Equity prices as a simple harmonic oscillator with noise

Ataullah, Ali and Tippett, Mark (2007). Equity prices as a simple harmonic oscillator with noise. Physica A: Statistical Mechanics and its Applications, 382(2) pp. 557–564.

DOI: https://doi.org/10.1016/j.physa.2007.04.010

Abstract

The centred return on the London Stock Exchange's FTSE All Share Index is modelled as a simple harmonic oscillator with noise over the period from 1 January, 1994 until 30 June 2006. Our empirical results are compatible with the hypothesis that there is a period in the FTSE All Share Index of between two and two and one half years. This means the centred return will on average continue to increase for about a year after reaching the minimum in its oscillatory cycle; alternatively, it will continue on average to decline for about a year after reaching a maximum. Our analysis also shows that there is potential to exploit the harmonic nature of the returns process to earn abnormal profits. Extending our analysis to the low energy states of a quantum harmonic oscillator is also suggested.