Forecasting extreme events in collective dynamics: an analytic signal approach to detecting discrete scale invariance
| dc.creator | Viswanathan, G. M. | |
| dc.date | 2006-11-28 | |
| dc.date | 2006-12-04 | |
| dc.date.accessioned | 2026-07-07T12:07:54Z | |
| dc.date.available | 2026-07-07T12:07:54Z | |
| dc.description | A challenging problem in physics concerns the possibility of forecasting rare but extreme phenomena such as large earthquakes, financial market crashes, and material rupture. A promising line of research involves the early detection of precursory log-periodic oscillations to help forecast extreme events in collective phenomena where discrete scale invariance plays an important role. Here I investigate two distinct approaches towards the general problem of how to detect log-periodic oscillations in arbitrary time series without prior knowledge of the location of the moveable singularity. I first show that the problem has a definite solution in Fourier space, however the technique involved requires an unrealistically large signal to noise ratio. I then show that the quadrature signal obtained via analytic continuation onto the imaginary axis, using the Hilbert transform, necessarily retains the log-periodicities found in the original signal. This finding allows the development of a new method of detecting log-periodic oscillations that relies on calculation of the instantaneous phase of the analytic signal. I illustrate the method by applying it to the well documented stock market crash of 1987. Finally, I discuss the relevance of these findings for parametric rather than nonparametric estimation of critical times. | |
| dc.description | Corrected minor mistakes, typos etc. Added new refs | |
| dc.identifier | https://arxiv.org/abs/physics/0611281 | |
| dc.identifier | http://arxiv.org/abs/physics/0611281 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209135 | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.subject | Physics and Society | |
| dc.subject | Statistical Finance | |
| dc.title | Forecasting extreme events in collective dynamics: an analytic signal approach to detecting discrete scale invariance | |
| dc.type | text |