The present invention utilizes a cross-prediction scheme to predict values of discrete and continuous time observation data, wherein conditional variance of each continuous time tube variable is fixed to a small positive value. By allowing cross-predictions in an ARMA based model, values of continuous and discrete observations in a time series are accurately predicted. The present invention accomplishes this by extending an ARMA model such that a first time series "tube" is utilized to facilitate or "cross-predict" values in a second time series tube to form an "ARMAxp" model. In general, in the ARMAxp model, the distribution of each continuous variable is a decision graph having splits only on discrete variables and having linear regressions with continuous regressors at all leaves, and the distribution of each discrete variable is a decision graph having splits only on discrete variables and having additional distributions at all leaves.