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y=1:4738;

lag1=y(6:end-1);

lag2=y(5:end-2);

M = [lag1, lag2,ones(size(y))];

b = M\y

John D'Errico
on 1 Apr 2019

Edited: John D'Errico
on 1 Apr 2019

The problem is, we do not see your data. Only you can. However the one thing that is painfully obvious is that your model is linear in the parameters. So the starting values are irrelevant.

This means that nothing in the universe will make your model fit the data better, because it is essentially the wrong model. (A linear model, which this is, has a unique optimal solution, regardless if you use a nonlinear solver or a linear one.)

How might we help you better? The only way to do this is to have your data. At the very least, it would be necessary to see it. Then we could know if some variation of the model you have chosen might fit better, or if that is not possible at all. So, if you want better help, you need to help us to help you.

John D'Errico
on 2 Apr 2019

I looked at your data. Your model is missing an important point, thatis, it has no constant term in it. Think of it as a DC bias. Using the data in the data1 array, for example, I can build the model as simply as:

M = [f1(pi/91,x(:,1)), f2(pi/91,x(:,1)), f2(pi/182,x(:,1)), x(:,2)];

b = M\Y

b =

78.886

23.973

24.334

38.694

There is no need to use fitnlm at all. Now, lets see what we just did.

plot(Y,'b.')

hold on

plot(M*b,'ro')

Essentially, your model has an oscillatory terms in it, but nothing that can account for a constant offset.

So, now add a constant term to the model.

M = [f1(pi/91,x(:,1)), f2(pi/91,x(:,1)), f2(pi/182,x(:,1)), x(:,2),ones(size(Y))];

b = M\Y

b =

75.29

11.665

11.694

36.762

1810.5

Now, redo the plot. Here, I've just plotted the first 400 points in the data set.

As you can see, it has the essential nature of your data, but your data is far more noisy than your model will ever account for. You can't expect much better than that. Just wanting a great fit is not sufficient. Good (i.e., low noise) data is important too.

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