Polynomial fit and Fourier transform plot

Question

I'm pretty new to Mathematica so excuse me for obvious questions. I have a dataset, second column contains invoice amount and the first column contains days passed between each invoice date starting at 0 (time data but not uniform spaced).

I'm trying to fit a polynomial function that best represents this data, apply a Fourier transform, and then plot the Fourier transform. I'm mainly aiming to catch weird invoice frequencies using the Fourier transform.

How would one go about this?

Any help would be appreciated.

Here is the full data: Full Data

I used this code from one of the users here to fit a simple sin curve

len = Subtract @@ data[[{-1, 1}, 1]];
funcfunc = Fit[data, Table[Sin[(π n)/len x], {n, 1, 50}], x];
Show[
  ListPlot[data], 
  Plot[funcfunc, {x, 0, len}, PlotStyle -> {{Thick, Red}}]]`

Would an $n$th degree polynomial fit be better?

Assuming I go ahead with this code and the sin series fit how would I plot the Fourier transform of the fit?

Answer 1

Here is something for you to experiment with

data = Import["C:\\Users\\zhk\\Desktop\\data.txt", "Data"];

NF = NonlinearModelFit[data, 
   a*x^7 + b*x^4 + c*x^3 + d*x^2 + e*x + f, {a, b, c, d, e, f, g}, x];

Show[ListPlot[data], 
 Plot[NF[x], {x, data[[1, 1]], data[[-1, 1]]}, PlotStyle -> Red]]

FT = FourierTransform[NF[x], x, \[Omega]]

Plot[Evaluate@Abs@FT, {\[Omega], -10, 10}, PlotRange -> All]

The FourierTransform plot doesn't make any sense to me but this is a sample exactly doing what you asked for.

Answer 2

Here are some thoughts on your data.

data = Import["semerkand.xlsx"][[1]];
data[[1]]

{"DAYS BETWEEN", "AMOUNT"}

Now let's plot the DAYS BETWEEN and the AMOUNT against point number

ListLinePlot[data[[2 ;; -1, 1]]]
ListLinePlot[data[[2 ;; -1, 2]]]

So I guess you have sorted your data so that small DAYS BETWEEN are at the start of the data. What appears to happen is that you get a small value invoice followed by a large value invoice followed by a small value invoice...

What are you actually trying to do? There is no point in trying to look at Fourier because you only have 2 points in a cycle. Do you wish to put a mean line through the data to even out the small, large, small fluctuation?