A stochastic differential equation approach to the analysis of the UK 2017 and 2019 general election polls

TL;DR

This paper introduces a stochastic differential equation model to analyze UK election polls, improving prediction accuracy by fitting a gamma distribution and simulating poll dynamics with the Euler-Maruyama method.

Contribution

The paper presents a novel SDE-based generative model for election polls that enhances forecasting accuracy over traditional poll-based methods.

Findings

Gamma distribution fits poll data well

Model improves election prediction accuracy

Simulation method provides reliable forecasts

Abstract

Human dynamics and sociophysics build on statistical models that can shed light on and add to our understanding of social phenomena. We propose a generative model based on a stochastic differential equation that enables us to model the opinion polls leading up to the UK 2017 and 2019 general elections, and to make predictions relating to the actual result of the elections. After a brief analysis of the time series of the poll results, we provide empirical evidence that the gamma distribution, which is often used in financial modelling, fits the marginal distribution of this time series. We demonstrate that the proposed poll-based forecasting model may improve upon predictions based solely on polls. The method uses the Euler-Maruyama method to simulate the time series, measuring the prediction error with the mean absolute error and the root mean square error, and as such could be used as part of a toolkit for forecasting elections.