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Annotation 150891147

#m249 #mathematics #open-university #statistics #time-series
The 1-step ahead forecast error at time t, which is denoted et, is the difference between the observed value and the 1-step ahead forecast of Xt:
et = xt - \(\hat{x}_t\)
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 x1 ,x2 ,...,xn ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.
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Flashcard 150891166

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
The 1-step ahead forecast error at time t, which is denoted et, is the difference between the observed value and the 1-step ahead forecast of Xt:
et = xt - \(\hat{x}_t\)
The sum of squared errors, or SSE, is given by
SSE = [...]
Given observed values x1 ,x2 ,...,xn ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that minimizes the sum of squared errors.
Answer
\(\large SSE = \sum_{t=1}^ne_t^2 = \sum_{t=1}^n(x_t-\hat{x}_t)^2\)

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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.<

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Flashcard 150891175

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
The 1-step ahead forecast error at time t, which is denoted et, is the difference between the observed value and the 1-step ahead forecast of Xt:
et = xt - \(\hat{x}_t\)
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 x1 ,x2 ,...,xn ,the optimal value of the smoothing parameter α for simple exponential smoothing is the value that [...].
Answer
minimizes the sum of squared errors

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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>

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Flashcard 150891307

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
Suppose that the time series Xt can be described by an additive non-seasonal model with a linear trend component, that is,
Xt = m + bt + Wt , where b is the [...] of the trend component mt = m + bt.
Note that
Xt+1 = m + b(t +1) + Wt+1
=(m + bt) + b + Wt+1
= mt + b + Wt+1
Answer
slope

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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

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