trigonemetric function fitting using matrice in matlab

2020 4 28
1 个回答
更新时间：2020 4 29
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0 个投票

hi
please explain me these line of codes from the matlab documentation:
Simulating Electricity Prices with Mean-Reversion and Jump-Diffusion
why do we have to put t in matrice function when we have f(t)= s1*sin(2.pi.t)+s2*cos(2.pi.t)+s3*sin(4.pi.t)+s4*cos(4.pi.t)+s5 ?
% Calibrate parameters for the seasonality model
seasonMatrix = @(t) [sin(2.*pi.*t) cos(2.*pi.*t) sin(4.*pi.*t) ...
cos(4.*pi.*t) t ones(size(t, 1), 1)];
C = seasonMatrix(PriceTimes);
seasonParam = C\logPrices;

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darova
darova 2020-4-28
Your equation is
f(t)= s1*sin(2.pi.t)+s2*cos(2.pi.t)+s3*sin(4.pi.t)+s4*cos(4.pi.t)+s5 ?
You have 5 uknowns s1 - s5
To calculate them you need 5 equations:
Where a1,b1,c1,d1,e1 == [cos(2.*pi.*t) sin(4.*pi.*t) cos(4.*pi.*t) 1];
karim bio gassi
karim bio gassi 2020-4-28
Thanks for your reply, I was expecting the same matrice, but in the help documentation of the problem resolution Matlab add the sixth variable t, thing that I didnot understand.
kindly find Simulating Electricity Prices with Mean-Reversion and Jump-Diffusion in help documentation to look at the code deeply.

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回答（1 个）

karim bio gassi
karim bio gassi 2020-4-28

0 个投票

ok thanks
what about this line of code
seasonParam = C\logPrices;
I used inv(X'X)X'Y to find the parameters of the fitting function. can you please explain me what they mean?

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karim bio gassi
karim bio gassi 2020-4-29
let's consider f the function to fit with the set of data x={x1,x2, x3....xn} and y={y1, y2, y3.... yn} and f(x)=a0+bx
fiting f with (x1,y1), (x2, y2).....(xn,yn) lead to
f(x1)=a0+bx1=y1
f(x2)=a0+bx2=y2
f(xn)=a0+bxn=yn
hence, X*A=Y with A the parameter matrice of the function f and is find by A=inv(X'X)X'Y, with X' the transpose of X
darova
darova 2020-4-29
A is just . No transposing needed
darova
darova 2020-4-29
where X and Y for this case:
X = [1 x1
1 x2];
Y = [y1; y2]

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