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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

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^