MATLAB: Extending a sine regression to forecast

plottingregressionsine wave

I would like to know the best way to extend my newly constructed sine wave fit to my data into the future another 20 days.
I have constructed a regression of 151 different sine waves to a data set across 501 days at a sample of 1 day.
y = Score(:);
n = 501;
t = (1:501)';
games = 1:501;
data(1:151) = struct('X',NaN(501,3),'bhat',NaN(3,1),'yhat',NaN);
for ii = 1:151
tmp = 2*pi*(sincos(ii))*t;
data(ii).X = rand(501,3);
data(ii).X(:,2) = cos(tmp)';
data(ii).X(:,3) = sin(tmp)';
data(ii).bhat = data(ii).X\y;
data(ii).yhat = data(ii).bhat(1)+data(ii).bhat(2)*cos(tmp)+data(ii).bhat(3)*sin(tmp);
end
After that, I have combined or superposed all of the 151 different sin waves into one sine wave
sum(horzcat(data.yhat),2) ./ 151
So ideally, I would like the combined sine wave to extend to 521 days (for a 20 day forecast) while my data set remains to be only 501 days long and plot them both. Help much appreciated!

Best Answer

   n = (0:500)';
   % create some fake data
   x = 1.5*cos(2*pi*(1/4)*n)+randn(size(n));
   X = ones(501,3);
   X(:,2) = cos(2*pi*(1/4)*n);
   X(:,3) = sin(2*pi*(1/4)*n);
   beta = X\x;
   nn = 0:520;
   xhat = beta(1)+beta(2)*cos(2*pi*(1/4)*n)+beta(3)*sin(2*pi*(1/4)*n);
    xhatpred = beta(1)+beta(2)*cos(2*pi*(1/4)*(501:520)')+beta(3)*sin(2*pi*(1/4)*(501:520)');
    xhat = [xhat; xhatpred];
    plot(n,x,'k');
    hold on;
    plot(1:521,xhat,'r');
    set(gca,'xlim',[490 512]);
    legend('original data','prediction for next 21 days');
    grid on;
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