Creating a number of matrices/vectors based on a number - matlab

Question

I have a simple for loop that is used to simulated data,
for t=2:T;
Y_star(t,1,b)=[Y_star(t-1,1,b) X_1_star(t-1,1,b) X_2_star(t-1,1,b) 1]*beta(:,i)+w(t-1)*e(t-1,i);
X_1_star(t,1,b)=Theta(1,1)+Phi(1,:,1)*[X_1_star(t-1,1,b) ; X_2_star(t-1,1,b)]+w(t-1)*v(t-1,1,i);
X_2_star(t,1,b)=Theta(2,1)+Phi(2,:,1)*[X_1_star(t-1,1,b) ; X_2_star(t-1,1,b)]+w(t-1)*v(t-1,2,i);
end;
The issue I am having is this is fine when I have two X variables, however, I would like to write the code so that I can increase the number of variables to change each time, 4 say.
In this case, I would need X_1_star, X_2_star, X_3_star and X_4_star.
I can handle the Phi and Theta coefficients, as well as the w and v and e however I am struggling with creating the matrices for X's.
Any ideas would be greatly, I have tried storing the matrices within cells but I struggled to get this working.
Following the commnets, here is a simple example
%% Simple example
%-------------------------------------------------------------------------%
Phi = [0.9954 0.0195;
0.0012 0.9567];
Theta= [0.007;0.051];
beta = [0.06;-0.10;1.66;-0.88];
N = 1;
e = rand(370,1);
v = randn(370,2);
t = 371;
T = 371;
yy = rand(370,1);
X_1 = rand(370,1);
X_2 = rand(370,1);
B=50;
Y_star=zeros(T,N,B);
X_1_star=zeros(T,N,B);
X_2_star=zeros(T,N,B);
for b=1:B;
Y_star(1,:,b)=yy(1,:);
X_1_star(1,:,b)=X_1(1,:);
X_2_star(1,:,b)=X_2(1,:);
w=randn(T-1,1);
for t=2:T;
for i=1:N;
Y_star(t,i,b)=[Y_star(t-1,i,b) X_1_star(t-1,i,b) ...
X_2_star(t-1,i,b) 1]*beta(:,i)+w(t-1)*e(t-1,i);
X_1_star(t,i,b)=Theta(1,i)+Phi(1,:,i)*[X_1_star(t-1,i,b) ; ...
X_2_star(t-1,i,b)]+w(t-1)*v(t-1,1,i);
X_2_star(t,i,b)=Theta(2,i)+Phi(2,:,i)*[X_1_star(t-1,i,b) ; ...
X_2_star(t-1,i,b)]+w(t-1)*v(t-1,2,i);
end;
end;
disp(b);
end;
I ideally this to do the same thing but not be dependent upon writing X_1 and X_2, as I would like to increase this sometimes to a larger number.
I have tried reshaping as the commnets suggested but not sure how this would or could work in this example.

Answer 1

I think this problem is simply one of matrix algebra.
With the X variables it appears like you are simulating a small VAR model.
Instead of dynamic matrices as the answer above, I think it would make more sense to simulating the x data as a larger matrix instead of vectors.
Here is a simple example,
First, I show you a two variable case, both in the method you use, and by jointly simulating the data...
Then I show with a 3 variable case how to extend this...
All you have to do is take the size of the beta matrix (or alpha) as I guessing these are determined before the matrix...
%Simulating a small VAR model
%% 2 - variable case
rng('default')
b = [0.4 0.5;0.6 0.07];
a = [0.1 0.2];
v=randn(100,2);
x1 = zeros(100,1);
x2 = zeros(100,1);
xm=zeros(100,2);
T=100;
for t=2:T;
x1(t)=a(1)+b(1,:)*[x1(t-1) ; x2(t-1)]+v(t-1,1);
x2(t)=a(2)+b(2,:)*[x1(t-1) ; x2(t-1)]+v(t-1,2);
end;
for t=2:T;
xm(t,:)=a+xm(t-1,:)*b'+v(t-1,:)
end;
[xm x1 x2]
%% 3 - variable case
rng('default')
b = [0.4 0.5 0.1;0.6 0.07 0.1; 0.3 0.4 0.7];
a = [0.1 0.2 0.3];
v=randn(100,size(b,2));
xm=zeros(100,size(b,2));
for t=2:T;
xm(t,:)=a+xm(t-1,:)*b'+v(t-1,:)
end;

Answer 2

I generally find structure arrays more useful for this kind of dynamic indexing (where you don't know how many you'll have of X_1_star, X_2_star...)
I didn't try to reproduce the whole example, but it might go something like this if you're trying to get up to X_4_star:
...
nX=4;
for i=1:N
Y_star(t,i,b)=[Y_star(t-1,i,b) X_1_star(t-1,i,b) ...
X_2_star(t-1,i,b) 1]*beta(:,i)+w(t-1)*e(t-1,i);
for n=1:nX
X(n).star(t,i,b)=...
end
end