dorsal/arxiv
View SchemaForecasting extreme events in collective dynamics: an analytic signal approach to detecting discrete scale invariance
| Authors | G. M. Viswanathan |
|---|---|
| Categories | |
| ArXiv ID | physics/0611281 |
| URL | https://arxiv.org/abs/physics/0611281 |
Abstract
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.
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"abstract": "A challenging problem in physics concerns the possibility of forecasting rare\nbut extreme phenomena such as large earthquakes, financial market crashes, and\nmaterial rupture. A promising line of research involves the early detection of\nprecursory log-periodic oscillations to help forecast extreme events in\ncollective phenomena where discrete scale invariance plays an important role.\nHere I investigate two distinct approaches towards the general problem of how\nto detect log-periodic oscillations in arbitrary time series without prior\nknowledge of the location of the moveable singularity. I first show that the\nproblem has a definite solution in Fourier space, however the technique\ninvolved requires an unrealistically large signal to noise ratio. I then show\nthat the quadrature signal obtained via analytic continuation onto the\nimaginary axis, using the Hilbert transform, necessarily retains the\nlog-periodicities found in the original signal. This finding allows the\ndevelopment of a new method of detecting log-periodic oscillations that relies\non calculation of the instantaneous phase of the analytic signal. I illustrate\nthe method by applying it to the well documented stock market crash of 1987.\nFinally, I discuss the relevance of these findings for parametric rather than\nnonparametric estimation of critical times.",
"arxiv_id": "physics/0611281",
"authors": [
"G. M. Viswanathan"
],
"categories": [
"physics.data-an",
"physics.soc-ph",
"q-fin.ST"
],
"title": "Forecasting extreme events in collective dynamics: an analytic signal approach to detecting discrete scale invariance",
"url": "https://arxiv.org/abs/physics/0611281"
},
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