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
0
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;
Your Answer
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;