# on 28-May-2016 (Sat)

#### 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)$$\hat{x}_n$$
expanded m-times is
$$\large \hat{x}_{n+1} = \sum_{i=0}^m\alpha(1-\alpha)^ix_{n-i}+(1-\alpha)^{m+1}\hat{x}_{n-m}$$

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#### Parent (intermediate) annotation

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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.

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#### Flashcard 1346509606156

Tags
#2015 #book-2 #cfa #cfa-level-1 #economics #has-images #schweser
[unknown IMAGE 1346510916876]
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#### Flashcard 1346516159756

Tags
#2015 #book-2 #cfa #cfa-level-1 #economics #has-images #schweser
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#### Flashcard 1346521926924

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#2015 #book-2 #cfa #cfa-level-1 #economics #has-images #schweser
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#### Flashcard 1346526121228

Tags
#2015 #book-2 #cfa #cfa-level-1 #economics #has-images #schweser
[unknown IMAGE 1346527956236]
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#### Flashcard 1346530315532

Tags
#2015 #book-2 #cfa #cfa-level-1 #economics #has-images #schweser
[unknown IMAGE 1346532150540]
[unknown IMAGE 1346520878348]

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#### Flashcard 1346536082700

Tags
#2015 #book-2 #cfa #cfa-level-1 #economics #has-images #schweser
[unknown IMAGE 1346537917708]
[unknown IMAGE 1346535034124]

status measured difficulty not learned 37% [default] 0

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