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Flashcard 150890360

Tags

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

Question

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= [...] .

Answer

log m_t +log s_t +log W_t

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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

Tags

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

Question

if a [...] 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 .

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 X_t , then [...] model is appropriate for the time series of logarithms, Y_t =log X_t .

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 X_t , then an additive model is appropriate for the time series of logarithms, Y_t = [...] .

Answer

log X_t

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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:
Y_t = [...] , where a = ... 1/4, 1/3, 1/2, 2, 3, 4, ....

Answer

X_t^a

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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:
Y_t = X_t^a , 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

Tags

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

Question

A [...] of order (or span) 11 can be written as Y_t = \(\large \frac{1}{11}\)(X_t−5 + ···+ X_t + ···+ X_t+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 Y_t = \(\large \frac{1}{11}\)(X_t−5 + ···+ X_t + ···+ X_t+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 Y_t = [...]

Answer

Y_t= \(\large \frac{1}{11}\)(X_t−5 + ···+ X_t + ···+ X_t+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 m_t ; 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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Annotation 150890552

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

A weighted moving average of order 2q + 1 has the form
MA(t)= a_−q X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ 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 150890559

Tags

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

Question

A [...] moving average of order 2q + 1 has the form
MA(t)= a_−q X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ X_t+1 + ···+ a_q X_t+q ,
where the weights a_j , 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 X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ X_t+1 + ···+ a_q X_t+q ,
where the weights a_j , 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 a_j , j = −q, −q +1,... ,q, add up to 1.

Answer

a_−q X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ X_t+1 + ···+ a_q X_t+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 X_t−q + ···+ a₋₁ X_t−1 + a₀ X_t + a₁ X_t+1 + ···+ a_q X_t+q ,
where the weights a_j , j = −q, −q +1,... ,q, add up to [...].

Answer

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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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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.

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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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Annotation 150890602

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

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.

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Flashcard 150890609

Tags

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

Question

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 [...]. 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

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?

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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Annotation 150890636

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

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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Flashcard 150890643

Tags

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

Question

The simple moving average is a weighted moving average in which the weights a_j 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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Edited, memorised or added to reading queue

on 29-Apr-2015 (Wed)

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