Modelling and prediction of the wildfire data using fractional Poisson process

TL;DR

This paper models California wildfire occurrences using a fractional Poisson process to account for event dependence, achieving significantly improved prediction accuracy over traditional models.

Contribution

It introduces a fractional Poisson process model with estimation methods for wildfire data, capturing dependence and reducing prediction error.

Findings

Estimated fractional parameter as 0.8 indicating dependence

Reduced prediction error by 90% compared to classical Poisson model

Demonstrated the model's effectiveness on California wildfire data

Abstract

Modelling wildfire events has been studied in the literature using the Poisson process, which essentially assumes the independence of wildfire events. In this paper, we use the fractional Poisson process to model the wildfire occurrences in California between June 2019 - April 2023 and predict the wildfire events that explains the underlying memory between these events. We introduce method of moments and maximum likelihood estimate approaches to estimate the parameters of the fractional Poisson process, which is an alternative to the method proposed by Cahoy (2010). We obtain the estimates of the fractional parameter as 0.8, proving that the wildfire events are dependent. The proposed model has reduced prediction error by 90\% compared to the classical Poisson process model.