Fourier Transform in Describing Collected Data
Let me just say before I begin that I am having a hard time grasping the concept of fourier transforms and that I am possibly using the wrong method to model my data.
Currently, I have collected data on the temperature for the first of every year since 1880. It has a slightly increasing slope with some periodic looking oscillations , so I took a fourier transform of the data. Once I had the transform, I took the interesting peaks into account and then did an inverse fourier transform. It is an alright fit to the data, but now how do I use this to predict future temperatures?
This is what I have so far:
The Data -
The Transform -
The Inverse Transform w/ the Data-
Am, I approaching this the right way? I don't just want to do a simple ODE exponential fit. Anyone have any ideas on how to take a trig function, and change the axis to an exponential function, so then I could possibly change the period on it to fit the data with an exponential curve?
Thanks in advance