MATLAB: Estimating a regression model using matlab

model

Dear all,
I have this regression model
g=randn(1000,1);  error=randn(1000,1);
g(2:end)=k1+ k2*(g(1:end-1)-k1) + error(2:end)*k3 ;
k1, k2 are intercept and slope parameters respectively and k3 is the standard deviation
Also the following restrictions must be satisfied: |k2|<1 and k3>0.
Is there a way to estimate such a model, given that 'error' and 'g' are known?
Thanks in advance

Best Answer

g=randn(1000,1);  error=randn(1000,1);
% Model: g(2:end)=k1+ k2*(g(1:end-1)-k1) + error(2:end)*k3 ;
y = g(2:end);
x1 = g(1:end-1);
x2 = error(2:end);
b = regress(y,[ones(size(x1)), x1, x2]);
k3 = b(3);
k2 = b(2);
k1 = b(1) / (1 - k2);
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