Improve speed of indexing

Hello,

I am trying to do a simple Monte Carlo simulation in a mean reverting AR(lags) model using the following code

for j = 1:nPaths
    for i = lags+1:nPeriods+1
        F(i,j) = Season(i) + ar*(Y(i-lags:i-1)-Season(i-lags:i-1)) + sqrt(S2(i-lags)).*R(i-lags,j);           
    end
end

where lags is the number of lags of the AR(lags) model, Season is a seasonality function, R are some random numbers, S2 is the variance and ar is the vector that contains the estimated parameters of the AR model (dimension [lags,1]).

By running the code I have noticed that it takes less than a second if lags = 1 but the time increases 20fold if lags is bigger number, e.g lags =3.

Using the profiler I found that the problem is in the indexing of Y and Season,

ar*(Y(i-lags:i-1)-Season(i-lags:i-1))

So, is there a way to improve this part? or the whole double loop.

Thank you in advance, Elric

[Ced]

Do you preallocate F?

Things you could/should do in case you have not yet done it:

- preallocate F, i.e. F = zeros(nPeriods+1,nPaths);

- precompute the whole season vector (unless it is already one, but you said it's a function).

- You could precompute dYS = Y-Season. The operation in the loop would then be ar*dYS(i-lags:i-1). This is essentially computing the correlation. There are methods to increase the speed here, but I don't see why this operation would be so expensive.

- The last term can also be precomputed in vector form, i.e. repmat(sqrt(S2),1,nPaths).*R.

- Then: None of the operations in the for loop are recursive as far as I can tell. In other words, you might be able to get rid of the for loop completely (at least the inner one, the outer one would be tricky) at the cost that it may not be readable anymore.

Not a complete solution, sorry, but maybe this helps.

Cheers

PS: Could you give us the dimensions/orientation of your matrices/vectors? E.g. I think the variance is saved in a vector? row, or column? etc.

EDIT: added tipps