Do you want BuboFlash to help you learning these things? Click here to log in or create user.

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}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 .

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 .

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 .

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}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 .

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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.

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, ....

Y

Answer

X_{t}^{a}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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, ....

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 = [...].

Y

Answer

... 1/4, 1/3, 1/2, 2, 3, 4, ...

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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, ....

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)

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 )

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)

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 )

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} )

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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 )

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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.

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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^

#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} + 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.

MA(t)= a

where the weights a

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

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} + 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.

MA(t)= a

where the weights a

Answer

weighted

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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,... ,

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} + 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.

MA(t)= a

where the weights a

Answer

2q + 1

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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.</

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.

MA(t)=

where the weights a

Answer

a_{−q} X_{t−q} + ···+ a_{−1} X_{t−1} + a_{0} X_{t} + a_{1} X_{t+1} + ···+ a_{q} X_{t+q}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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.

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} + 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 [...].

MA(t)= a

where the weights a

Answer

1

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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>

#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.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

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)

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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

#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.

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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>

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.

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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).

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

#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}

status | not read | reprioritisations | ||
---|---|---|---|---|

last reprioritisation on | reading queue position [%] | |||

started reading on | finished reading on |

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}

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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