Detecting nonlinearity in time series driven by non-Gaussian noise: the case of river flows

Laio, Francesco; Porporato, Amilcare; Ridolfi, Luca; Tamea, Stefania

doi:10.5194/npg-11-463-2004

Cited by 18 publications

(11 citation statements)

References 42 publications

(49 reference statements)

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“…We are currently investigating how nonlinearities in the processes that govern sandbar behavior express themselves in time series of sandbar positions. Work of Laio, Porporato, Ridolfi, and Tamea (2004) on rainfall-runoff time series, for instance, demonstrates that the presence of nonlinear processes in a system does not necessarily imply that time series from specific variables in this system are nonlinear themselves.…”

Section: Discussionmentioning

confidence: 99%

Recurrent neural network modeling of nearshore sandbar behavior

et al. 2007

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The temporal evolution of nearshore sandbars (alongshore ridges of sand fringing coasts in water depths less than 10 m and of paramount importance for coastal safety) is commonly predicted using process-based models. These models are autoregressive and require offshore wave characteristics as input, properties that find their neural network equivalent in the NARX (Nonlinear AutoRegressive model with eXogenous input) architecture. Earlier literature results suggest that the evolution of sandbars depends nonlinearly on the wave forcing and that the sandbar position at a specific moment contains 'memory', that is, time-series of sandbar positions show dependencies spanning several days. Using observations of an outer sandbar collected daily for over seven years at the double-barred Surfers Paradise, Gold Coast, Australia several data-driven models are compared. Nonlinear and linear models as well as recurrent and nonrecurrent parameter estimation methods are applied to investigate the claims about nonlinear and long-term dependencies. We find a small performance increase for long-term predictions (>40 days) with nonlinear models, indicating that nonlinear effects expose themselves for larger prediction horizons, and no significant difference between nonrecurrent and recurrent methods meaning that the effects of dependencies spanning several days are of no importance.

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Section: Discussionmentioning

confidence: 99%

Recurrent neural network modeling of nearshore sandbar behavior

et al. 2007

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“…Studies in Ref. 37 showed that DVS plots can effectively be employed when time series is noisy, short, and non-Gaussian; these features assure DVS as an ideal option for exploiting the nonlinear behavior of ambient noise. This technique aids in overcoming the liability faced by traditional nonlinear methods, such as correlation dimension and Lyapunov exponents.…”

Section: Nonlinear Predictionmentioning

confidence: 99%

On the dynamics of ocean ambient noise: Two decades later

Siddagangaiah

Guo

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Two decades ago, it was shown that ambient noise exhibits low dimensional chaotic behavior. Recent new techniques in nonlinear science can effectively detect the underlying dynamics in noisy time series. In this paper, the presence of low dimensional deterministic dynamics in ambient noise is investigated using diverse nonlinear techniques, including correlation dimension, Lyapunov exponent, nonlinear prediction, and entropy based methods. The consistent interpretation of different methods demonstrates that ambient noise can be best modeled as nonlinear stochastic dynamics, thus rejecting the hypothesis of low dimensional chaotic behavior. The ambient noise data utilized in this study are of duration 60 s measured at South China Sea.

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“…Though it is robust towards non-Gaussianity, it is difficult to distinguish between a nonlinear non-Gaussian system with a linear Gaussian system, since the possible nonlinearities tend to be dominated by the stochastic component. Furthermore, it is not a real statistical test "since no test statistics are produced which allows a unequivocal acceptance or rejection of the null hypothesis of linearity" (Laio et al, 2004). Laio et al (2004) also showed that a surrogate data set generated from a linear decay system with non-Gaussian shot noise (see Eq.…”

Section: Surrogate Data Testmentioning

confidence: 99%

“…Furthermore, it is not a real statistical test "since no test statistics are produced which allows a unequivocal acceptance or rejection of the null hypothesis of linearity" (Laio et al, 2004). Laio et al (2004) also showed that a surrogate data set generated from a linear decay system with non-Gaussian shot noise (see Eq. 3 below) appeared significantly different than an original data set and tested for reversibility using a simple third order statistic.…”

Section: Surrogate Data Testmentioning

confidence: 99%

“…This scheme indicates that the surrogate volatility does not always diminish the seasonal periodicity of the volatility series, but rather eliminates the nonlinear part of the process which is proportional to the noise level. Laio et al (2004) applied deterministic versus stochastic (DVS) plots to the decay phases of daily discharges of three rivers in Italy and detected nonlinearity from the data. DVS was first introduced by Casdagli (1991).…”

Section: Surrogate Data Testmentioning

confidence: 99%

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Streamflow dynamics at the Puget Sound, Washington: application of a surrogate data method

She¹,

Basketfield²

2005

Nonlin. Processes Geophys.

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Abstract. Recent progress in nonlinear dynamic theory has inspired hydrologists to apply innovative nonlinear time series techniques to the analysis of streamflow data. However, regardless of the method employed to analyze streamflow data, the first step should be the identification of underlying dynamics using one or more methods that could distinguish between linear and nonlinear, deterministic and stochastic processes from data itself. In recent years a statistically rigorous framework to test whether or not the examined time series is generated by a Gaussian (linear) process undergoing a possibly nonlinear static transform is provided by the method of surrogate data. The surrogate data, generated to represent the null hypothesis, are compared to the original data under a nonlinear discriminating statistic in order to reject or approve the null hypothesis. In recognition of this tendency, the method of "surrogate data" is applied herein to determine the underlying linear stochastic or nonlinear deterministic nature of daily streamflow data observed from the central basin of Puget Sound, and as applicable, distinguish between the static or dynamic nonlinearity of the data in question.

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Detecting nonlinearity in time series driven by non-Gaussian noise: the case of river flows

Cited by 18 publications

References 42 publications

Recurrent neural network modeling of nearshore sandbar behavior

Recurrent neural network modeling of nearshore sandbar behavior

On the dynamics of ocean ambient noise: Two decades later

Streamflow dynamics at the Puget Sound, Washington: application of a surrogate data method

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