error message using polynom

Question

Locks 2013-4-25

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/73607-error-message-using-polynom

hi,

I have the following code:

    data16=zeros(size(data12,1),16);
     data16(:,1:12)=data12;
     numberEl=length(data16(:,9));
     numberID=[1:numberEl]';
     data16(:,13)=numberID;
    dates=730755;
      for i= 1:length(dates)
          date=dates(i);
          %msgbox(num2str(date))
          dataDate = data16(data16(:,6) == date,:);
          Ts = 0.22192
          for indexT = 1:length(Ts)
              T = Ts(indexT);
              %msgbox(num2str(T))
              dataT = dataDate(dataDate(:,5) == T,:);
              number=dataT(:,13);
              if length(dataT(:,1))==1
              SlopeSkew(number)=0;
              elseif length(dataT(:,1))==2
              SlopeSkew(number)=0;
              elseif length(dataT(:,1))==3
              SlopeSkew(number)=0;
              elseif length(dataT(:,1))==4
              SlopeSkew(number)=0;
              %nur zum probieren
              else                
              % x is the Strike
              x= dataT(:,2);
              %is the implied volatility
              y=dataT(:,10);
              p = polyfit(x,y,2);
             f = polyval(p,x);
              plot(x,y,'o',x,f,'-')
               xlabel('Strike Price  K');
             ylabel('Implied volatility  \sigma');
              a=p(3);
              b=p(2);
              c=p(1);
              SlopeSkew(number)=b+2*c.*x;
              Slope=SlopeSkew';
              end
          end
      end

for whatever reson the polynom function gives me the following error message:

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

I thought that I have fixed the problem, but unfortunately I havent reallly,

the data on which the code is run is the following:

 1500  1  27.3125  0.22192  730755  0.068116  0.963071  60  0.183247087  0.342050308  247.5717725  60
 1500  2  81.875  0.22192  730755  0.068116  1.038345044  61  0.183247281  -0.642946883  247.5718217  61
 1505  1  24.625  0.22192  730755  0.068116  0.959871429  62  0.178451585  0.323180754  242.1932319  62
 1505  2  85.75  0.22192  730755  0.068116  1.041806194  63  0.185184067  -0.654919572  244.2372928  63
 1515  1  21.5  0.22192  730755  0.068116  0.953535644  64  0.177080297  0.294048585  232.5459004  64
 1520  1  19.875  0.22192  730755  0.068116  0.950399013  65  0.175645711  0.278919192  226.8732368  65
 1525  1  18.5  0.22192  730755  0.068116  0.947282951  66  0.174985304  0.264986129  221.2360078  66
 1530  1  17.125  0.22192  730755  0.068116  0.944187255  67  0.174006888  0.25092381  215.1342839  67
    1550  1  12.125  0.22192  730755  0.068116  0.932004194  68  0.169039366  0.196212196  187.2126905  68
 1575  1  7.625  0.22192  730755  0.068116  0.917210476  69  0.164247859  0.138365666  149.5401411  69

Obviously the original dataset was much larger but I have reduced it to the part which is not working. The dataset consists of more than 3 point and therefore I do not see why polyfit is not working

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Answer 1

Walter Roberson 2013-4-25

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The 4th line, (1505, 0.185184067) is a big difference in trend compared to the other lines. combine with the fact that it is the same x (1505) as the previous value (1505, 0.178451585), and you get a poorly determined polynomial.

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Answer 2

Ahmed A. Selman 2013-4-25

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A polynomial P(x) is said to be (badly conditioned) when a small variances of x leads to large errors of P, causing unstable error estimation, i.e., error doesn't converge between x and x+dx for even small dx. This is also called (ill-conditioned polynomial) in parallel to (ill-conditioned matrix).

So, as the warning message suggests, try including other (and outer) values of x to walk around the anomaly, or use polyfit(x,y,1).

Keep in mind this is a warning, so it might still work fine within your data set, but even if it does, however, do not fully trust it for other values of data.