A stochastic differential equation approach to the analysis of the UK 2016 EU referendum polls

Abstract

Human dynamics and sociophysics suggest statistical models that may explain and provide us with better insight into social phenomena. Here we propose a generative model based on a stochastic differential equation that allows us to analyse the polls leading up to the UK 2016 EU referendum. After a preliminary analysis of the time series of poll results, we provide empirical evidence that the beta distribution, which is a natural choice when modelling proportions, fits the marginal distribution of this time series. We also provide evidence of the predictive power of the proposed model.

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.…”

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

“…In particular, we present a companion paper to [Fenner et al, 2018] using the same methodology, which is based on SDEs applied to opinion polls leading up to an election rather than to a referendum. We deploy a novel stochastic process based on the Cox-Ingersoll-Ross (CIR) process [Cox et al, 1985, Chou andLin, 2006], used to model the term structure of interest rates [Berk and DeMarzo, 2017].…”

“…We refer the reader to [Fenner et al, 2018] for the background in human dynamics and sociophysics [Sen and Chakrabarti, 2014] (also known as social physics), noting that statistical physics [Castellano et al, 2009] has played a central role in its formulation; humans are viewed as "social atoms", each exhibiting simple individual behaviour having limited complexity, but nevertheless collectively they yield complex social patterns . In the context of human dynamics, the SDE model we propose is a generative model in the form of a stochastic process the evolution of which gives rise to distributions such as power law and Weibull distributions [Fenner et al, 2015].…”

“…In [Fenner et al, 2018] we took a fresh look at the time series approach, going beyond the model suggested in [Wlezien and Erikson, 2002], and made use of the availability of a large number of polls conducted at regular intervals. In particular, we proposed a novel model based on SDEs, which are widely used in physics and mathematical finance to model diffusion processes, that can be viewed as continuous approximations to discrete processes modelling how the polls vary over time.…”

“…One disadvantage of this model is that its autocorrelation function is decreases exponentially [Bibby et al, 2005], while in reality the tails of the autocorrelation function may be heavier. We address this problem in Section 4 by extending the model of [Fenner et al, 2018] to allow processes that are sums of diffusions [Bibby et al, 2005, Forman andSørensen, 2008], in which case the autocorrelation function is a sum of exponentials.…”