An Exactly Solvable Discrete Stochastic Process with Correlated Properties

TL;DR

This paper introduces a new exactly solvable discrete stochastic process with non-Gaussian properties, capable of modeling correlated financial data and accurately predicting distributions in small sample regimes.

Contribution

It presents a novel correlated stochastic process with an exactly derived non-Gaussian probability mass function, advancing modeling of discrete financial time-series.

Findings

Process is convergent and scale invariant in large but finite samples

Accurately models distribution and correlation of financial data

Predicts data distribution with high precision in small samples

Abstract

We propose a correlated stochastic process of which the novel non-Gaussian probability mass function is constructed by exactly solving moment generating function. The calculation of cumulants and auto-correlation shows that the process is convergent and scale invariant in the large but finite number limit. We demonstrate that the model consistently explains both the distribution and the correlation of discrete financial time-series data, and predicts the data distribution with high precision in the small number regime.