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Flashcard 150890360

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#m249 #mathematics #open-university #statistics #time-series
Question
Consider the multiplicative model Xt = mt × st × Wt .Let Yt denote the time series of logarithms: Yt =log Xt .Then
  • Yt =log Xt
  • Yt= log(mt × st × Wt)
  • Yt= [...] .
Answer
log mt +log st +log Wt


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Consider the multiplicative model X t = m t × s t × W t .Let Y t denote the time series of logarithms: Y t =log X t .Then Y t =log X t Y t = log(m t × s t × W t ) Y t = log m t +log s t +log W t .

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Flashcard 150890373

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#m249 #mathematics #open-university #statistics #time-series
Question
if a [...] model is appropriate for the time series Xt , then an additive model is appropriate for the time series of logarithms, Yt =log Xt .
Answer
multiplicative


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if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

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Flashcard 150890379

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
if a multiplicative model is appropriate for the time series Xt , then [...] model is appropriate for the time series of logarithms, Yt =log Xt .
Answer
an additive


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if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

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Flashcard 150890385

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
if a multiplicative model is appropriate for the time series Xt , then an additive model is appropriate for the time series of logarithms, Yt = [...] .
Answer
log Xt


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if a multiplicative model is appropriate for the time series X t , then an additive model is appropriate for the time series of logarithms, Y t =log X t .

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Flashcard 150890398

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
by [...], a time series for which a multiplicative model is appropriate can be transformed into a time series for which an additive model is appropriate.
Answer
taking logarithms


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by taking logarithms, a time series for which a multiplicative model is appropriate can be transformed into a time series for which an additive model is appropriate.

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Flashcard 150890411

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
Transformations of time series that are commonly used include the power transformations:
Yt = [...] , where a = ... 1/4, 1/3, 1/2, 2, 3, 4, ....
Answer
Xta


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Transformations of time series that are commonly used include the power transformations: Y t = X t a , where a = ... 1/4, 1/3, 2, 3, 4, ....

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Flashcard 150890417

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
Transformations of time series that are commonly used include the power transformations:
Yt = Xta , where a = [...].
Answer
... 1/4, 1/3, 1/2, 2, 3, 4, ...


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Transformations of time series that are commonly used include the power transformations: Y t = X t a , where a = ... 1/4, 1/3, 2, 3, 4, ....

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Flashcard 150890430

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#m249 #mathematics #open-university #statistics #time-series
Question
A [...] of order (or span) 11 can be written as Yt = \(\large \frac{1}{11}\)(Xt−5 + ···+ Xt + ···+ Xt+5 )
Answer
simple moving average (or just a moving average)


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A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

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Flashcard 150890436

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
A simple moving average (or just a moving average) of [...] 11 can be written as Yt = \(\large \frac{1}{11}\)(Xt−5 + ···+ Xt + ···+ Xt+5 )
Answer
order (or span)


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A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

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Flashcard 150890442

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
A simple moving average (or just a moving average) of order (or span) 11 can be written as Yt = [...]
Answer
Yt = \(\large \frac{1}{11}\)(Xt−5 + ···+ Xt + ···+ Xt+5 )


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A simple moving average (or just a moving average) of order (or span) 11 can be written as Y t = 111(X t−5 + ···+ X t + ···+ X t+5 )

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Flashcard 150890455

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
For the purpose of smoothing time series, only moving averages for which the order is an odd number will be used. These are said to be [...] on the middle value.
Answer
centred


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For the purpose of smoothing time series, only moving averages for which the order is an odd number will be used. These are said to be centred on the middle value.

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Flashcard 150890471

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
With a suitable degree of smoothing — that is, with a suitable choice of the order of the moving average — the moving average provides [...] of the trend component mt ; this is denoted \(\hat{m_t}\)
Answer
an estimate


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With a suitable degree of smoothing — that is, with a suitable choice of the order of the moving average — the moving average provides an estimate of the trend component m t ; this is denoted mt^

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#m249 #mathematics #open-university #statistics #time-series
A weighted moving average of order 2q + 1 has the form
MA(t)= a−q Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q ,
where the weights aj , j = −q, −q +1,... ,q, add up to 1.

