# on 29-Apr-2015 (Wed)

#### Flashcard 150890360

Tags
#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= [...] .
log mt +log st +log Wt

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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 .

#### Original toplevel document (pdf)

cannot see any pdfs

#### Flashcard 150890373

Tags
#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 .
multiplicative

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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 .

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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 .

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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 .

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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 = [...] .
log Xt

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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 .

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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.
taking logarithms

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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.

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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, ....
Xta

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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, ....

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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 = [...].
... 1/4, 1/3, 1/2, 2, 3, 4, ...

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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, ....

#### Original toplevel document (pdf)

cannot see any pdfs

#### Flashcard 150890430

Tags
#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 )
simple moving average (or just a moving average)

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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 )

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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 )
order (or span)

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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 )

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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 = [...]
Yt = $$\large \frac{1}{11}$$(Xt−5 + ···+ Xt + ···+ Xt+5 )

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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 )

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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.
centred

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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.

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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 $$\hat{m_t}$$
an estimate

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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^

#### Original toplevel document (pdf)

cannot see any pdfs

#### Annotation 150890552

 #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.

#### pdf

cannot see any pdfs

#### 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.
weighted

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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,... ,

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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.
2q + 1

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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.</

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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.
a−q Xt−q + ···+ a−1 Xt−1 + a0 Xt + a1 Xt+1 + ···+ aq Xt+q

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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.

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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 [...].
1

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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>

#### Original toplevel document (pdf)

cannot see any pdfs

#### Annotation 150890583

 #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.

#### pdf

cannot see any pdfs

#### 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.
SA(t)

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

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

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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 [...].
seasonal variation

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

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

#### Original toplevel document (pdf)

cannot see any pdfs

#### Annotation 150890602

 #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.

#### pdf

cannot see any pdfs

#### Flashcard 150890609

Tags
#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.
the period T of the seasonal cycle

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
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>

#### Original toplevel document (pdf)

cannot see any pdfs

#### 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?
No, the period is an even number.

status measured difficulty not learned 37% [default] 0

#### pdf

cannot see any pdfs

#### Flashcard 150890624

Tags
#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?
Use T = 5 weighted average and weight down the season counted twice with 0.5 (relative to other periods' weights).

status measured difficulty not learned 37% [default] 0

#### pdf

cannot see any pdfs

#### Annotation 150890636

 #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

#### pdf

cannot see any pdfs

#### Flashcard 150890643

Tags
#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 [...]