This article studies a general theory of estimating functions of independent component analysis when the independent source signals are temporarily correlated. Estimating functions are used for deriving both batch and on-line learning algorithms, and they are applicable to blind cases where spatial and temporal probability structures of the sources are unknown. Most algorithms proposed so far can be analyzed in the framework of estimating functions. An admissible class of estimating functions is derived, and related efficient on-line learning algorithms are introduced. We analyze dynamical stability and statistical efficiency of these algorithms. Different from the independently and identically distributed case, the algorithms work even when only the second-order moments are used. The method of simultaneous diagonalization of cross-covariance matrices is also studied from the point of view of estimating functions.