# Nonlinear forecasting for the classification of natural time series

@article{Sugihara1994NonlinearFF, title={Nonlinear forecasting for the classification of natural time series}, author={George Sugihara}, journal={Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences}, year={1994}, volume={348}, pages={477 - 495} }

There is a growing trend in the natural sciences to view time series as products of dynamical systems. This viewpoint has proven to be particularly useful in stimulating debate and insight into the nature of the underlying generating mechanisms. Here I review some of the issues concerning the use of forecasting in the detection of nonlinearities and possible chaos, particularly with regard to stochastic chaos. Moreover, it is shown how recent attempts to measure meaningful Lyapunov exponents… Expand

#### Figures and Tables from this paper

#### 232 Citations

On Nonlinear, Stochastic Dynamics in Economic and Financial Time Series

- Mathematics
- 2000

The search for deterministic chaos in economic and financial time series has attracted much interest over the past decade. Evidence of chaotic structures is usually blurred, however, by large random… Expand

The intrinsic predictability of ecological time series and its potential to guide forecasting

- Ecological Monographs
- 2019

Successfully predicting the future states of systems that are complex, stochastic, and potentially chaotic is a major challenge. Model forecasting error (FE) is the usual measure of success; however… Expand

The intrinsic predictability of ecological time series and its potential to guide forecasting

- Computer Science, Biology
- 2018

A theoretically-grounded basis for a model-free evaluation of a system’s intrinsic predictability is demonstrated and a correlation exists between estimated PE and FE and how stochasticity, process error, and chaotic dynamics affect the relationship is shown. Expand

Assessing the predictability of nonlinear dynamics under smooth parameter changes

- Computer Science, Medicine
- Journal of the Royal Society Interface
- 2020

This study shows that, in changing environments, the predictability of nonlinear dynamics can be associated with the time-varying stability of the system with respect to smooth changes in model parameters, i.e. its local structural stability. Expand

On non-linear , stochastic dynamics in economic and nancial time series

- 1999

The search for deterministic chaos in economic and nancial time series has attracted much interest over the past decade. However, clear evidence of chaotic structures is usually prevented by large… Expand

Detecting nonlinearity in run-up on a natural beach

- Computer Science
- 2007

Oscillatory data provide a similar challenge to differentiating chaotic signals from correlated noise in that the deterministic shape causes an additional source of autocorrelation which in turn influences the predictability at small forecasting distances. Expand

Uncovering nonlinear dynamics-the case study of sea clutter

- Computer Science
- Proc. IEEE
- 2002

Experimental results show that on timescales smaller than a few seconds, sea clutter is very well described as a complex autoregressive process of order four or five, and it is shown that the amount of frequency modulation is correlated with the nonlinearity of the clutter signal. Expand

Data-based prediction and causality inference of nonlinear dynamics

- Computer Science, Mathematics
- 2017

In this review, the development of statespace reconstruction techniques will be introduced and the recent advances in systems prediction and causality inference using state space reconstruction will be presented, particularly the cutting-edge method to deal with short-term time series data. Expand

Regularized local linear prediction of chaotic time series

- Mathematics
- 1998

Abstract Local linear prediction, based on the ordinary least squares (OLS) approach, is one of several methods that have been applied to prediction of chaotic time series. Apart from potential… Expand

Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems

- Physics
- 2016

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social… Expand

#### References

SHOWING 1-10 OF 54 REFERENCES

Nonlinear prediction as a way of distinguishing chaos from random fractal sequences

- Mathematics
- Nature
- 1992

NONLINEAR forecasting has recently been shown to distinguish between deterministic chaos and uncorrelated (white) noise added to periodic signals1, and can be used to estimate the degree of chaos in… Expand

Calculating the rate of loss of information from chaotic time series by forecasting

- Computer Science
- Nature
- 1991

A method for estimating from such forecasting the largest Liapunov exponent of the dynamics, which provides a measure of how chaotic the system is—that is, how rapidly information is lost from the system. Expand

Finding Chaos in Noisy Systems

- Mathematics
- 1992

In the past twenty years there has been much interest in the physical and biological sciences in nonlinear dynamical systems that appear to have random, unpredictable behavior. One important… Expand

Distinguishing error from chaos in ecological time series.

- Biology, Medicine
- Philosophical transactions of the Royal Society of London. Series B, Biological sciences
- 1990

It is shown that completely deterministic regulatory factors can lead to apparently random fluctuations in population density, and a new method is developed to make practical distinctions between apparently noisy dynamics produced by low-dimensional chaos and population variation that in fact derives from random (high-dimensional) noise. Expand

Coloured noise or low - dimensional chaos?

- Geography, Medicine
- Proceedings of the Royal Society of London. Series B: Biological Sciences
- 1992

The methodology confirms that, if there is in fact a chaotic signal in the measles data, it is extremely difficult to detect in time series of such limited length, and a nonlinear predictive scheme is found to be unable to differentiate between their characteristic time series. Expand

Using surrogate data to detect nonlinearity in time series

- Mathematics
- 1991

We address the issue of reliably discriminating between chaos and noise from a time series. In particular, we are interested in avoiding claims of chaos when simpler models (such as linearly… Expand

The analysis of observed chaotic data in physical systems

- Physics
- 1993

Chaotic time series data are observed routinely in experiments on physical systems and in observations in the field. The authors review developments in the extraction of information of physical… Expand

A Note on Noisy Chaos

- Mathematics
- 1994

SUMMARY We prove that, under appropriate conditions, in a noisy environment an embedded deterministic dynamical system which admits a compact attractor can give rise to an ergodic stochastic system.… Expand

Is there chaos in plankton dynamics

- Environmental Science
- 1993

A controversial issue in ecosystem modeling is whether the irregular fluctuations that one observes in nature are due solely to random environmental factors or whether, at least partially, a… Expand

The case for chaos in childhood epidemics. II. Predicting historical epidemics from mathematical models

- Geography, Medicine
- Proceedings of the Royal Society of London. Series B: Biological Sciences
- 1993

This paper compares the predictive abilities of stochastic models with those of mechanistic scenarios that admit to chaotic solutions, and concludes that simple mechanistic models are equal if not superior to more detailed schemes that include age structure. Expand