In this paper we introduce a statistical downscaling method that incorporates the spatial and temporal variability associated with quasi-periodic climate signals, such as ENSO, by using Multichannel Singular Spectrum Analysis (M-SSA). In addition, the method preserves the expected values and variances of downscaled climate variables. The lump value of a climate variable is dissagregated over a grid of higher spatial resolution by using time series projections calculated on a cell-by-cell basis. To do this, we use a stochastic model consisting of the sum of the mean value, a quasi-periodic component related to climate signals, and a random component associated with the residual variance of historic records. The technique is employed to downscale standardized precipitation values, from historic records and projections of coupled climate models, taking into account the variability associated with ENSO.