Point process model of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:math>noise vs a sum of Lorentzians

Kaulakys, B.; Gontis, Vygintas; Alaburda, M.

doi:10.1103/physreve.71.051105

Cited by 84 publications

(140 citation statements)

References 110 publications

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“…These equations and parameters σ ′ = σ/τ 0 , λ, ǫ ′ and m = 2 define model, which has to reproduce, in details, power-law statistics of the trading activity in the financial markets. From the analysis based on the research of fractal stochastic point processes Gontis & Kaulakys (2004;2007); Kaulakys et al (2005; and by fitting the numerical calculations to the empirical data we arrive at the conclusion that model parameters should be set as σ ′ = 0.006, λ = 4.3, ǫ ′ = 0.05 in order to achieve best results. In Figure 3 we have presented statistical properties obtained from our model using aforementioned parameter values -PDF of the sequence of τ k = h k , (a), and the PSD of the sequence of trades as point events, (b).…”

Section: Analysis Of Empirical Stock Trading Datamentioning

confidence: 99%

“…Thus as of now we have introduced the complete set of equations defining the stochastic model of the trading activity in the financial markets. We have proposed this model following our growing interest in the stochastic fractal point processes Gontis & Kaulakys (2004); Kaulakys et al (2005;. Our objective to reproduce, in details, statistics of trading activity is the cause for rather complicated form of the SDE (27) and thus there is low expectation of analytical results.…”

Section: Fractal Point Process Driven By the Nonlinear Stochastic Difmentioning

confidence: 99%

“…with 0.5 < β < 2, 4 − η < λ < 1 + 2η and η > 1. were first derived for the multiplicative point process in Gontis & Kaulakys (2004); Kaulakys et al (2005) and generalized for the nonlinear SDE (42) We will need a more sophisticated version of the SDE to reproduce a stochastic process with a fractured PSD of the absolute return, which is observable in financial markets. Having in mind the statistics of the stochastic model (45) defined by Eqs.…”

Section: Analysis Of Empirical Stock Trading Datamentioning

confidence: 99%

“…From our previous experience modeling one-over-f noise and trading activity in financial markets Gontis & Kaulakys (2004); Kaulakys et al (2005), building nonlinear stochastic differential equations exhibiting power law statistics Kaulakys et al (2006); Kaulakys & Alaburda (2009), described here in previous sections, we know that processes with power spectrum S( f ) ∼ 1/ f β can be obtained using the multiplicative term b(r) ∼ r η or even a slightly modified form (r 2 0 + r 2 ) η 2 . Therefore, we choose the term b(r) as…”

Section: Analysis Of Empirical Stock Trading Datamentioning

confidence: 99%

See 3 more Smart Citations

A Non-Linear Double Stochastic Model of Return in Financial Markets

Gontis¹,

Ruseckas²,

Kononovičius³

2010

Stochastic Control

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Section: Analysis Of Empirical Stock Trading Datamentioning

confidence: 99%

Section: Fractal Point Process Driven By the Nonlinear Stochastic Difmentioning

confidence: 99%

Section: Analysis Of Empirical Stock Trading Datamentioning

confidence: 99%

Section: Analysis Of Empirical Stock Trading Datamentioning

confidence: 99%

See 2 more Smart Citations

A Non-Linear Double Stochastic Model of Return in Financial Markets

Gontis¹,

Ruseckas²,

Kononovičius³

2010

Stochastic Control

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“…Nonlinear flows subject to multiplicative noise can also generate a 1/f α spectrum with the exponent being in the range 0.5 < α < 2 [19]. There have been proposals to treat 1/f α noise as a generalized renewal process [20,21]. The case we treat here is that of an input Brownian noise, although our analysis is valid for considerably more general cases.…”

