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

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

The 1-step ahead forecast error at time t, which is denoted e_{t}, is the diﬀerence between the observed value and the 1-step ahead forecast of X_{t}:

e_{t }= x_{t} - \(\hat{x}_t\)

The sum of squared errors, or SSE, is given by

SSE = \(\large \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2\)

Given observed values x_{1} ,x_{2} ,...,x_{n} ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.

e

The sum of squared errors, or SSE, is given by

SSE = \(\large \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2\)

Given observed values x

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 1-step ahead forecast error at time t, which is denoted e_{t}, is the diﬀerence between the observed value and the 1-step ahead forecast of X_{t}:

e_{t }= x_{t} - \(\hat{x}_t\)

The sum of squared errors, or SSE, is given by

SSE = [...]

Given observed values x_{1} ,x_{2} ,...,x_{n} ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.

e

The sum of squared errors, or SSE, is given by

SSE = [...]

Given observed values x

Answer

\(\large SSE = \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2\)

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 |

step ahead forecast error at time t, which is denoted e t , is the diﬀerence between the observed value and the 1-step ahead forecast of X t : e t = x t - \(\hat{x}_t\) The sum of squared errors, or SSE, is given by SSE <span>= \(\large \sum_{t=t}^ne_t^2 = \sum_{t=t}^n(x_t-\hat{x}_t)^2\) Given observed values x 1 ,x 2 ,...,x n ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.<

Tags

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

Question

The 1-step ahead forecast error at time t, which is denoted e_{t}, is the diﬀerence between the observed value and the 1-step ahead forecast of X_{t}:

e_{t }= x_{t} - \(\hat{x}_t\)

The sum of squared errors, or SSE, is given by

SSE = \(\large \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2\)

Given observed values x_{1} ,x_{2} ,...,x_{n} ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that [...].

e

The sum of squared errors, or SSE, is given by

SSE = \(\large \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2\)

Given observed values x

Answer

minimizes the sum of squared errors

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 |

is given by SSE = \(\large \sum_{t=t}^ne_t^2 = \sum_{t=t}^n(x_t-\hat{x}_t)^2\) Given observed values x 1 ,x 2 ,...,x n ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that <span>minimizes the sum of squared errors.<span><body><html>

Tags

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

Question

Suppose that the time series X_{t} can be described by an additive non-seasonal model with a linear trend component, that is,

X_{t} = m + bt + W_{t} , where b is the [...] of the trend component m_{t} = m + bt.

Note that

X_{t+1} = m + b(t +1) + W_{t+1}

=(m + bt) + b + W_{t+1}

= m_{t} + b + W_{t+1}

X

Note that

X

=(m + bt) + b + W

= m

Answer

slope

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 |

Suppose that the time series X t can be described by an additive non-seasonal model with a linear trend component, that is, X t = m + b t + W t , where b is the slope of the trend component m t = m + bt. Note that X t+1 = m + b(t +1) + W t+1 =(m + bt) + b + W t+1 = m t + b + W t+1