In this paper, we present an online adaptive PCA algorithm that is able tocompute the full dimensional eigenspace per new time-step of sequential data.The algorithm is based on a one-step update rule that considers all secondorder correlations between previous samples and the new time-step. Ouralgorithm has O(n) complexity per new time-step in its deterministic mode andO(1) complexity per new time-step in its stochastic mode. We test our algorithmon a number of time-varying datasets of different physical phenomena. Explainedvariance curves indicate that our technique provides an excellent approximationto the original eigenspace computed using standard PCA in batch mode. Inaddition, our experiments show that the stochastic mode, despite its much lowercomputational complexity, converges to the same eigenspace computed using thedeterministic mode.