  A Spartan random process (SRP) is used to estimate the correlation structure
of time series and to predict (extrapolate) the data values. SRP's are
motivated from statistical physics, and they can be viewed as Ginzburg-Landau
models. The temporal correlations of the SRP are modeled in terms of
`interactions' between the field values. Model parameter inference employs the
computationally fast modified method of moments, which is based on matching
sample energy moments with the respective stochastic constraints. The
parameters thus inferred are then compared with those obtained by means of the
maximum likelihood method. The performance of the Spartan predictor (SP) is
investigated using real time series of the quarterly S&P 500 index. SP
prediction errors are compared with those of the Kolmogorov-Wiener predictor.
Two predictors, one of which explicit, are derived and used for extrapolation.
The performance of the predictors is similarly evaluated.
