Journal ArticleDOI
Improved Surrogate Data for Nonlinearity Tests.
Thomas Schreiber,Andreas Schmitz +1 more
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TLDR
It is shown that nonlinear rescalings of a Gaussian linear stochastic process cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity.Abstract:
Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of the data. We propose a more general null hypothesis allowing for nonlinear rescalings of a Gaussian linear process. We show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity. An iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution.read more
Citations
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Impact of complexity on daily and multi-step forecasting of streamflow with chaotic, stochastic, and black-box models
Hakan Tongal,Ronny Berndtsson +1 more
TL;DR: In this article, the authors investigated the entropy/complexity resulting from hydrological and climatological conditions and employed mutual information function, correlation dimension, averaged false nearest neighbor with E1 and E2 quantities, and complexity analysis that uses sample entropy coupled with iterative amplitude adjusted Fourier transform were employed as nonlinear deterministic identification tools.
Journal ArticleDOI
Causality across rainfall time scales revealed by continuous wavelet transforms
TL;DR: In this article, the authors explored the presence of causal cascade signatures within the rainfall process using both continuous wavelet decomposition (CWT) and scale-by-scale causality measures such as cross-scale correlation and linearized transfer entropy.
Journal ArticleDOI
Detection of nonlinearity and chaoticity in time series using the transportation distance function
TL;DR: A systematic two-step framework to assess the presence of nonlinearity and chaoticity in time series using the transportation distance function, the newly proposed discriminating statistic, offers several advantages over traditional measures of non linearity.
Journal ArticleDOI
Evidence for inherent nonlinearity in temporal rainfall
Stéphane Roux,Stéphane Roux,V. Venugopal,Kurt Fienberg,Alain Arneodo,Alain Arneodo,Efi Foufoula-Georgiou +6 more
TL;DR: This paper examined the underlying structure of high resolution temporal rainfall by comparing the observed series with surrogate series generated by a invertible nonlinear transformation of a linear process and found that the scaling properties and long range magnitude correlations of high-resolution temporal rainfall series are inconsistent with an inherently linear model, but are consistent with the nonlinear structure of a multiplicative cascade model.
Journal ArticleDOI
Stochastic Rainfall Downscaling of Climate Models
TL;DR: In this article, a stochastic rainfall downscaling technique is used to identify the fine structure of precipitation intensity fields. But, the spatial resolution currently achieved by global climate models (GCMs) and regional climate models is still insufficient to correctly identify the precipitation intensity field, and this scale gap can be at least temporarily bridged by adopting a Stochastic Rainfall Filtered Autoregressive Model (RainFARM).
References
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Book
Time Series Prediction: Forecasting The Future And Understanding The Past
TL;DR: By reading time series prediction forecasting the future and understanding the past, you can take more advantages with limited budget.
Book
Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence
TL;DR: In this paper, the changing structure of stock returns nonlinearity in foreign exchange summary, relation to other work, and future horizons are discussed, as well as the size and distribution of the BDS statistic quantiles.
Journal ArticleDOI
Constrained-realization Monte-Carlo method for hypothesis testing
TL;DR: The typical-realization approach, on the other hand, does not share this requirement, and can provide an accurate and powerful test without having to sacrifice flexibility in the choice of discriminating statistic, and is found to depend on whether or not the discriminating statistic is pivotal.