Function to find ar coefficients using Least squres

Hi,

Can someone help me write a FUNCTION to estimate AR(p) coefficients using LEAST SQUARES?

Thanks

[Azzi Abdelmalek]

Give an example

[dav]

I am new to writing functions. If I have data set called y, I need to write a function to get the coefficients after fitting an AR(15) model to y

Thanks

[Azzi Abdelmalek]

What is AR(15)?

[dav]

Auto Regressive model of order 15.

Thanks

Answer 1

[Azzi Abdelmalek]

Construct your measure matrix Fi,

yourcoeff=FI\y

Example

% y(n)=a1 y(n-1)+a2 y(n-2)+ a3 y(n-3)  your system
% if y=[1 2 3 4 5 6  7 8 9 10]
y= [4;5;6;7] % Using 4 samples     
FI=[3 2 1    % measure matrix    
  4 3 2            
  5 4 3            
  6 5 4]
% coeff=[a1;a2;a3]  coefficients to find

coeff=FI\y

[dav]

thanks. this is nice. Can u give an example to estimate arma parameter also but with the condition that parameter should be positive.

[Azzi Abdelmalek]

Give an example of your model.

[dav]

Here is the code that generates some data. I need to fit an arma model to yt1 and get the coef. estimates with that condition that paremeter estimates are positive.

lc; clear;

m=160; n=10;

ftyPI=zeros(10,100); fsigPI=zeros(10,100);

Lbyth=zeros(10,100); Lbsigh=zeros(10,100);

mccounty =zeros(10,100); mccountsig =zeros(10,100);

for mc= 1:100

a0 = 0.05; a1 = 0.1; b1 = 0.85;

epsi=zeros(3000,1); simsig=zeros(3000,1);

for i = 1:3000 if (i==1) simsig(i) = a0 ; s=(simsig(i))^0.5; epsi(i) = normrnd(0,1) * s; else simsig(i) = a0+ a1*(epsi(i-1))^2+ b1*simsig(i-1); s=(simsig(i))^0.5; epsi(i) = normrnd(0,1) * s; end end

yt1=epsi.^2;