Adding a extra variable to a model

 Hi guys,

    I have the following model:

        function [R_e, dp] = VAR_CRSP(M,T,r_f);

        epsilon = zeros(M,T,2);
        r = zeros(M,T);
        dp= zeros(M,T);

        for m=1:M
            epsilon(m,:,:,: ) = mvnrnd([0;0;0], [0.0012,-0.001;-0.001,0.0027],T)
        end

        for m=1:M
           dp0=-3.461;
           r(m,1) = 0.1161+0.060*dp0 + epsilon(m,1,1);
           dp(m,1)=-0.052+0.9702*dp0 + epsilon(m,1,2);

           for i = 1:T-1
               r(m,i+1) = 0.1161+0.060*dp(m,i) + epsilon(m,i+1,1);
               dp(m,i+1) = -0.052+0.9702*dp(m,i) + epsilon(m,i+1,2);

           end
        end

        end

Now i want to add a extra variable to the model. I did it as simply as this, but I don't think it's the correct way:

    function [R_e, dp] = VAR_CRSP(M,T,r_f);

    epsilon = zeros(M,T,3);
    r = zeros(M,T);
    dp= zeros(M,T);
    mom=zeros(M,T);

    for m=1:M
        epsilon(m,:,:,: ) = mvnrnd([0;0;0], [0.0012,-0.001,0.0001;-0.001,0.0027,0.001;0.001,0.001,0.001],T)
    end

    for m=1:M
       dp0=-3.461;
       r(m,1) = 0.1161+0.060*dp0 + epsilon(m,1,1);
       dp(m,1)=-0.052+0.9702*dp0 + epsilon(m,1,2);
       mom(m,1)=-0.344+0.966*dp0 + epsilon(m,1,3);

       for i = 1:T-1
           r(m,i+1) = 0.1161+0.060*dp(m,i) + epsilon(m,i+1,1);
           dp(m,i+1) = -0.052+0.9702*dp(m,i) + epsilon(m,i+1,2);
           mom(m,i+1) = -0.533+0.931*dp(m,i) + epsilon(m,i+1,3); 
       end
    end

    R_e = r_f*exp(r)-r_f;

    end

My first error is:

    Error using mvnrnd (line 110)
    SIGMA must be a symmetric positive semi-definite matrix.

    Error in VAR_CRSP (line 9)
        epsilon(m,:,:,:) = mvnrnd([0;0;0], [0.0012,-0.001,0.0001;-0.001,0.0027,0.001;0.001,0.001,0.001],T)

So anyone knows how to resolve this?

Many thanks in advance!!

Answer 1

[Matt J]

    >> SIGMA=[0.0012,-0.001,0.0001;-0.001,0.0027,0.001;0.001,0.001,0.001];
    >> eig(SIGMA)

    ans =

       -0.0001
        0.0016
        0.0034

As you can see, your SIGMA matrix has a negative eigenvalue, and is therefore not positive semi-definite.

Answer 2

[Kevin van Berkel]

Thanks Matt! Solved it.