Universal and non-universal properties of recurrence intervals of rare events

Zhao, Xiaochuan; Shang, Pengjian; Lin, Aijing

doi:10.1016/j.physa.2015.12.082

Cited by 9 publications

(4 citation statements)

References 48 publications

(35 reference statements)

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“…Step Two and Extended Data Algorithm 1 line [11][12][13][14][15][16][17][18][19][20][21][22]. As an added bonus, this approach also addresses the problem of vanishing and exploding gradients.…”

Section: A10mentioning

confidence: 99%

Deep Learning Without Neural Networks: Fractal-nets for Rare Event Modeling

Chattopadhyay

Huang

Evans

2020

Preprint

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Complex phenomena of societal interest such as weather, seismic activity and urban crime, are often punctuated by rare and extreme events, which are difficult to model and predict. Evidence of long-range persistence of such events has underscored the need to learn deep stochastic structures in data for effective forecasts. Recently neural networks (NN) have emerged as a defacto standard for deep learning. However, key problems remain with NN inference, including a high sample complexity, a general lack of transparency, and a limited ability to directly model stochastic phenomena. In this study we suggest that deep learning and the NN paradigm are conceptually distinct -- and that it is possible to learn ``deep' associations without invoking the ubiquitous NN strategy of global optimization via back-propagation. We show that deep learning of stochastic phenomena is related to uncovering the emergent self-similarities in data, which avoids the NN pitfalls offering crucial insights into underlying mechanisms. Using the Fractal Net (FN) architecture introduced here, we actionably forecast various categories of rare weather and seismic events, and property and violent crimes in major US cities. Compared to carefully tuned NNs, we boost recall at 90% precision by 161.9% for extreme weather events, 191.3% for light-to-severe seismic events with magnitudes above the local third quartile, and 50.8% - 404.9% for urban crime, demonstrating applicability in diverse systems of societal interest. This study opens the door to precise prediction of rare events in spatio-temporal phenomena, adding a new tool to the data science revolution.

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Section: A10mentioning

confidence: 99%

Deep Learning Without Neural Networks: Fractal-nets for Rare Event Modeling

Chattopadhyay

Huang

Evans

2020

Preprint

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“…The degree of the predictability became larger than that of the logarithmic return. There existed long-range persistent correlations in the volatility series [ 37 ], so that the clustering of extreme volatilities emerged. A larger volatility was more likely to be followed by a large volatility, and vice versa [ 38 , 39 ].…”

Section: Financial Time Series Analysismentioning

confidence: 99%

Quantifying the Multiscale Predictability of Financial Time Series by an Information-Theoretic Approach

Zhao

Liang

Zhang

et al. 2019

Entropy

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Making predictions on the dynamics of time series of a system is a very interesting topic. A fundamental prerequisite of this work is to evaluate the predictability of the system over a wide range of time. In this paper, we propose an information-theoretic tool, multiscale entropy difference (MED), to evaluate the predictability of nonlinear financial time series on multiple time scales. We discuss the predictability of the isolated system and open systems, respectively. Evidence from the analysis of the logistic map, Hénon map, and the Lorenz system manifests that the MED method is accurate, robust, and has a wide range of applications. We apply the new method to five-minute high-frequency data and the daily data of Chinese stock markets. Results show that the logarithmic change of stock price (logarithmic return) has a lower possibility of being predicted than the volatility. The logarithmic change of trading volume contributes significantly to the prediction of the logarithmic change of stock price on multiple time scales. The daily data are found to have a larger possibility of being predicted than the five-minute high-frequency data. This indicates that the arbitrage opportunity exists in the Chinese stock markets, which thus cannot be approximated by the effective market hypothesis (EMH).

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“…One of the key parameters needed for the assessment of seismic hazards is the recurrence interval of large earthquakes which relates to the seismogenic fault's dynamic process. In a recurrence cycle, small earthquakes can also be background earthquakes [17]. Paleoseismic studies have shown that quasiperiodic is the nature of large earthquakes, that is, its unpredictability nature and does not give itself to precise measurement.…”

Section: Earthquake Recurrence Intervalmentioning

confidence: 99%

Probabilistic Seismic Hazard Analysis of Southwestern Nigeria

Oluwafemi¹,

Ofuyatan²,

Oyebisi³

et al. 2018

GEOMATE

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For about ten decades, the seismic record of Nigeria has shown the occurrence of several magnitudes of earthquakes. This is contrary to the belief of some people in time past that Nigeria is aseismic. In number and in size, most of the witnessed earthquakes in Nigeria are found to occur in her South-Western region. Researchers have also begun to warn recently that some regions of Nigeria should prepare for devastating earthquakes in years to come. Hence this paper aimed at the probabilistic seismic hazard analysis of the South-Western region of Nigeria using the available historical and instrumentally recorded data. The Gutenberg-Richter (G-R) recurrence law was used to assess the seismicity parameters and to generate a model for calculating the mean annual rate of exceedance and to forecast probable future earthquake occurrence in the South-West. The findings of this assessment established that the South-West region of Nigeria is likely to experience earthquake magnitude as high as 7.2 in the year 2028 with a probability of 36.79%. Hence, this work enlightens on the extent of probable future earthquake magnitude in South-Western Nigeria and it is recommended that the government of Nigeria and inclined agencies begin to look into earthquake in this region.

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Universal and non-universal properties of recurrence intervals of rare events

Cited by 9 publications

References 48 publications

Deep Learning Without Neural Networks: Fractal-nets for Rare Event Modeling

Deep Learning Without Neural Networks: Fractal-nets for Rare Event Modeling

Quantifying the Multiscale Predictability of Financial Time Series by an Information-Theoretic Approach

Probabilistic Seismic Hazard Analysis of Southwestern Nigeria

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