The subject invention leverages the conditional Gaussian (CG) nature of a continuous variable stochastic ARMA.sup.xp time series model to efficiently determine its parametric gradients. The determined gradients permit an easy means to construct a parametric structure for the time series model. This provides a gradient-based alternative to the expectation maximization (EM) process for learning parameters of the stochastic ARMA.sup.xp time series model. Thus, gradients for parameters can be computed and utilized with a gradient-based learning method for estimating the parameters. This allows values of continuous observations in a time series to be predicted utilizing the stochastic ARMA.sup.xp time series model, providing efficient and accurate predictions.