers to the fact that the weights α(1 − α) i lie on an exponential curve.

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Flashcard 150891359

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
what does the expanded m-times (i.e. non recursive) simple exponential smoothing formula looks like?
fully recursive is:

$$\hat{x}_{n+1}$$= αxn + (1 − α)$$\hat{x}_n$$
$$\large \hat{x}_{n+1} = \sum_{i=0}^m\alpha(1-\alpha)^ix_{n-i}+(1-\alpha)^{m+1}\hat{x}_{n-m}$$
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: 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.