My aim is to best fit sin waves to a dataset. I am using a data set with 501 days of data with a sample rate of 1 day.
After doing a spectral analysis on the data set (using a separate program) the following cycles have been identified:
31.19552 day cycle 5.87064 day cycle 8.00192 day cycle
Previously on this board I received help on how to code a similar task with a cycle of 3.5678 days.:
y = data(:);
X = ones(501,3);
n = 0:500;
X(:,2) = cos(2*pi*0.2794*n)';
X(:,3) = sin(2*pi*0.2794*n)';
betahat = X\y;
Fit is
yhat = betahat(1)+betahat(2)*cos(2*pi*0.2794*n)+betahat(3)*sin(2*pi*0.2794*n);
My question is: how do I calculate what I am supposed to multiply pi with for both the sin and cosine equations used to complete the regression. In the above example a 3.5678 day cycle has .2794 used in the above equations.
I only partially understand this to be because 140/501 creates the most accurate number = .2794. However a simpler calculation of 1/3.5678 or .2803 could be used without any major significance to the outcome.
But what should I do for the 31.19552 day cycle 5.87064 day cycle 8.00192 day cycle?? is there some easy calculation process that I don't know about?
I'm a beginner...any code or insights would be most helpful! MAJOR props to Wayne for his on going help with this!
