Moving averages in Excel

Great help, thanks!
Now, what if I'd like to use some exponential or weighted averaging? That
is, in exponential/weighted averaging the most recent value is of great
weight than an older value. In the '10-day temperature' example, yesterday's
temperature of 90-degrees is better and weighted more than the temperature of
58-degrees of ten days ago.
How do I do the exponential/weighted average? Do I have to create my own
formula for my 'own' average methodology (non-standard)?
Thanks

"Biff" wrote:

> Ooops!
>
> Correction:
>
> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
>
> Should be:
>
> =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*E$1,,E$1))
>
> Biff
>
> "Biff" <biffinpitt@comcast.net> wrote in message
> news:eWXX5qKbFHA.1660@tk2msftngp13.phx.gbl...
> > Hi!
> >
> > Assume your values to average are in column A, starting in A1.
> >
> > Enter the interval you want to use in a cell, say, E1.
> >
> > E1 = 10
> >
> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
> >
> > Copy down until you get #DIV/0! errors meaning the data has been
> > exhausted.
> >
> > Depending on the interval size, the last average may not be a full
> > interval.
> >
> > Biff
> >
> > "Tom" <Tom@discussions.microsoft.com> wrote in message
> > news:EAE3F0BD-D655-4ADA-9F0A-3AA119168D4B@microsoft.com...
> >>I have a need to calculate a 10-interval vs x-interval moving average.
> >> Without totaling the last '10' measurements and dividing by 10 to get an
> >> average and then comparing it to, say, '13' by totaling the last 13 and
> >> dividing by 13, how can I make the calculations vary by the '# of
> >> intervals'?
> >> For example, if I want to average the high temperatures from Jan 1-Dec
> >> 31, I
> >> have 365 intervals. If I want to compare the 10 day average vs a 13 day
> >> average I can establish the formula pretty easy for the SPECIFIC number
> >> of
> >> days. I want to vary the # days, in this example, so I can see if I can
> >> spot
> >> trends in the data.
> >> So how do I do the GENERAL case of x-intervals?
> >> TIA
> >
> >
>
>
>

Hi!

>Do I have to create my own formula for my 'own' average methodology
>(non-standard)?

Well, that would fall into the category of statistics which I really don't
know much about!

Coming up with a "roll your own" weighting formula and applying it against
the data should be easy enough. Can you give an example of what the criteria
would be? I understand latest has greater weight, but how do you want to
weight that against the oldest?

Biff

"Tom" <Tom@discussions.microsoft.com> wrote in message
news:9C617793-BA0C-4B17-8C35-F68F7D72C2C9@microsoft.com...
> Great help, thanks!
> Now, what if I'd like to use some exponential or weighted averaging? That
> is, in exponential/weighted averaging the most recent value is of great
> weight than an older value. In the '10-day temperature' example,
> yesterday's
> temperature of 90-degrees is better and weighted more than the temperature
> of
> 58-degrees of ten days ago.
> How do I do the exponential/weighted average? Do I have to create my own
> formula for my 'own' average methodology (non-standard)?
> Thanks
>
> "Biff" wrote:
>
>> Ooops!
>>
>> Correction:
>>
>> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
>>
>> Should be:
>>
>> =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*E$1,,E$1))
>>
>> Biff
>>
>> "Biff" <biffinpitt@comcast.net> wrote in message
>> news:eWXX5qKbFHA.1660@tk2msftngp13.phx.gbl...
>> > Hi!
>> >
>> > Assume your values to average are in column A, starting in A1.
>> >
>> > Enter the interval you want to use in a cell, say, E1.
>> >
>> > E1 = 10
>> >
>> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
>> >
>> > Copy down until you get #DIV/0! errors meaning the data has been
>> > exhausted.
>> >
>> > Depending on the interval size, the last average may not be a full
>> > interval.
>> >
>> > Biff
>> >
>> > "Tom" <Tom@discussions.microsoft.com> wrote in message
>> > news:EAE3F0BD-D655-4ADA-9F0A-3AA119168D4B@microsoft.com...
>> >>I have a need to calculate a 10-interval vs x-interval moving average.
>> >> Without totaling the last '10' measurements and dividing by 10 to get
>> >> an
>> >> average and then comparing it to, say, '13' by totaling the last 13
>> >> and
>> >> dividing by 13, how can I make the calculations vary by the '# of
>> >> intervals'?
>> >> For example, if I want to average the high temperatures from Jan 1-Dec
>> >> 31, I
>> >> have 365 intervals. If I want to compare the 10 day average vs a 13
>> >> day
>> >> average I can establish the formula pretty easy for the SPECIFIC
>> >> number
>> >> of
>> >> days. I want to vary the # days, in this example, so I can see if I
>> >> can
>> >> spot
>> >> trends in the data.
>> >> So how do I do the GENERAL case of x-intervals?
>> >> TIA
>> >
>> >
>>
>>
>>

