Surrogate Monte Carlo

TL;DR

This paper introduces a simple, customizable surrogate data generation algorithm using permutation of Monte Carlo samples, optimized by an objective function to preserve key features of the original time series.

Contribution

It presents a novel permutation-based surrogate data method that effectively captures essential characteristics of stochastic processes.

Findings

Successfully simulated S&P 500 log-returns

Preserved key statistical features of original data

Demonstrated flexibility and simplicity of the method

Abstract

This article proposes an artificial data generating algorithm that is simple and easy to customize. The fundamental concept is to perform random permutation of Monte Carlo generated random numbers which conform to the unconditional probability distribution of the original real time series. Similar to constraint surrogate methods, random permutations are only accepted if a given objective function is minimized. The objective function is selected in order to describe the most important features of the stochastic process. The algorithm is demonstrated by producing simulated log-returns of the S\&P 500 stock index.