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Tags

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

Question

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:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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 [...].

Answer

a smoothing parameter, 0 ≤ α ≤ 1

Tags

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

Question

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:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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 [...].

Answer

?

Tags

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

Question

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:_{1} : \(\hat{x}_1\) = x_{1}.

\(\hat{x}_{n+1}\) = αx

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 [...].

Answer

a smoothing parameter, 0 ≤ α ≤ 1

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e obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n+1 , and α is <span>a smoothing parameter, 0 ≤ α ≤ 1. The method requires an initial value \hat{x}_1, which is often chosen to be x 1 : \hat{x}_1 = x 1 .<span><body><html>

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e obtained by simple exponential smoothing using the formula x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n+1 , and α is <span>a smoothing parameter, 0 ≤ α ≤ 1. The method requires an initial value \hat{x}_1, which is often chosen to be x 1 : \hat{x}_1 = x 1 .<span><body><html>

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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