trigonemetric function fitting using matrice in matlab

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;

[darova]

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]

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.

[darova]

I think it's a mistake

Answer 1

[karim bio gassi]

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?

[darova]

Please explain what is X Y

[karim bio gassi]

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]

A is just . No transposing needed

[darova]

where X and Y for this case:

X = [1 x1
    1 x2];
Y = [y1; y2]