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#### Annotation 150890986

 #m249 #mathematics #open-university #statistics #time-series If a time series Xt 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 $$\hat{x}_{n+1}$$= αxn + (1 − α)$$\hat{x}_n$$ where: xn is the observed value at time n,$$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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 x1 : $$\hat{x}_1$$ = x1.

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#### Flashcard 150890996

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#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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 x1 : $$\hat{x}_1$$ = x1.
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$

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#### Flashcard 150891005

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#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn 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.
The method requires an initial value $$\hat{x}_1$$, which is often chosen to be x1 : $$\hat{x}_1$$ = x1.
the 1-step ahead forecasts of Xn and Xn+1,

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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}_n​and \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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#### Flashcard 150891011

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+1,
• and α is [...].
The method requires an initial value $$\hat{x}_1$$, which is often chosen to be x1 : $$\hat{x}_1$$ = x1.
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}_n​and \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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#### Flashcard 150891017

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$ and $$\hat{x}_{n+1}$$ are the 1-step ahead forecasts of Xn and Xn+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 x1 : $$\hat{x}_1$$ = x1.

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

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#### Flashcard 150891023

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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 x1 : $$\hat{x}_1$$ = x1.
constant

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

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#### Flashcard 150891029

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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 x1 : $$\hat{x}_1$$ = x1.
no

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

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#### Flashcard 150891035

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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 x1 : $$\hat{x}_1$$ = x1.
1

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

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#### Flashcard 150891041

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple [...] using the formula
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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 x1 : $$\hat{x}_1$$ = x1.
exponential smoothing

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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 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

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#### Flashcard 150891047

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
If a time series Xt 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
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
where:
• xn is the observed value at time n,
• $$\hat{x}_n$$​and $$\hat{x}_{n+1}$$are the 1-step ahead forecasts of Xn and Xn+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 [...].
$$\hat{x}_1$$ = x1

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#### Annotation 150891059

 #m249 #mathematics #open-university #statistics #time-series In simple exponential smoothing satisfying the formula: $$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$ if α =1, then $$\hat{x}_{n+1}$$ = xn, so the 1-step ahead forecast is just the current value.

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#### Flashcard 150891099

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
In simple exponential smoothing satisfying the formula:
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$
if α =1, then $$\hat{x}_{n+1}$$ = xn, so the 1-step ahead forecast is just the [...] value.
current

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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.

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#### Annotation 150891105

 #m249 #mathematics #open-university #statistics #time-series In simple exponential smoothing satisfying the formula: $$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$, if α = 0, then $$\hat{x}_{n+1}$$ = $$\hat{x}_n$$ = ··· = $$\hat{x}_1$$ = x1, the initial value.

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#### Flashcard 150891112

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
In simple exponential smoothing satisfying the formula:
$$\hat{x}_{n+1}$$ = αxn + (1 − α)$$\hat{x}_n$$,
if α = 0, then $$\hat{x}_{n+1}$$ = [...]
$$\hat{x}_{n+1}$$ = $$\hat{x}_n$$ = ··· = $$\hat{x}_1$$ = x1, the initial value.

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#### Annotation 150891121

 #m249 #mathematics #open-university #statistics #time-series In simple exponential smoothing satisfying the formula: $$\hat{x}_{n+1}$$ = αxn + (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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#### Flashcard 150891128

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
In simple exponential smoothing satisfying the formula:
$$\hat{x}_{n+1}$$ = αxn + (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.
lower

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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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#### Flashcard 150891134

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#m249 #mathematics #open-university #statistics #time-series
Question
In simple exponential smoothing satisfying the formula:
$$\hat{x}_{n+1}$$ = αxn + (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.
smoother

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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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#### Flashcard 150891141

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#m249 #mathematics #open-university #statistics #time-series
Question
In simple exponential smoothing satisfying the formula:
$$\hat{x}_{n+1}$$ = αxn + (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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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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#### Annotation 150891147

 #m249 #mathematics #open-university #statistics #time-series The 1-step ahead forecast error at time t, which is denoted et, is the diﬀerence between the observed value and the 1-step ahead forecast of Xt: et = xt - $$\hat{x}_t$$ 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 x1 ,x2 ,...,xn ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.

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#### Flashcard 150891166

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
The 1-step ahead forecast error at time t, which is denoted et, is the diﬀerence between the observed value and the 1-step ahead forecast of Xt:
et = xt - $$\hat{x}_t$$
The sum of squared errors, or SSE, is given by
SSE = [...]
Given observed values x1 ,x2 ,...,xn ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.
$$\large SSE = \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2$$

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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.<

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#### Flashcard 150891175

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
The 1-step ahead forecast error at time t, which is denoted et, is the diﬀerence between the observed value and the 1-step ahead forecast of Xt:
et = xt - $$\hat{x}_t$$
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 x1 ,x2 ,...,xn ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that [...].
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>

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#### Annotation 150891216

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

Mark Wadsworth: Economic Myths: Governments don't issue currency.
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

#### Annotation 150891228

 #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.

Mark Wadsworth: Economic Myths: Governments don't issue currency.
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

#### Annotation 150891234

 #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".

Mark Wadsworth: Economic Myths: Governments don't issue currency.
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

#### Annotation 150891240

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