Biff,
Thanks AGAIN!
One easy way of weighting is to approach a 10-interval set of data as
follows [each interval is the same difference from the previous or next]:
Latest: (1.0) * value(Latest)
Latest-1: (1.0-.1) * value(Latest-1)
Latest-2: (1.0-.2) * value(Latest-2)
.....
Latest-9: (1.0-.9) * value(Latest-9)

You can see that the weighting is based off the most recent measurement
times the value at the time of THAT measurement [value(Latest-i)]. Hence,
any weighting would have to take into account A) the number of measurements
in a set of intervals [# of intervals] and B) the values during each interval
[value(Latest-i)].

There are a lot of different ways to obtain a weighting factor, (1.0-i) in
the example above, so any method of calculating the weighting factor should
keep this in mind. That is, you could some up with logarithmic weighting
factor which puts more weight on the first few intervals rather than the
assigning each weighting factor the same DIFFERENCE from the previous or next
weighting factor like the above example. Does this help!?!?
TIA


"Biff" wrote:

> Hi!
>
> >Do I have to create my own formula for my 'own' average methodology
> >(non-standard)?
>
> Well, that would fall into the category of statistics which I really don't
> know much about!
>
> Coming up with a "roll your own" weighting formula and applying it against
> the data should be easy enough. Can you give an example of what the criteria
> would be? I understand latest has greater weight, but how do you want to
> weight that against the oldest?
>
> Biff
>
> "Tom" <Tom@discussions.microsoft.com> wrote in message
> news:9C617793-BA0C-4B17-8C35-F68F7D72C2C9@microsoft.com...
> > Great help, thanks!
> > Now, what if I'd like to use some exponential or weighted averaging? That
> > is, in exponential/weighted averaging the most recent value is of great
> > weight than an older value. In the '10-day temperature' example,
> > yesterday's
> > temperature of 90-degrees is better and weighted more than the temperature
> > of
> > 58-degrees of ten days ago.
> > How do I do the exponential/weighted average? Do I have to create my own
> > formula for my 'own' average methodology (non-standard)?
> > Thanks
> >
> > "Biff" wrote:
> >
> >> Ooops!
> >>
> >> Correction:
> >>
> >> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
> >>
> >> Should be:
> >>
> >> =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*E$1,,E$1))
> >>
> >> Biff
> >>
> >> "Biff" <biffinpitt@comcast.net> wrote in message
> >> news:eWXX5qKbFHA.1660@tk2msftngp13.phx.gbl...
> >> > Hi!
> >> >
> >> > Assume your values to average are in column A, starting in A1.
> >> >
> >> > Enter the interval you want to use in a cell, say, E1.
> >> >
> >> > E1 = 10
> >> >
> >> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
> >> >
> >> > Copy down until you get #DIV/0! errors meaning the data has been
> >> > exhausted.
> >> >
> >> > Depending on the interval size, the last average may not be a full
> >> > interval.
> >> >
> >> > Biff
> >> >
> >> > "Tom" <Tom@discussions.microsoft.com> wrote in message
> >> > news:EAE3F0BD-D655-4ADA-9F0A-3AA119168D4B@microsoft.com...
> >> >>I have a need to calculate a 10-interval vs x-interval moving average.
> >> >> Without totaling the last '10' measurements and dividing by 10 to get
> >> >> an
> >> >> average and then comparing it to, say, '13' by totaling the last 13
> >> >> and
> >> >> dividing by 13, how can I make the calculations vary by the '# of
> >> >> intervals'?
> >> >> For example, if I want to average the high temperatures from Jan 1-Dec
> >> >> 31, I
> >> >> have 365 intervals. If I want to compare the 10 day average vs a 13
> >> >> day
> >> >> average I can establish the formula pretty easy for the SPECIFIC
> >> >> number
> >> >> of
> >> >> days. I want to vary the # days, in this example, so I can see if I
> >> >> can
> >> >> spot
> >> >> trends in the data.
> >> >> So how do I do the GENERAL case of x-intervals?
> >> >> TIA
> >> >
> >> >
> >>
> >>
> >>
>
>
>

Hi!

