Estimating a regression model using matlab

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

Answer 1

[Jeff Miller]

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);

[ektor]

This approach does not satisfy the restrictions

[Jeff Miller]

Sorry, I missed the restrictions.

Maybe with fminsearch. The error function would look something like this:

function sse = myErrFunc(x)  % x is a vector of 3 reals
% Convert real x's to k's satisfying constraints
k1 = x(1);
k2 = x(2)^2/(1+x(2)^2);  % abs(k2)<1
if x(2)<0
    k2 = -k2;
end
k3 = x(3)^2;   % k3 must be positive
global y, x, error  % trim these in advance so they only contain 1:end-1 or 2:end
predicted = k1 + k2*(g-k1) + error*k3; 
sse = sum((y-predicted).^2);
end