- #1
emmasaunders12
- 43
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Hi everyone, hopefully someone can help
For an vector AR(1) model of the form
y(t)=Ay(t-1) + et
How does one estimate the variance of the white noise input. I was under the impression that one can simply use the residual of the model fit and estimate the variance from this, when I do a simple simulation in MATLAB however I get very different results
%A small MATLAB
%simulated data
y=[1 2 4 8 16 32 64 128];
%remove mean for yule walker
y=y-repmat(mean(y),1,8);
[ar_coeffs err] = aryule(y,1);
%gives an estimate of the error variance as 1.3985e+003
inity=y(1);
estY(:,1)=inity;
for i=2:8
estY(:,i)=-ar_coeffs(2:end)*estY(i-1);
end
resid=y-estY;
var=sqrt((sum(resid.^2))/8-1);
Now variance in error = 38.3082 very different from before
Can anyone enlighten me, am I calculating the variance in the error correctly?
Thanks
Emma
For an vector AR(1) model of the form
y(t)=Ay(t-1) + et
How does one estimate the variance of the white noise input. I was under the impression that one can simply use the residual of the model fit and estimate the variance from this, when I do a simple simulation in MATLAB however I get very different results
%A small MATLAB
%simulated data
y=[1 2 4 8 16 32 64 128];
%remove mean for yule walker
y=y-repmat(mean(y),1,8);
[ar_coeffs err] = aryule(y,1);
%gives an estimate of the error variance as 1.3985e+003
inity=y(1);
estY(:,1)=inity;
for i=2:8
estY(:,i)=-ar_coeffs(2:end)*estY(i-1);
end
resid=y-estY;
var=sqrt((sum(resid.^2))/8-1);
Now variance in error = 38.3082 very different from before
Can anyone enlighten me, am I calculating the variance in the error correctly?
Thanks
Emma