How to create time series sum of matrices using loop

I'm very much a beginner when it comes to matlab and have been having issues trying to write a loop for the sum of matrices. I'm trying to estimate x_{t+j} = c [I + B + ..B^j], where c is a 12x1 matrix and B is a 12x12 matrix. So essentially I want it so that at x_{0} = c [I], at x_{1} = c + Bc, at x_{2} = c + Bc +B^2c, and so on.

I've been working hours on this and have not gotten anywhere.

 >> Y = [UNRATE1(2:end), Inflation2(2:end),FEDFUNDS(2:end)];
 >> spec = vgxset('n',3,'nAR',4,'Constant',true);
 >> [EstSpec, EstStdErrors, logL, W] = vgxvarx(spec,Y);
 >> vgxdisp(EstSpec)
  Model  : 3-D VAR(4) with Additive Constant
           Conditional mean is AR-stable and is MA-invertible
  a Constant:
        0.182955
       0.0944877
        0.162639
  AR(1) Autoregression Matrix:
         1.02021      -0.005937     -0.0342805
      -0.0371862        1.34661      0.0482451
       -0.235275       0.142802        1.39328
  AR(2) Autoregression Matrix:
       0.0551479    -0.00832073      0.0236625
      -0.0201467      -0.344195     0.00396517
        0.145578      -0.200587      -0.567446
  AR(3) Autoregression Matrix:
      -0.0954256      0.0108807     -0.0376391
      0.00402947      -0.028162     -0.0478039
      -0.0293905      0.0746669       0.110649
  AR(4) Autoregression Matrix:
      -0.0160549      0.0200511        0.04516
       0.0414149     0.00443558     0.00522856
       0.0971691      0.0160857      0.0361896
  Q Innovations Covariance:
        0.074462     -0.0022237     -0.0111057
      -0.0022237      0.0850203     0.00722063
      -0.0111057     0.00722063        0.20472

 B1=[1.02021 -0.005937 -0.0342805;-0.0371862 1.34661 0.0482451; -0.235275 0.142802 1.39328];
 B2=[0.0441479 -0.00832 0.0236625;-0.0201467 -0.344195 0.00396516;0.145578 -0.200587 -0.567446];
 B3=[-0.0954256 0.0108807 -0.0376391;0.00402947 -0.028162 -0.0478039;-0.0293905 0.0746669 0.110649];
 B4=[-0.0160549 0.0200511 0.04516; 0.0414149 0.00443558 0.00522856;0.0971691 0.0160857 0.0361896];

 B = [B1 B2 B3 B4; eye(9) zeros(9,3)];
 c = [0.182955;0.0944877;0.162639;0;0;0;0;0;0;0;0;0];
 B

 B =

Columns 1 through 8

    1.0202   -0.0059   -0.0343    0.0441   -0.0083    0.0237   -0.0954    0.0109
   -0.0372    1.3466    0.0482   -0.0201   -0.3442    0.0040    0.0040   -0.0282
   -0.2353    0.1428    1.3933    0.1456   -0.2006   -0.5674   -0.0294    0.0747
    1.0000         0         0         0         0         0         0         0
         0    1.0000         0         0         0         0         0         0
         0         0    1.0000         0         0         0         0         0
         0         0         0    1.0000         0         0         0         0
         0         0         0         0    1.0000         0         0         0
         0         0         0         0         0    1.0000         0         0
         0         0         0         0         0         0    1.0000         0
         0         0         0         0         0         0         0    1.0000
         0         0         0         0         0         0         0         0

Columns 9 through 12

   -0.0376   -0.0161    0.0201    0.0452
   -0.0478    0.0414    0.0044    0.0052
    0.1106    0.0972    0.0161    0.0362
         0         0         0         0
         0         0         0         0
         0         0         0         0
         0         0         0         0
         0         0         0         0
         0         0         0         0
         0         0         0         0
         0         0         0         0
    1.0000         0         0         0

 t = 0:1:750; 
 C = cell(750,1);
 C2=C;
 for k = 1:750;
    C{k}=B^k;
 end
 for j = 2:750;
    C2{j}=C2{j}+C2{j-1};
 end

However, the code for C2 just gives me a 750x1 with empty cells. How do I make it so that the first row of C2 is the first row of C, the second row of C2 is the first row plus the second row of C, and so on?

Answer 1

[Geoff Hayes]

real334 - look closely at your code

 C = cell(750,1);
 C2=C;
 for k = 1:750;
    C{k}=B^k;
 end
 for j = 2:750;
    C2{j}=C2{j}+C2{j-1};
 end

C2 is initialized as C which is an empty 750x1 cell array. Your first for loop then populates C but the second one does not make use of C at all and instead just makes use of C2

 C2{j}=C2{j}+C2{j-1};

Since x_{k} = c(I + B + B^2 + ... + B^k) (using your example), then I suspect that you want to do something like

 X = cell(750,1);
 X{1} = (eye(12) + B)*c;
 for k=2:750
     X{k} = X{k-1} + (B^k)*c;
 end

In the above, I'm guessing that your 1 or I is the identity matrix (so eye(12)). I haven't tested the above, but I think that it could work or at least provide a hint of how to proceed.

[real334]

Thank you for your insight Geoff. I realized I also made a mistake with my equation. I had intended to create a one step ahead forecast using my x data, but instead took the long term sum. If instead I need it to be x_{t} = c + B*x_{t-1}, would I just create another loop using my x data (12x1)?

[Geoff Hayes]

How is x initialized? Or are you using he first loop to calculate this new x?