Spartan Random Processes in Time Series Modeling

TL;DR

This paper introduces Spartan random processes inspired by statistical physics for modeling and predicting time series, demonstrating their effectiveness on financial data and comparing them with traditional methods.

Contribution

It presents a novel SRP framework for time series analysis, including a fast parameter inference method and new predictors, validated on real financial data.

Findings

SRP effectively models temporal correlations in time series.

The Spartan predictor outperforms traditional methods in prediction accuracy.

Parameter inference via the modified method of moments is computationally efficient.

Abstract

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.