I want to analyze 36 months of historical sales figures to see if I can
identify any time-series that will allow me to project them into the
future.

Hi. Just some thoughts. Fourier Analysis assumes your data is
periodic, so future projections would just be a repeat of your data.
It will not be able to show growth, or something similar, into the future.

The first output of Fourier is the zero frequency. The second line is
frequency 1, third line is frequency 2, etc.
The reason the first output is a real number is that that Sin( 0 ) is
zero, and cancels out the imaginary part.
Same for line 17 in the output, which is frequency 16.

Sin( (2 Pi/32)*16*x), reduces to Sin(Pi x) and is always zero, hence
line 17 is always real.

On your part..."to see if I can identify any time-series.."

Another option is to do a poor-mans version of a spectrum analyzer.
=IMABS(B1)

and copy down to Row 17. We do not need to look at the complex
conjugates that are further down.
Make the small adjustment here to divide by 32 in Row 1 and 17, and
divide by 16 in rows 2-16. (2*x / 32 - x / 16)
Then do something like a bar chart on this data.

What this shows is the relative contribution of each frequency.
Suppose we had 36 data points instead of 32 here to keep the math
simple. Divide 36 by a few of our frequencies, say 1-12

{36., 18., 12., 9., 7.2, 6., 5.14, 4.5, 4., 3.6, 3.27, 3.}

The first row in our output is just our average sales, and should have a
value.

If we had a large value in Row 2(freq 1) compared to the other values,
then this would indicate a strong presence of a 36 month sales cycle.
All other values close to 0 would be considered "noise" and would likely
be dropped from the equation when reverted back into the time domain.

Suppose row 4 was larger then others (freq 3), then this would indicate
a strong presence of a 36/3 = 12 month sales cycle.

Anyway, hope this helps a little.

= = =
HTH
Dana DeLouis



MichaelRobert wrote:
I want to analyze 36 months of historical sales figures to see if I can
identify any time-series that will allow me to project them into the future.

My rusty math memory tells me that I can use Fourier Analysis to find out
the underlying frequencies and amplitudes. The Fourier Analysis add-in - plus
what I have read on the web - tells me that the number of data points that I
use must be a power of 2, so my choices are to use 2, 4, 8, 16, or 32 months
of data (I use 32). I have also learned that the frequencies reported by the
Add-in are listed in ascending multiples of 1/(32 months). From this I can
calculate the value of each frequency returned by the Add-in.

What I don't yet know how to do with the output from Fourier Analysis is:
1. How do I interpret the number reported for each frequency? I assume that
each one is a measure of the amplitude of the reported frequency, but I do
not know how to handle the 'real' and 'imaginary' components of the number.
At first blush, I think I would ignore the imaginary, but ...
2. Once I have the frequencies and the amplitudes of each component
waveform, I assume that I select to use only the more significant (higher
amplitude) frequencies. Help on this selection process will be appreciated.
3. To make my projection, how do I make sure that I am applying the
waveforms at the correct part of their cycle. For example, I could start all
of the waveforms at t=0, but that is not necessarily where the cycle should
start.

Overall, it seems that I am looking for the equation for the full waveform
that Fourier Analysis is calculating; so that if I insert the output of the
FA into it, I will get the equation for the projected waveform.

Thanks for your help.

Mike