%Example of the one-step-ahead forecast%%Predicts the difference between decadal%average sunspot number, which is mostly a sunspot number derived from tree ring radiocarbon content by Solanki, S. K., Usoskin, I. G., Kromer, B., Sch?ssler, M. and Beer, J.: 2004, Nature, 431, 1084., continued by group sunspot number by Hoyt, D. V. and Schatten, K. H.: 1996, Solar Phys., 165, 181.  %Volobuev, D.M., Makarenko, N.G. FORECAST OF THE DECADAL AVERAGE SUNSPOT NUMBER. Submitted to Solar Physics,2007.close allclear allload composite.txtsc=composite(:,2);tsc=composite(:,1);sigma_l=std(diff(sc(1:end-102))); %sigma for the learn set (to normalize prediction error)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%for j=1:100,  Y=diff(sc)/sigma_l;%difference removes trend and systematic error in data  figure;subplot(211);plot(tsc,sc);ylabel('Composite')  subplot(212); plot(tsc(2:end),Y);ylabel('Differences')  w=3;%dimension  Ft=[];Fe=[]; for k=103:-1:0,      n=0;   y0=fs01(Y(1:end-k),w);         yy0=((([Y(1:end-k);y0])*sigma_l));%  try  yyt=((([Y(1:end-k+1)])*sigma_l));%catch    disp('last point')    yyt=0;  endFt=[Ft yyt(end)];%Fe=[Fe yy0(end)];end%fordisp('Average normalized prediction error')ET=std(Ft(1:end-1)-Fe(1:end-1))/sigma_lfigure;plot(tsc(end-102:end),Ft(1:end-1),'-k.',[tsc(end-102:end); 2015],Fe,'-bo')ylabel('Difference');legend('Actual','Predicted')xlabel('Years')disp('correlation in differences')Cd=corrcoef(Ft(1:end-1),Fe(1:end-1))figure;plot(tsc(end-102:end),sc(end-102:end),'-k.',[tsc(end-102:end); 2015],sc(end-103:end)+Fe(1:end)','-bo')ylabel('Sunspot Number');legend('Actual','Predicted')xlabel('Years')disp('correlation in values')Cv=corrcoef(sc(end-102:end),sc(end-103:end-1)+Fe(1:end-1)')