Let me see if I can come up with something.

Biff

"Tom" <Tom@discussions.microsoft.com> wrote in message
news:2A3396AC-F445-4180-A48F-E9BE992C80BB@microsoft.com...
> Biff,
> Thanks AGAIN!
> One easy way of weighting is to approach a 10-interval set of data as
> follows [each interval is the same difference from the previous or next]:
> Latest: (1.0) * value(Latest)
> Latest-1: (1.0-.1) * value(Latest-1)
> Latest-2: (1.0-.2) * value(Latest-2)
> ....
> Latest-9: (1.0-.9) * value(Latest-9)
>
> You can see that the weighting is based off the most recent measurement
> times the value at the time of THAT measurement [value(Latest-i)]. Hence,
> any weighting would have to take into account A) the number of
> measurements
> in a set of intervals [# of intervals] and B) the values during each
> interval
> [value(Latest-i)].
>
> There are a lot of different ways to obtain a weighting factor, (1.0-i) in
> the example above, so any method of calculating the weighting factor
> should
> keep this in mind. That is, you could some up with logarithmic weighting
> factor which puts more weight on the first few intervals rather than the
> assigning each weighting factor the same DIFFERENCE from the previous or
> next
> weighting factor like the above example. Does this help!?!?
> TIA
>
>
> "Biff" wrote:
>
>> Hi!
>>
>> >Do I have to create my own formula for my 'own' average methodology
>> >(non-standard)?
>>
>> Well, that would fall into the category of statistics which I really
>> don't
>> know much about!
>>
>> Coming up with a "roll your own" weighting formula and applying it
>> against
>> the data should be easy enough. Can you give an example of what the
>> criteria
>> would be? I understand latest has greater weight, but how do you want to
>> weight that against the oldest?
>>
>> Biff
>>
>> "Tom" <Tom@discussions.microsoft.com> wrote in message
>> news:9C617793-BA0C-4B17-8C35-F68F7D72C2C9@microsoft.com...
>> > Great help, thanks!
>> > Now, what if I'd like to use some exponential or weighted averaging?
>> > That
>> > is, in exponential/weighted averaging the most recent value is of great
>> > weight than an older value. In the '10-day temperature' example,
>> > yesterday's
>> > temperature of 90-degrees is better and weighted more than the
>> > temperature
>> > of
>> > 58-degrees of ten days ago.
>> > How do I do the exponential/weighted average? Do I have to create my
>> > own
>> > formula for my 'own' average methodology (non-standard)?
>> > Thanks
>> >
>> > "Biff" wrote:
>> >
>> >> Ooops!
>> >>
>> >> Correction:
>> >>
>> >> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
>> >>
>> >> Should be:
>> >>
>> >> =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*E$1,,E$1))
>> >>
>> >> Biff
>> >>
>> >> "Biff" <biffinpitt@comcast.net> wrote in message
>> >> news:eWXX5qKbFHA.1660@tk2msftngp13.phx.gbl...
>> >> > Hi!
>> >> >
>> >> > Assume your values to average are in column A, starting in A1.
>> >> >
>> >> > Enter the interval you want to use in a cell, say, E1.
>> >> >
>> >> > E1 = 10
>> >> >
>> >> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
>> >> >
>> >> > Copy down until you get #DIV/0! errors meaning the data has been
>> >> > exhausted.
>> >> >
>> >> > Depending on the interval size, the last average may not be a full
>> >> > interval.
>> >> >
>> >> > Biff
>> >> >
>> >> > "Tom" <Tom@discussions.microsoft.com> wrote in message
>> >> > news:EAE3F0BD-D655-4ADA-9F0A-3AA119168D4B@microsoft.com...
>> >> >>I have a need to calculate a 10-interval vs x-interval moving
>> >> >>average.
>> >> >> Without totaling the last '10' measurements and dividing by 10 to
>> >> >> get
>> >> >> an
>> >> >> average and then comparing it to, say, '13' by totaling the last 13
>> >> >> and
>> >> >> dividing by 13, how can I make the calculations vary by the '# of
>> >> >> intervals'?
>> >> >> For example, if I want to average the high temperatures from Jan
>> >> >> 1-Dec
>> >> >> 31, I
>> >> >> have 365 intervals. If I want to compare the 10 day average vs a
>> >> >> 13
>> >> >> day
>> >> >> average I can establish the formula pretty easy for the SPECIFIC
>> >> >> number
>> >> >> of
>> >> >> days. I want to vary the # days, in this example, so I can see if
>> >> >> I
>> >> >> can
>> >> >> spot
>> >> >> trends in the data.
>> >> >> So how do I do the GENERAL case of x-intervals?
>> >> >> TIA
>> >> >
>> >> >
>> >>
>> >>
>> >>
>>
>>
>>