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Flashcard 150890559

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
A [...] moving average of order 2q + 1 has the form
MA(t)= a−q Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q ,
where the weights aj , j = −q, −q +1,... ,q, add up to 1.
Answer
weighted


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A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,

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Flashcard 150890565

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
A weighted moving average of order [...] has the form
MA(t)= a−q Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q ,
where the weights aj , j = −q, −q +1,... ,q, add up to 1.
Answer
2q + 1


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A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.</

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Flashcard 150890571

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
A weighted moving average of order 2q + 1 has the form
MA(t)= [...] ,
where the weights aj , j = −q, −q +1,... ,q, add up to 1.
Answer
a−q Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q


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A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.

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Flashcard 150890577

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
A weighted moving average of order 2q + 1 has the form
MA(t)= a−q Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q ,
where the weights aj , j = −q, −q +1,... ,q, add up to [...].
Answer
1


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l>A weighted moving average of order 2q + 1 has the form MA(t)= a −q X t−q + ···+ a −1 X t−1 + a 0 X t + a 1 X t+1 + ···+ a q X t+q , where the weights a j , j = −q, −q +1,... ,q, add up to 1.<html>

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#m249 #mathematics #open-university #statistics #time-series
The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out seasonal variation.

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Flashcard 150890590

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
The weighted moving averages are denoted [...] rather than MA(t) when their particular use in smoothing out seasonal variation.
Answer
SA(t)


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The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out seasonal variation.

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Flashcard 150890596

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out [...].
Answer
seasonal variation


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The weighted moving averages are denoted SA(t) rather than MA(t) when their particular use in smoothing out seasonal variation.

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#m249 #mathematics #open-university #statistics #time-series
The first step is to find an initial estimate of the trend component mt that is not unduly influenced by the seasonal component st. A reasonable starting point would be to use a simple moving average with order equal to the period T of the seasonal cycle. Such a moving average would smooth out the seasonal variation, as the annual highs and lows would cancel out.

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Flashcard 150890609

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#m249 #mathematics #open-university #statistics #time-series
Question
The first step is to find an initial estimate of the trend component mt that is not unduly influenced by the seasonal component st. A reasonable starting point would be to use a simple moving average with order equal to [...]. Such a moving average would smooth out the seasonal variation, as the annual highs and lows would cancel out.
Answer
the period T of the seasonal cycle


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ead>The first step is to find an initial estimate of the trend component m t that is not unduly influenced by the seasonal component s t . A reasonable starting point would be to use a simple moving average with order equal to the period T of the seasonal cycle. Such a moving average would smooth out the seasonal variation, as the annual highs and lows would cancel out.<html>

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Flashcard 150890615

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
Suppose that the data are quarterly, so that T = 4; can we use simple moving average with period T = 4 to smoothen out seasonal variations?
Answer
No, the period is an even number.


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Flashcard 150890624

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#m249 #mathematics #open-university #statistics #time-series
Question
Suppose that the data are quarterly, so that T = 4; to smoothen out seasonal variations we cannot use simple moving average with period T = 4 (because number is even), and if we use T = 5, one season (e.g. winter and next winter) would be counted twice. How to recover from this?
Answer
Use T = 5 weighted average and weight down the season counted twice with 0.5 (relative to other periods' weights).


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#m249 #mathematics #open-university #statistics #time-series
The simple moving average is a weighted moving average in which the weights aj are all equal to (2q +1) −1

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Flashcard 150890643

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#m249 #mathematics #open-university #statistics #time-series
Question
The simple moving average is a weighted moving average in which the weights aj are all equal to [...]
Answer
N −1


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The simple moving average is a weighted moving average in which the weights a j are all equal to (2q +1) −1

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