Two-tier femtocell-based networks have been proposed as an economic solution to improve coverage and capacity in wireless cellular systems. Although widely studied in the literature, interference management in these networks remains as a technical challenge in need of effective solutions. In particular, the interference estimation is a relevant portion of the problem that enables correct operation of interference management schemes relying on this information. In this paper, a novel downlink cross-tier interference estimation approach is proposed based on spatio-temporal correlation techniques. An ordinary Kriging interpolator using Semivariogram Analysis is applied to the interfering signal followed by an autorregressive model. The signal estimation at the interfered users' location is exploited at the radio resource manager of the femtocell or macrocell base station by formulating a resource allocation problem that is solved by means of a heuristic algorithm. A practical procedure implementing this scheme in the network is also proposed. Numerical results show how performance of cross-tier interference management approaches can be optimized by implementing this idea.