Ok, let's see if I understand:

Here's a one interval (interval = 10) set of values in the range B1:B10. The
dates are in column A ascending so B1 is the oldest and B10 is the latest.

66
64
52
55
61
53
49
49
52
55

Weighted as per your example:

=B1*(1.0-0.9)
=B2*(1.0-0.8)
=B3*(1.0-0.7)
=B4*(1.0-0.6)
=B5*(1.0-0.5)
=B6*(1.0-0.4)
=B7*(1.0-0.3)
=B8*(1.0-0.2)
=B9*(1.0-0.1)
=B10*1.0

So, what you want is:

=AVERAGE {

B1*(1.0-0.9)
B2*(1.0-0.8)
B3*(1.0-0.7)
B4*(1.0-0.6)
B5*(1.0-0.5)
B6*(1.0-0.4)
B7*(1.0-0.3)
B8*(1.0-0.2)
B9*(1.0-0.1)
B10*1.0

}

If that's correct, entered as an array with the key combo of
CTRL,SHIFT,ENTER:

=AVERAGE(INDEX(OFFSET(B1,(ROW(1:1)-1)*J1,,J1),,1)*{0.1;0.2;0.3;0.4;0.5;0.6;0.7;0.8;0.9;1})

Where J1 = interval size = 10

OR, use a defined name for {0.1;0.2;0.3;0.4;0.5;0.6;0.7;0.8;0.9;1}, named
Interval:

=AVERAGE(INDEX(OFFSET(B1,(ROW(1:1)-1)*J1,,J1),,1)*Interval)

I don't see how you could use that weighting method on an interval of 13. On
the 11th element you end up with:

X*(1.0-1.0) = 0

Let me know if I'm getting this!

