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

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 a smoothing parameter, 0 ≤ α ≤ 1.

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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

\(\hat{x}_{n+1}\) =**[...]**

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

\(\hat{x}_{n+1}\) =

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.

Answer

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\)

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scheduled repetition interval | last repetition or drill |

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#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 [...]
- and α is a smoothing parameter, 0 ≤ α ≤ 1.

Answer

the 1-step ahead forecasts of X_{n} and X_{n+1},

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

t level and no seasonality, 1-step ahead forecasts may be 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 <span>the 1-step ahead forecasts of X n and X n+1 , and α is 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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#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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

Question

If a time series X_{t} is described by an [...] 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 a smoothing parameter, 0 ≤ α ≤ 1.

Answer

additive

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

scheduled repetition interval | last repetition or drill |

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 x n+1 = αx n + (1 − α)\hat{x}_n where:&

Tags

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

Question

If a time series X_{t} is described by an additive model with [...] 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 a smoothing parameter, 0 ≤ α ≤ 1.

Answer

constant

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the ob

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 [...] 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 a smoothing parameter, 0 ≤ α ≤ 1.

Answer

no

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value

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, [...]-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 a smoothing parameter, 0 ≤ α ≤ 1.

Answer

1

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 |

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 x n+1 = αx n + (1 − α)\hat{x}_n where: x n is the observed value at time n, \ha

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 [...] 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 a smoothing parameter, 0 ≤ α ≤ 1.

Answer

exponential smoothing

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 |

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 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

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:**[...]**.

\(\hat{x}_{n+1}\) = 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 a smoothing parameter, 0 ≤ α ≤ 1.

Answer

\(\hat{x}_1\) = x_{1}

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 |

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

In simple exponential smoothing satisfying the formula:

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\)

\(\hat{x}_{n+1}\) = αx

if α =1, then \(\hat{x}_{n+1}\) = x_{n}, so the 1-step ahead forecast is just the current value.

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

Question

In simple exponential smoothing satisfying the formula:

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\)

\(\hat{x}_{n+1}\) = αx

if α =1, then \(\hat{x}_{n+1}\) = x_{n}, so the 1-step ahead forecast is just the [...] value.

Answer

current

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 |

In simple exponential smoothing satisfying the formula: \hat{x}_{n+1} = αx n + (1 − α)\hat{x}_n if α =1, then \hat{x}_{n+1} = x n , so the 1-step ahead forecast is just the current value.

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

In simple exponential smoothing satisfying the formula:

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\),

if α = 0, then \(\hat{x}_{n+1}\) = \(\hat{x}_n\) = ··· = \(\hat{x}_1\) = x_{1}, the initial value.

\(\hat{x}_{n+1}\) = αx

if α = 0, then \(\hat{x}_{n+1}\) = \(\hat{x}_n\) = ··· = \(\hat{x}_1\) = x

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

Question

In simple exponential smoothing satisfying the formula:

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\),

if α = 0, then \(\hat{x}_{n+1}\) =**[...]**

\(\hat{x}_{n+1}\) = αx

if α = 0, then \(\hat{x}_{n+1}\) =

Answer

\(\hat{x}_{n+1}\) = \(\hat{x}_n\) = ··· = \(\hat{x}_1\) = x_{1}, the initial value.

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

In simple exponential smoothing satisfying the formula:

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\), the lower the value of α, the smoother the forecasts will be because they are not aﬀected much by recent values.

\(\hat{x}_{n+1}\) = αx

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Question

In simple exponential smoothing satisfying the formula:

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\), the [...] the value of α, the smoother the forecasts will be because they are not aﬀected much by recent values.

\(\hat{x}_{n+1}\) = αx

Answer

lower

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

In simple exponential smoothing satisfying the formula: \hat{x}_{n+1} = αx n + (1 − α)\hat{x}_n, the lower the value of α, the smoother the forecasts will be because they are not aﬀected much by recent values.

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

Question

In simple exponential smoothing satisfying the formula:

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\), the lower the value of α, the [smoother or rougher?] the forecasts will be because they are not aﬀected much by recent values.

\(\hat{x}_{n+1}\) = αx

Answer

smoother

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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scheduled repetition interval | last repetition or drill |

In simple exponential smoothing satisfying the formula: \hat{x}_{n+1} = αx n + (1 − α)\hat{x}_n, the lower the value of α, the smoother the forecasts will be because they are not aﬀected much by recent values.

