A novel framework called Memory-Based Forecasting is proposed to forecast complex and time-varying natural patterns. In this framework, past patterns similar to the present pattern are retrieved, and the forecast pattern is produced by using the patterns that follow the retrieved sequences. We represent the dynamic features of a sequence by using the spatial distribution of the patterns, velocity field, and temporal texture features; the sequences are transformed into paths in eigenspaces. The relationship between retrieval error and prediction error are modeled to define a similarity measure for retrieval. Forecast images are constructed from a future point in the eigenspace which is estimated by a nonlinear prediction scheme. Several experiments using weather radar images confirm the effectiveness of our method especially for drastically changing patterns.