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

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.

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

“…Braha et al [ 124 ] have considered spatiotemporal US election data and have also emphasized the role of opinion leaders and spatial variability of external influences. Fenner et al [ 125 , 126 ] have started from a generative model inspired by survival analysis, but in later works transition to the SDE framework [ 127 , 128 ]. Michaud and Szilva [ 129 ] have fixed issues with the model originally proposed by Fernandez–Garcia et al [ 122 ], mainly, they have redefined how the noise term is handled so that the model would be more mathematically well-posed.…”