ECONOMETRIC METHODS II TA session 1 MATLAB Intro ...

ECONOMETRIC METHODS II TA Session 1
3 Introducing the model in MATLAB
In this section we simulate data using the system (2:1). We set matrices Ai, i = 1; : : : ; p
such that the VAR(p) is stationary.
3.1 Data simulation
We set K = 4, p = 2 and the number of observations T = 100.
p=4; % Lag-order
T=100; % Observations
K=4; % Variables;
Then, we set the matrix u such that it is positive de…nite:
scale=2*rand(K,1)+1e-30;
Sigma_U=0.5*rand(K,K)+diag(scale);
Sigma_U=Sigma_U’*Sigma_U;
if all(eig((Sigma_U+Sigma_U’)/2)) >= 0
disp(’Sigma_U is positive definite’)
else
error(’Sigma_U must be positive definite’)
end
And we set lag matrices Ai (K K) for each i = 1; : : : ; p in a 3-dimensional vector:
Alag=zeros(K,K,p);
lambda=2.5;
for k=1:p Alag(:,:,k)=(lambda^(-k))*rand(K,K)-((2*lambda)^(-k))*ones(K,K);
end
With all these ingredients, we procced to simulate T = 100 observations of the process
(2:1) assuming ut N (0; u) and p initial conditions Y p+1; : : : ; Y 1; Y0 that come from
the same distribution. Besides, the intercept v is a vector of ones:
Ylag=zeros(K,p);
for k=1:p
Ylag(:,k)=mvnrnd(zeros(K,1),Sigma_U)’;
end
Y=Ylag;
v=ones(K,1);
for i=1:T
Fernando Pérez Forero 4