Deriving weight formula for exponential moving average
According to this and many other places, weight for exponential moving average is just being defined as $omega_t=(1-alpha)alpha^t$, where $t$ is current index and $alpha$ is a smoothing factor.
How does one derives this formula itself and what does $alpha$ mean, and where does one can plug size of averaging window?
This is the problem for me as I expected $omega$ to be a function of window size $N$ and index $t$, but here and everywhere else I got only $t$ and mysterious $alpha$.
I understand that $0<alpha<1$ and that it describes the steepness of the exponential slope, but I am confused that I cant find the derivation of this formula. That is why I cant understand it to the end. Could anybody provide step by step derivation of this?
numerical-methods average
asked Feb 24 '18 at 13:23
bl17zarbl17zar
11
add a comment |
According to this and many other places, weight for exponential moving average is just being defined as $omega_t=(1-alpha)alpha^t$, where $t$ is current index and $alpha$ is a smoothing factor.
How does one derives this formula itself and what does $alpha$ mean, and where does one can plug size of averaging window?
This is the problem for me as I expected $omega$ to be a function of window size $N$ and index $t$, but here and everywhere else I got only $t$ and mysterious $alpha$.
I understand that $0<alpha<1$ and that it describes the steepness of the exponential slope, but I am confused that I cant find the derivation of this formula. That is why I cant understand it to the end. Could anybody provide step by step derivation of this?
numerical-methods average
asked Feb 24 '18 at 13:23
bl17zarbl17zar
11
add a comment |
According to this and many other places, weight for exponential moving average is just being defined as $omega_t=(1-alpha)alpha^t$, where $t$ is current index and $alpha$ is a smoothing factor.
How does one derives this formula itself and what does $alpha$ mean, and where does one can plug size of averaging window?
This is the problem for me as I expected $omega$ to be a function of window size $N$ and index $t$, but here and everywhere else I got only $t$ and mysterious $alpha$.
I understand that $0<alpha<1$ and that it describes the steepness of the exponential slope, but I am confused that I cant find the derivation of this formula. That is why I cant understand it to the end. Could anybody provide step by step derivation of this?
numerical-methods average
asked Feb 24 '18 at 13:23
bl17zarbl17zar
11
According to this and many other places, weight for exponential moving average is just being defined as $omega_t=(1-alpha)alpha^t$, where $t$ is current index and $alpha$ is a smoothing factor.
How does one derives this formula itself and what does $alpha$ mean, and where does one can plug size of averaging window?
This is the problem for me as I expected $omega$ to be a function of window size $N$ and index $t$, but here and everywhere else I got only $t$ and mysterious $alpha$.
I understand that $0<alpha<1$ and that it describes the steepness of the exponential slope, but I am confused that I cant find the derivation of this formula. That is why I cant understand it to the end. Could anybody provide step by step derivation of this?
numerical-methods average
numerical-methods average
asked Feb 24 '18 at 13:23
bl17zarbl17zar
11
asked Feb 24 '18 at 13:23
bl17zarbl17zar
11
asked Feb 24 '18 at 13:23
bl17zarbl17zar
11
asked Feb 24 '18 at 13:23
bl17zarbl17zar
11
asked Feb 24 '18 at 13:23
bl17zarbl17zar
11
11
add a comment |
add a comment |
1 Answer
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With exponential moving average, your averaging window includes all previous values, although most recent values weight more.
A finite w can not thus be defined in this case.
On the other hand, you can select $alpha$ so that the last w samples make up for a given portion of your current estimate.
In your discrete case, an $alpha$ value such that the last w samples make up for about 62.3% of the current estimate would be:
$$
alpha = 1 - e^{(-1/w)}
$$
https://en.wikipedia.org/wiki/Exponential_smoothing#Time_Constant
answered Nov 29 '18 at 11:33
GianniGianni
284
add a comment |
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1 Answer
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1 Answer
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active
oldest
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oldest
votes
With exponential moving average, your averaging window includes all previous values, although most recent values weight more.
A finite w can not thus be defined in this case.
On the other hand, you can select $alpha$ so that the last w samples make up for a given portion of your current estimate.
In your discrete case, an $alpha$ value such that the last w samples make up for about 62.3% of the current estimate would be:
$$
alpha = 1 - e^{(-1/w)}
$$
https://en.wikipedia.org/wiki/Exponential_smoothing#Time_Constant
answered Nov 29 '18 at 11:33
GianniGianni
284
add a comment |
With exponential moving average, your averaging window includes all previous values, although most recent values weight more.
A finite w can not thus be defined in this case.
On the other hand, you can select $alpha$ so that the last w samples make up for a given portion of your current estimate.
In your discrete case, an $alpha$ value such that the last w samples make up for about 62.3% of the current estimate would be:
$$
alpha = 1 - e^{(-1/w)}
$$
https://en.wikipedia.org/wiki/Exponential_smoothing#Time_Constant
answered Nov 29 '18 at 11:33
GianniGianni
284
add a comment |
With exponential moving average, your averaging window includes all previous values, although most recent values weight more.
A finite w can not thus be defined in this case.
On the other hand, you can select $alpha$ so that the last w samples make up for a given portion of your current estimate.
In your discrete case, an $alpha$ value such that the last w samples make up for about 62.3% of the current estimate would be:
$$
alpha = 1 - e^{(-1/w)}
$$
https://en.wikipedia.org/wiki/Exponential_smoothing#Time_Constant
answered Nov 29 '18 at 11:33
GianniGianni
284
With exponential moving average, your averaging window includes all previous values, although most recent values weight more.
A finite w can not thus be defined in this case.
On the other hand, you can select $alpha$ so that the last w samples make up for a given portion of your current estimate.
In your discrete case, an $alpha$ value such that the last w samples make up for about 62.3% of the current estimate would be:
$$
alpha = 1 - e^{(-1/w)}
$$
https://en.wikipedia.org/wiki/Exponential_smoothing#Time_Constant
answered Nov 29 '18 at 11:33
GianniGianni
284
answered Nov 29 '18 at 11:33
GianniGianni
284
answered Nov 29 '18 at 11:33
GianniGianni
284
answered Nov 29 '18 at 11:33
GianniGianni
284
284
add a comment |
add a comment |
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