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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}_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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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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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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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

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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

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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 at time n, \ha

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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 at time n, \hat{x}_nand \hat{x}_{n+1}are the 1-step ahead forecasts of X n and X n

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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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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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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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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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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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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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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

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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

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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

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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: