Optimization Procedure for Predicting Nonlinear Time Series Based on a Non-Gaussian Noise Model

In this paper we investigate the influence of a power-law noise model, also called Pareto noise, on the performance of a feed-forward neural network used to predict nonlinear time series. We introduce an optimization procedure that optimizes the parameters of the neural networks by maximizing the likelihood function based on the power-law noise model. We show that our optimization procedure minimizes the mean squared error leading to an optimal prediction. Further, we present numerical results applying our method to time series from the logistic map and the annual number of sunspots and demonstrate that a power-law noise model gives better results than a Gaussian noise model.

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Localization for visible light communication with practical non-Gaussian noise model

2017 9th International Conference on Wireless Communications and Signal Processing (WCSP) ◽

10.1109/wcsp.2017.8171147 ◽

2017 ◽

Cited By ~ 1

Author(s):

Yueyue Zhang ◽

Yaping Zhu ◽

Weiwei Xia ◽

Feng Yan ◽

Lianfeng Shen ◽

...

Keyword(s):

Visible Light ◽

Gaussian Noise ◽

Visible Light Communication ◽

Noise Model ◽

Non Gaussian

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

Nonlinear Processes in Geophysics ◽

10.5194/npg-11-463-2004 ◽

2004 ◽

Vol 11 (4) ◽

pp. 463-470 ◽

Cited By ~ 15

Author(s):

F. Laio ◽

A. Porporato ◽

L. Ridolfi ◽

S. Tamea

Keyword(s):

Time Series ◽

Gaussian Noise ◽

Driving Force ◽

Surrogate Data ◽

Rainfall Runoff ◽

River Flows ◽

Dynamical Characteristics ◽

Univariate Time Series ◽

Poissonian Noise ◽

Non Gaussian

Abstract. Several methods exist for the detection of nonlinearity in univariate time series. In the present work we consider riverflow time series to infer the dynamical characteristics of the rainfall-runoff transformation. It is shown that the non-Gaussian nature of the driving force (rainfall) can distort the results of such methods, in particular when surrogate data techniques are used. Deterministic versus stochastic (DVS) plots, conditionally applied to the decay phases of the time series, are instead proved to be a suitable tool to detect nonlinearity in processes driven by non-Gaussian (Poissonian) noise. An application to daily discharges from three Italian rivers provides important clues to the presence of nonlinearity in the rainfall-runoff transformation.

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Predictability and Non-Gaussian Characteristics of the North Atlantic Oscillation

Journal of Climate ◽

10.1175/jcli-d-17-0101.1 ◽

2018 ◽

Vol 31 (2) ◽

pp. 537-554 ◽

Cited By ~ 4

Author(s):

Thomas Önskog ◽

Christian L. E. Franzke ◽

Abdel Hannachi

Keyword(s):

Time Series ◽

North Atlantic Oscillation ◽

North Atlantic ◽

Gaussian Noise ◽

Weather Conditions ◽

Dominant Mode ◽

The North ◽

The North Atlantic ◽

Non Gaussian ◽

The North Atlantic Oscillation

The North Atlantic Oscillation (NAO) is the dominant mode of climate variability over the North Atlantic basin and has a significant impact on seasonal climate and surface weather conditions. It is the result of complex and nonlinear interactions between many spatiotemporal scales. Here, the authors study the statistical properties of two time series of the daily NAO index. Previous NAO modeling attempts only considered Gaussian noise, which can be inconsistent with the system complexity. Here, it is found that an autoregressive model with non-Gaussian noise provides a better fit to the time series. This result holds also when considering time series for the four seasons separately. The usefulness of the proposed model is evaluated by means of an investigation of its forecast skill.

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