Do you want BuboFlash to help you learning these things? Or do you want to add or correct something? Click here to log in or create user.

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

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)$$\hat{x}_n$$
?

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
$$\large \hat{x}_{n+1} = \sum_{i=0}^m\alpha(1-\alpha)^ix_{n-i}+(1-\alpha)^{m+1}\hat{x}_{n-m}$$
If you want to change selection, open original toplevel document below and click on "Move attachment"

Parent (intermediate) annotation

Open it
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.

Original toplevel document (pdf)

cannot see any pdfs

Summary

status measured difficulty not learned 37% [default] 0

No repetitions

Discussion

Do you want to join discussion? Click here to log in or create user.