Biff

"Biff" <biffinpitt@comcast.net> wrote in message
news:%23nK3fzebFHA.3444@TK2MSFTNGP10.phx.gbl...
> Hi!
>
> Let me see if I can come up with something.
>
> Biff
>
> "Tom" <Tom@discussions.microsoft.com> wrote in message
> news:2A3396AC-F445-4180-A48F-E9BE992C80BB@microsoft.com...
>> Biff,
>> Thanks AGAIN!
>> One easy way of weighting is to approach a 10-interval set of data as
>> follows [each interval is the same difference from the previous or next]:
>> Latest: (1.0) * value(Latest)
>> Latest-1: (1.0-.1) * value(Latest-1)
>> Latest-2: (1.0-.2) * value(Latest-2)
>> ....
>> Latest-9: (1.0-.9) * value(Latest-9)
>>
>> You can see that the weighting is based off the most recent measurement
>> times the value at the time of THAT measurement [value(Latest-i)].
>> Hence,
>> any weighting would have to take into account A) the number of
>> measurements
>> in a set of intervals [# of intervals] and B) the values during each
>> interval
>> [value(Latest-i)].
>>
>> There are a lot of different ways to obtain a weighting factor, (1.0-i)
>> in
>> the example above, so any method of calculating the weighting factor
>> should
>> keep this in mind. That is, you could some up with logarithmic weighting
>> factor which puts more weight on the first few intervals rather than the
>> assigning each weighting factor the same DIFFERENCE from the previous or
>> next
>> weighting factor like the above example. Does this help!?!?
>> TIA
>>
>>
>> "Biff" wrote:
>>
>>> Hi!
>>>
>>> >Do I have to create my own formula for my 'own' average methodology
>>> >(non-standard)?
>>>
>>> Well, that would fall into the category of statistics which I really
>>> don't
>>> know much about!
>>>
>>> Coming up with a "roll your own" weighting formula and applying it
>>> against
>>> the data should be easy enough. Can you give an example of what the
>>> criteria
>>> would be? I understand latest has greater weight, but how do you want to
>>> weight that against the oldest?
>>>
>>> Biff
>>>
>>> "Tom" <Tom@discussions.microsoft.com> wrote in message
>>> news:9C617793-BA0C-4B17-8C35-F68F7D72C2C9@microsoft.com...
>>> > Great help, thanks!
>>> > Now, what if I'd like to use some exponential or weighted averaging?
>>> > That
>>> > is, in exponential/weighted averaging the most recent value is of
>>> > great
>>> > weight than an older value. In the '10-day temperature' example,
>>> > yesterday's
>>> > temperature of 90-degrees is better and weighted more than the
>>> > temperature
>>> > of
>>> > 58-degrees of ten days ago.
>>> > How do I do the exponential/weighted average? Do I have to create my
>>> > own
>>> > formula for my 'own' average methodology (non-standard)?
>>> > Thanks
>>> >
>>> > "Biff" wrote:
>>> >
>>> >> Ooops!
>>> >>
>>> >> Correction:
>>> >>
>>> >> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
>>> >>
>>> >> Should be:
>>> >>
>>> >> =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*E$1,,E$1))
>>> >>
>>> >> Biff
>>> >>
>>> >> "Biff" <biffinpitt@comcast.net> wrote in message
>>> >> news:eWXX5qKbFHA.1660@tk2msftngp13.phx.gbl...
>>> >> > Hi!
>>> >> >
>>> >> > Assume your values to average are in column A, starting in A1.
>>> >> >
>>> >> > Enter the interval you want to use in a cell, say, E1.
>>> >> >
>>> >> > E1 = 10
>>> >> >
>>> >> > =AVERAGE(OFFSET(A$1,(ROW(1:1)-1)*10,,E$1))
>>> >> >
>>> >> > Copy down until you get #DIV/0! errors meaning the data has been
>>> >> > exhausted.
>>> >> >
>>> >> > Depending on the interval size, the last average may not be a full
>>> >> > interval.
>>> >> >
>>> >> > Biff
>>> >> >
>>> >> > "Tom" <Tom@discussions.microsoft.com> wrote in message
>>> >> > news:EAE3F0BD-D655-4ADA-9F0A-3AA119168D4B@microsoft.com...
>>> >> >>I have a need to calculate a 10-interval vs x-interval moving
>>> >> >>average.
>>> >> >> Without totaling the last '10' measurements and dividing by 10 to
>>> >> >> get
>>> >> >> an
>>> >> >> average and then comparing it to, say, '13' by totaling the last
>>> >> >> 13
>>> >> >> and
>>> >> >> dividing by 13, how can I make the calculations vary by the '# of
>>> >> >> intervals'?
>>> >> >> For example, if I want to average the high temperatures from Jan
>>> >> >> 1-Dec
>>> >> >> 31, I
>>> >> >> have 365 intervals. If I want to compare the 10 day average vs a
>>> >> >> 13
>>> >> >> day
>>> >> >> average I can establish the formula pretty easy for the SPECIFIC
>>> >> >> number
>>> >> >> of
>>> >> >> days. I want to vary the # days, in this example, so I can see if
>>> >> >> I
>>> >> >> can
>>> >> >> spot
>>> >> >> trends in the data.
>>> >> >> So how do I do the GENERAL case of x-intervals?
>>> >> >> TIA
>>> >> >
>>> >> >
>>> >>
>>> >>
>>> >>
>>>
>>>
>>>
>
>