I'm recently dealing a set of market data where it had the following properties:
it does not blow up but has unique signature of removable singularities/discounity, the one that usually appear in Laurent series of some order $p$.
It does not have any obvious period oscillation except a period variation when plotting a 23 week's variance.(It's possible due to the market policy, and is thus understandable.)
The data is in the range of 2000-6000 and has around 1000 data points.(Enough for some simple fitting, but not enough for a deep mining.)
My question was that:
What's your suggestion for techniques to fit such data?
I thought about using dynamic system/differential system for the data set, i.e. ($X'=AX$), because a 1000 data points gave us an advantage in fitting such set of data by calculating matrix $A$, and by using a range of data to calculate matrix $A$ by row, we could obtain a well calculated $A$ or a function $A(t)$, and it's much easier than fitting a actual function.
I also thought about transferring the data to "frequence" by FFT but I'm not sure if that's going to be any helpful, as it doesn't have any obvious period at all. By fitting the data, we were simply fit a set of data without any meaning. What's your suggestion?
Similar, I tried to fit the function with laurent series, but the function blowed up or converged to 0 too quickly, and it didn't help much even if I transfering the t by using log function or by setting it really small. I also thought about using laurent series and furier series together but it's going to be too many columns in $X$. What's your suggestion for a sets of fitting functions?
An other question was that, in order to let the fitting function better describe the near by data in order to predict the results, I need to let the fitting function more sensitive to "now". The way I did was to weight the $Y$ data by multiply a linear sequence form $1$ to $1.25$. What's other methods available for such process?
I also thought about using neuron network or hyper graph, but the available data set is too small(in a level of 1000 data points), but still, is there any way to accommodate this request?
In general, what's your suggestion for fitting such set of data?