Edited, memorised or added to reading list

on 17-May-2015 (Sun)

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

Flashcard 150891134

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
In simple exponential smoothing satisfying the formula:
\(\hat{x}_{n+1}\) = αxn + (1 − α)\(\hat{x}_n\), the lower the value of α, the [smoother or rougher?] the forecasts will be because they are not affected much by recent values.
Answer
smoother

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
In simple exponential smoothing satisfying the formula: \hat{x}_{n+1} = αx n + (1 − α)\hat{x}_n, the lower the value of α, the smoother the forecasts will be because they are not affected much by recent values.

Original toplevel document (pdf)

cannot see any pdfs







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

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
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.<

Original toplevel document (pdf)

cannot see any pdfs







Flashcard 150891282

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
Give a formula for additive time series model with constant level and no seasonality
Answer
Xt = m + Wt

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

pdf

cannot see any pdfs







#m249 #mathematics #open-university #statistics #time-series
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 slope 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
statusnot read reprioritisations
last reprioritisation on reading queue position [%]
started reading on finished reading on

pdf

cannot see any pdfs




Flashcard 150891298

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 = [...] , where b is the slope 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
m + bt + Wt

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
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 <

Original toplevel document (pdf)

cannot see any pdfs







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

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
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

Original toplevel document (pdf)

cannot see any pdfs







Flashcard 150891319

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 slope of the trend component mt = [...].
Note that
Xt+1 = m + b(t +1) + Wt+1
=(m + bt) + b + Wt+1
= mt + b + Wt+1
Answer
m + bt

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
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 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

Original toplevel document (pdf)

cannot see any pdfs







Flashcard 150891325

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 slope of the trend component mt = m + bt.
Note that
Xt+1 = m + b[...] + Wt+1
=(m + bt) + b + Wt+1
= mt + b + Wt+1
Answer
(t +1)

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
pose 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 slope of the trend component m t = m + bt. Note that X t+1 = m + b<span>(t +1) + W t+1 =(m + bt) + b + W t+1 = m t + b + W t+1 <span><body><html>

Original toplevel document (pdf)

cannot see any pdfs







Flashcard 150891331

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 slope of the trend component mt = m + bt.
Note that
Xt+1 = m + b(t +1) + Wt+1
=[...]
= mt + b + Wt+1
Answer
(m + bt) + b + Wt+1

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
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 slope of the trend component m t = m + bt. Note that X t+1 = m + b(t +1) + W t+1 =<span>(m + bt) + b + W t+1 = m t + b + W t+1 <span><body><html>

Original toplevel document (pdf)

cannot see any pdfs







Flashcard 150891340

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 slope of the trend component mt = m + bt.
Note that
Xt+1 = m + b(t +1) + Wt+1
=(m + bt) + b + Wt+1
= [...]
Answer
mt + b + Wt+1

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
n-seasonal model with a linear trend component, that is, X t = m + bt + 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 = <span>m t + b + W t+1 <span><body><html>

Original toplevel document (pdf)

cannot see any pdfs







#m249 #mathematics #open-university #statistics #time-series
simple exponential smoothing: the term exponential refers to the fact that the weights α(1 − α)i lie on an exponential curve.
statusnot read reprioritisations
last reprioritisation on reading queue position [%]
started reading on finished reading on

pdf

cannot see any pdfs




Flashcard 150891353

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
simple exponential smoothing: the term exponential refers to the fact that the weights [give formula] lie on an exponential curve.
Answer
α(1 − α)i

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
simple exponential smoothing: the term exponential refers to the fact that the weights α(1 − α) i lie on an exponential curve.

Original toplevel document (pdf)

cannot see any pdfs







Flashcard 150891359

Tags
#m249 #mathematics #open-university #statistics #time-series
Question
what does the expanded m-times (i.e. non recursive) simple exponential smoothing formula looks like?
fully recursive is:

\(\hat{x}_{n+1}\)= αxn + (1 − α)\(\hat{x}_n\)
Answer
expanded m-times is
\(\large \hat{x}_{n+1} = \sum_{i=0}^m\alpha(1-\alpha)^ix_{n-i}+(1-\alpha)^{m+1}\hat{x}_{n-m}\)

statusnot learnedmeasured difficulty37% [default]last interval [days]               
repetition number in this series0memorised on               scheduled repetition               
scheduled repetition interval               last repetition or drill

Parent (intermediate) annotation

Open it
If a time series X t is described by an additive model with constant level and no seasonality, 1-step ahead forecasts may be obtained by simple exponential smoothing using the formula \(\hat{x}_{n+1}\)= αx n + (1 − α)\(\hat{x}_n\) where: x n is the observed value at time n, \(\hat{x}_n\)​and \(\hat{x}_{n+1}\)are the 1-step ahead forecasts of X n and X n+1 , and α is a smoothing parameter, 0 ≤ α ≤ 1.

Original toplevel document (pdf)

cannot see any pdfs