Why does this rank 1 cholupdate result in a matrix with negative eigenvalues?

I'm trying to use rank 1 cholesky updates to ensure positive-definiteness of my matrices. However, the resulting matrices has small negative eigenvalues, and I'm not sure what I can do about it. Suggestions?

Y1 = cov(series(:,1:start)');

tmp = chol(Y1);

count=0;

for t = start+1:size(series,2)

      count = count+1;

      tmp = cholupdate(tmp,series(:,t)); 

      Y(:,:,count) = tmp'*tmp;
  end