error message using polyfit (nonlinear regression)

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Locks
Locks 2013-4-21
hi,
I get the following error meesage using the polyfit function:
Warning: Polynomial is badly conditioned. Add points with distinct X
values, reduce the degree of the polynomial, or try centering
and scaling as described in HELP POLYFIT.
Has anybody see that before and has an idea what I need to do? I tried it with the help function, but I didn't understand what excatly could be false
the code I am using if the following, in case it helps:
if length(dataT(:,1))==1
SlopeSkew(number)=0;
elseif length(dataT(:,1))==2
SlopeSkew(number)=0;
else
% x is the Strike
x= dataT(:,2);
%is the implied volatility
y=dataT(:,10);
p = polyfit(x,y,2);
f = polyval(p,x);
thanks!
a=p(3);
b=p(2);
c=p(1);
SlopeSkew(number)=b+2*c.*x;
Slope=SlopeSkew';

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采纳的回答

Image Analyst
Image Analyst 2013-4-21
So what is the length of x and y, and do you have any repeated x values?
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Locks
Locks 2013-4-21
yes, I have repeated x and y values
the full code looks like this:
for putCall =1:2
dataPutCall = data16(data16(:,3)==putCall,:);
dates=unique(dataPutCall(:,6));
for i=1:length(dates)
date=dates(i);
dataDate = dataPutCall(dataPutCall(:,6) == date,:);
Ts = unique(dataDate(:,5));
for indexT = 1:length(Ts)
T = Ts(indexT);
dataT = dataDate(dataDate(:,5) == T,:);
number=dataT(:,13);
if length(dataT(:,1))==1
SlopeSkew(number)=0;
elseif length(dataT(:,1))==2
SlopeSkew(number)=0;
else
% x is the Strike
x= dataT(:,2);
%is the implied volatility
y=dataT(:,10);
p = polyfit(x,y,2);
f = polyval(p,x);
a=p(3);
b=p(2);
c=p(1);
SlopeSkew(number)=b+2*c.*x;
Slope=SlopeSkew';
end
end
end
end
so there is not a specific lenght of x, because x is for each iteration different and from the error message I can't see, which x is causing a problem.
do you know what the error message stands for?
Image Analyst
Image Analyst 2013-4-21
If you have two Y values for the same x value, then it doesn't like that and will complain. All your x values have to be unique. You can use
uniqueX = unique(x)
and see if length(uniqueX) is the same length as length(x). If they're the same then there are no repeats. If unique() returns a shorter vector, then at least one x value is repeated and you need to decide how to handle that. You might be able to just add a very small amount to one of the x's, like 0.000001, just to make sure they are not the same anymore.

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更多回答（2 个）

Tom Lane
Tom Lane 2013-4-22
There was a time when this function issued an error asking you not to have repeated X values. But the new error message is more accurate. You don't need unique X values. It's just that repeated X values won't allow you to estimate higher-order polynomials. So for instance:
x = [1;2;3;3;4];
y = (1:5)';
polyfit(x,y,2)
polyfit(x,y,4)
The first call to polyfit works. The second would work if we had 5 points with distinct X values, but it doesn't work here because the 4 distinct X values allow polynomials only up to an exponent of 3.
In your example of fitting up to power 2, it seems like you either don't have 3 distinct points, or you have very ill-conditioned data.
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Locks
Locks 2013-4-22
I tried it first for a smaller sample and there I had no issues doing that, but for the larger sample the error message appeared. This part of the code here:
if length(dataT(:,1))==1
SlopeSkew(number)=0;
elseif length(dataT(:,1))==2
SlopeSkew(number)=0;
else
should make sure that for the computation, there should be always at least 3 datapoints, so do you have any idea what else it could be
Tom Lane
Tom Lane 2013-4-23
I don't know exactly. Of the following three, the first one works. The second does not because there are only two distinct x values. The third does not because it is very ill-conditioned.
polyfit([0;1;2],[10;20;30],2);
polyfit([0;1;1],[10;20;30],2);
polyfit([0;eps;1],[10;20;30],2);
I don't know what the issue is in your case. Try to boil this down to a specific call to polyfit, then examine the x and y values in that call and see how they look.

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Jan
Jan 2013-4-23
Instead of repeated values, did you test the condition of the problem already? The docs suggest to use
[p, S, mu] = polyfit(x,y,n)
for a proper scaling. The matrix for the least-squares fit is ill-conditioned, when the values of x have a wide range and are far away from zero. Therefore the scaling does:
xx = (x - mean(x)) / std(x)
to get all data near to zero. The conversion back to the original values in POLIVAL is trivial.
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Locks
Locks 2013-4-23
sorry but I am not sure what excatly I need to change. I looked at the docs youre mentionning http://www.mathworks.ch/ch/help/matlab/ref/polyfit.html before startig with the code and p = polyfit(x,y,n) should work as well or am I mistaken? a bit strage is, that everything is working fine for different datasets with each 8000 rows, but for a dataset that consists of 30'000 rows it's not worwing. I am tring to find out at which point the problem is but it would be really heplful to get a hint what I need to focus at.
Locks
Locks 2013-4-24
I have found the error, thanks for the support!

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