Extending a sine regression to forecast
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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!
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채택된 답변
Wayne King
2012년 5월 6일
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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Wayne King
2012년 5월 6일
I would not expect them to agree exactly. You have to keep in mind that the regression model will not fit the data exactly. The regression model parameters minimize the overall sum of squares of the residuals.
추가 답변 (1개)
Wayne King
2012년 5월 6일
Once you have the parameters, which are the amplitudes of the cosines and sines, then you can easily extend your model to make predictions by simply increasing the length of the time vector. Of course how far into the future you can make reasonable predictions is a tricky question.
n = (0:500)';
% create some fake data
x = 1.5*cos(2*pi*(1/4)*n-pi/4)+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)*nn)+beta(3)*sin(2*pi*(1/4)*nn);
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