Hi

I'm doing the State Space Form with 3 independent variables. Obviously there are 1 measurement equation and 3 transition equations, it's hard to find example of using CHOLSOL over the internet.

Measurement equation:

Rs(t) = b0 + Beta(t)*X(t)+ Alpha(t)*Y(t) +Gamma(t)*Z(t) + e(t)

Transition equation:

1. Apha(t)= Alpha(t-1)+u(t)

2. Beta(t)= Beta(t-1)+w(t)

3. Gamma(t)= Gamma(t-1)+v(t)

For 2 variables I used covariance matrix or Q as sqrt(sma2*sma3); sma2, sma3 are sigma of u(t) and w(t) respectively.

Can anyone please help to figure out how can I use Cholesky Decomposition CHOLSOL command to find the covariance of 3 independent variables.

Thanks!

## 1 Answer

I am not sure specifically about your State Space problem. Below is an example of using `cholsol` that should be helpful if your questions are about how to use `cholsol` correctly.

y = { -2.24, 13.57, 17.81, 8.26, 7.50 }; //Symmetric Postive-Definite matrix X = { 7 6 -12 1 3, 6 36 7 23 0, -12 7 34 9 0, 1 23 9 17 -5, 3 0 0 -5 15 }; //Compute Cholesky decomposition C = chol(X); //Solve system of linear equations with 'cholsol' b_hat_1 = cholsol(y, C); //Solve system of linear equations using //the 'normal equation' b_hat_2 = invpd(X'X)*X'y; //Print both parameter estimates format /rd 10,4; print " b_hat_1 : b_hat_2"; print b_hat_1~b_hat_2;