The paper considers the problem of the optimal on-line estimation of digital stochastic sequences. Specifically a calculus of variations approach is used to prove that for stationary stochastic sequences exponential and moving average algorithms are equally viable, both techniques representing close approximations to the theoretical optimum solution. For non-stationary sequences the moving average algorithm is shown to be the better choice, due to its symmetrical weighting function. The paper concludes with a discussion of the influence of induced correlation on the estimation process.