Hi, I want to ask is there any proper way to decompose a complex function into multiple simples ones (not Fourier Series).
For example, I may manually code the following curve as f(x)=ax+bsin(x)+c, because I observe there is a periodic component and a linear component in the plotted curve. However, if the empirical data are not so apparent, is there any approach to decompose the function into varied components? Is there any study (better in urban and regional planning area) that did so?
Why not a Fourier Series? What make that unsuitable for your data? And you don't mention what the observations of the real world are - there is all sorts of noise that can look like a regular pattern.
Michael John Patrick
Hi Michael, thanks for the answer. But Fourier series does not apply to my goal. I want to decompose the curve into explainable components. For the curve that I displayed, the periodic version may be explained as the seasonable periodic of sale amounts and the linear component may be explained as the continuous increments in production.
I am looking for a general answer because I still do not get the data yet..
Haiyan Hao
Hi,
Be extremely careful when you do "curve-fitting" with data and then make claims. All sorts of things can affect that "fitting", especially when you deal with dynamic nonlinearities, where available statistical tests are weak. Curve-fitting can't be a good substitute for a logical and sound theory. That is what you need first.
You mentioned in your previous answer "seasonality" and "production increments". That is the supply side, to which there's a demand side also (to seasonality"). You need a good nonlinear (deterministic or stochastic) dynamic theory of spatial markets first; then you look to see what the empirical evidence says about it. Hidden variables may play a significant role in the search, and so is "random" noise.
At the end, always keep in mind what Mark Twain once said: there're three types of lies: "simple lies, damn lies and statistics".
BTW, Google-search "nonlinear dynamics and statistical tests", you may find some references of interest.
Good luck!
If you take data from an integer number of periods, you can fit with y=asinx+c, then subtract the calculated values from the original data and fit the sinx.
But if you still need it, I could add this function in my software:
www.lerenisplezant.be/fitting.htm