Spartan Random Processes in Time Series Modeling

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.

💡 Research Summary

The paper introduces Spartan Random Processes (SRP) as a physics‑inspired framework for modeling temporal correlations in time‑series data and for making forecasts. An SRP treats a scalar field x(t) defined on continuous time as a stochastic variable governed by an energy functional H