mentioning

confidence: 91%

Memoryless nonlinear response: A simple mechanism for the 1/f noise

Yadav

Ramaswamy

Dhar

2013

EPL

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-Discovering the mechanism underlying the ubiquity of "1/f α " noise has been a longstanding problem. The wide range of systems in which the fluctuations show the implied long-time correlations suggests the existence of some simple and general mechanism that is independent of the details of any specific system. We argue here that a memoryless nonlinear response suffices to explain the observed non-trivial values of α: a random input noisy signal S(t) with a power spectrum varying as 1/f α ′ , when fed to an element with such a response function R gives an output R(S(t)) that can have a power spectrum 1/f α with α < α ′ . As an illustrative example, we show that an input Brownian noise (α ′ = 2) acting on a device with a sigmoidal response function R(S) = sgn(S)|S| x , with x < 1, produces an output with α = 3/2 + x, for 0 ≤ x ≤ 1/2. Our discussion is easily extended to more general types of input noise as well as more general response functions.Although first observed almost ninety years ago and subsequently found to occur in very diverse systems, the origins of the ubiquitous low frequency noise with power spectrum 1/f α where α ≈ 1-called flicker noise or pink noise-has been a long-standing conundrum [1]. Some examples are the fluctuations in voltage across a resistor or other components in electronic equipment [1], river discharges [2, 3], traffic flow [4], the frictional force in sliding friction under wear conditions [5], and the acoustic power in music or speech [6]. Many signals involving response to physical stimuli in living systems, such as fluctuations in the response time of motor-response to a periodic stimulus in humans [7], in the time series of errors of replication of spatial or temporal intervals by memory in humans [8], or in human colour vision [9] have also been found to have 1/f α spectrum. While it seems unlikely that these very diverse types of processes could share a single underlying mechanism, it also seems reasonable that the number of mathematical mechanisms underlying this behaviour would not be very large. Considerable effort has therefore been devoted to discovering these [1].In this Letter, we point out that memoryless nonlinear response (MNR) is sufficient to explain the observed nontrivial values of α. Despite its simplicity, this very general mechanism does not appear to have been explicitly discussed in the literature so far. When the response-time of the system is much shorter than the time-scale of fluctuations under discussion, we may model the system as a nonlinear device which when subjected to the input signal produces a response that is a nonlinear function of the instantaneous value of the input noise. Thus if S(t) is some noise process, we obtain another process R(t), whose value at any time t is related to the value of S(t) at the same time by the transformation: R(t) = h(S(t)), where h is a simple nonlinear function. The process R(t) can have a different value of the spectral power exponent, and we expect that this gives rise to the observed nontrivial val...

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Fractal degassing from Erebus and Mayon volcanoes revealed by a new method to monitor H₂O emission cycles

et al. 2015

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Many active volcanoes around the world release passively large amounts of gas between eruptions. Monitoring how these gas emissions fluctuate over time is crucial to infer the physical processes occurring within volcanic conduits and reservoirs. Here we report a new method to capture remotely the spectral properties of the emissions of H 2 O, the major component of most volcanic plumes. The method is based on a new theoretical model that correlates the volcanogenic water content of condensed volcanic plumes with the intensity of the light scattered by the droplets moving with the gas. In turn, we show that light intensity of the plume, and thus steam pulses time series, can be obtained with a proper analysis of digital images. The model is experimentally validated by generating condensed plumes with an ultrasonic humidifier, and then the method is applied to the gas plumes of Erebus and Mayon volcanoes. Our analysis reveals three main features: (1) H 2 O time series are composed of numerous periodic components of finite duration; (2) some periodic components are common in H 2 O and SO 2 time series, but others are not; and (3) the frequency spectra of the H 2 O emissions follow a well-defined fractal distribution, that is, amplitude (Δ) and frequency (ν) are correlated by means of power laws (Δ ∝ ν γ ), with exponent γ ≈ À 1 for Erebus and forMayon. These findings suggest that quiescent degassing emerges from the complex coupling between different processes occurring within magma plumbing systems. Our method is ideal for real-time monitoring of high-frequency H 2 O cycles at active volcanoes.

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Point process model of1∕fnoise vs a sum of Lorentzians

Abstract: To be published in Phys. Rev. E (2005).We present a simple point process model of 1/f β noise, covering different values of the exponent

Cited by 84 publications

References 110 publications

A Non-Linear Double Stochastic Model of Return in Financial Markets

A Non-Linear Double Stochastic Model of Return in Financial Markets

Memoryless nonlinear response: A simple mechanism for the 1/f noise

Fractal degassing from Erebus and Mayon volcanoes revealed by a new method to monitor H₂O emission cycles

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Point process model of1∕fnoise vs a sum of Lorentzians

Abstract: To be published in Phys. Rev. E (2005).We present a simple point process model of 1/f β noise, covering different values of the exponent

Cited by 84 publications

References 110 publications

A Non-Linear Double Stochastic Model of Return in Financial Markets

A Non-Linear Double Stochastic Model of Return in Financial Markets

Memoryless nonlinear response: A simple mechanism for the 1/f noise

Fractal degassing from Erebus and Mayon volcanoes revealed by a new method to monitor H2O emission cycles

Contact Info

Product

Resources

About

Fractal degassing from Erebus and Mayon volcanoes revealed by a new method to monitor H₂O emission cycles