Tags

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

Question

In simple exponential smoothing satisfying the formula:

\(\hat{x}_{n+1}\) = αx_{n} + (1 − α)\(\hat{x}_n\), the lower the value of α, the smoother the forecasts will be because [...].

\(\hat{x}_{n+1}\) = αx

Answer

they are not aﬀected much by recent values

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 |

In simple exponential smoothing satisfying the formula: \hat{x}_{n+1} = αx n + (1 − α)\hat{x}_n, the lower the value of α, the smoother the forecasts will be because they are not aﬀected much by recent values.

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

Question

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 = [...]

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 = [...]

Given observed values x

Answer

\(\large SSE = \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2\)

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scheduled repetition interval | last repetition or drill |

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 <span>= \(\large \sum_{t=t}^ne_t^2 = \sum_{t=t}^n(x_t-\hat{x}_t)^2\) 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.<

Tags

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

Question

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 [...].

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

Answer

minimizes the sum of squared errors

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is given by SSE = \(\large \sum_{t=t}^ne_t^2 = \sum_{t=t}^n(x_t-\hat{x}_t)^2\) 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 <span>minimizes the sum of squared errors.<span><body><html>

#economics #money

The general rule that *"loans create deposits"* applies to the government just as much as it does to banks *or anybody else.*

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created by the credit system and governments borrow deposits that allready exist i.e. the Bond market. Private sector borrowing comes first in the process creating deposits then the government taxes or borrows those deposits. Again, nope. <span>The general rule that "loans create deposits" applies to the government just as much as it does to banks or anybody else. Borrowing money, taking out a mortgage, printing notes, minting coins, running up credit, issuing currency or signing IOUs, leaving bills unpaid etc. are all shades of the same thing and

#economics #money

Borrowing money, taking out a mortgage, printing notes, minting coins, running up credit, issuing currency or signing IOUs, leaving bills unpaid etc. are all shades of the same thing and there are the same two sides to each of them - the issuer/borrower has a financial LIABILITY and the holder of the mortgage, bank notes, bank deposit, IOU etc. has a financial ASSET. It always nets off to precisely zero.

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s first in the process creating deposits then the government taxes or borrows those deposits. Again, nope. The general rule that "loans create deposits" applies to the government just as much as it does to banks or anybody else. <span>Borrowing money, taking out a mortgage, printing notes, minting coins, running up credit, issuing currency or signing IOUs, leaving bills unpaid etc. are all shades of the same thing and there are the same two sides to each of them - the issuer/borrower has a financial LIABILITY and the holder of the mortgage, bank notes, bank deposit, IOU etc. has a financial ASSET. It always nets off to precisely zero. So the government can pay people with coins and notes, bank deposits, new bonds, or simply pay a supplier over an extended credit period. It is all shades of the same thing. It does not

#economics #money

the government can pay people with coins and notes, bank deposits, new bonds, or simply pay a supplier over an extended credit period. It is all shades of the same thing. It does not need to borrow a penny beforehand. It is the expenditure which creates the liability and asset, collectively referred to as "money".

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he same thing and there are the same two sides to each of them - the issuer/borrower has a financial LIABILITY and the holder of the mortgage, bank notes, bank deposit, IOU etc. has a financial ASSET. It always nets off to precisely zero. So <span>the government can pay people with coins and notes, bank deposits, new bonds, or simply pay a supplier over an extended credit period. It is all shades of the same thing. It does not need to borrow a penny beforehand. It is the expenditure which creates the liability and asset, collectively referred to as "money". ------------------------------------------------------------- As a quite separate matter, having printed or issued currency, the government also claws back or unprints money by collectin

#economics #money

government SPENDING creates money, in the same way as government TAXATION destroys money.

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, or more of one that the other. ------------------------------------------------------------- Dinero adds: "Government borrowing does not create money." No it doesn't, but I never said it did. Read the post. What I said was that <span>government SPENDING creates money, in the same way as government TAXATION destroys money. My latest blogpost: Economic Myths: Governments don't issue currency.Tweet this! Posted by Mark Wadsworth at 11:23 Labels: EM 25 comments: