(* Using linear or non-linear list square fit for USD/EUR rates *)

(* To run on command line:  math -run "<<least.square.FOREX.math" *)
(* The above line assumes that math kernel is aliased to "math" *)
(* For example, on my machine alias
math='/Applications/Mathematica.app/Contents/MacOS/MathKernel' *)
(* or simply use << least.square.FOREX.math once math kernel is already running
*)

<<JavaGraphics`


a = 2.0; b= 1150.0; (* define the interpolating interval, in days *) 


(* read in real exchange rate data *)

data = ReadList["USD.EUR.data", {Number, Number}]



plotdata = ListPlot[data, PlotLabel -> "Data points", Prolog-> AbsolutePointSize
[1] ]



(* Do linear least square fit to a 3rd degree polynomial*)



fit = Fit[data, {1, x, x^2, x^3}, x]
 


fit2 = NonlinearModelFit[data, K0 + 0.1*Sin[x/30 +K2 ],  {K0, K2}, x ] 
 
(* having too many fitting constants may not be a good idea *) 
(*
fit2 = NonlinearModelFit[data, K0 + K3*Sin[x/K4 +K2 ],  {K0, K2, K3, K4}, x ] 
*) 



(* Perhaps one can combine the two? *) 

Print[]
Print[fit]
Print[]
Print[Normal[fit2]]

plotfit = Plot[fit, {x, a, b}, PlotStyle->{Hue[0.5], Thickness[0.005]}, PlotLabel-> "Least Square", DisplayFunction -> Identity ]



 
plotfit2 = Plot[fit2[x], {x, a, b}, PlotStyle->{Hue[0.8], Thickness[0.005]}, PlotLabel-> "Least Square", DisplayFunction -> Identity ]




(* Show only data and the fit *)

Show[plotdata, plotfit, PlotLabel -> FontForm["circles - data, blue - Least S. Fit ", {"Courier", 15}], Prolog-> AbsolutePointSize[2], DisplayFunction -> $DisplayFunction ]


Show[plotdata, plotfit2, PlotLabel -> FontForm["circles - data, blue - Least S. Fit ", {"Courier", 15}], Prolog-> AbsolutePointSize[2], DisplayFunction -> $DisplayFunction ]


Clear[data]

Clear[fit]

Clear[fit2]