Testing for nonlinearity in European climatic time series by the method of surrogate data

2005 ◽  
Vol 83 (1-4) ◽  
pp. 21-33 ◽  
Author(s):  
J. Mikšovský ◽  
A. Raidl
Keyword(s):  
Time Series ◽  
Surrogate Data ◽  
Climatic Time Series

scholarly journals Nonlinear analysis of magnetospheric data Part I. Geometric characteristics of the AE index time series and comparison with nonlinear surrogate data

1999 ◽  
Vol 6 (1) ◽  
pp. 51-65 ◽  
Author(s):  
G. P. Pavlos ◽  
M. A. Athanasiu ◽  
D. Kugiumtzis ◽  
N. Hatzigeorgiu ◽  
A. G. Rigas ◽  
...  
Keyword(s):  
Time Series ◽  
State Space ◽  
Null Hypothesis ◽  
Surrogate Data ◽  
Statistical Testing ◽  
Geometrical Parameters ◽  
Geometric Characteristics ◽  
Geometrical Characteristics ◽  
Ae Index ◽  
Index Time Series

Abstract. A long AE index time series is used as a crucial magnetospheric quantity in order to study the underlying dynainics. For this purpose we utilize methods of nonlinear and chaotic analysis of time series. Two basic components of this analysis are the reconstruction of the experimental tiine series state space trajectory of the underlying process and the statistical testing of an null hypothesis. The null hypothesis against which the experimental time series are tested is that the observed AE index signal is generated by a linear stochastic signal possibly perturbed by a static nonlinear distortion. As dis ' ' ating statistics we use geometrical characteristics of the reconstructed state space (Part I, which is the work of this paper) and dynamical characteristics (Part II, which is the work a separate paper), and "nonlinear" surrogate data, generated by two different techniques which can mimic the original (AE index) signal. lie null hypothesis is tested for geometrical characteristics which are the dimension of the reconstructed trajectory and some new geometrical parameters introduced in this work for the efficient discrimination between the nonlinear stochastic surrogate data and the AE index. Finally, the estimated geometric characteristics of the magnetospheric AE index present new evidence about the nonlinear and low dimensional character of the underlying magnetospheric dynamics for the AE index.

scholarly journals An Efficient Prediction Model for Water Discharge in Schoharie Creek, NY

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Katerina G. Tsakiri ◽  
Antonios E. Marsellos ◽  
Igor G. Zurbenko
Keyword(s):  
New York ◽  
Time Series ◽  
Water Discharge ◽  
Winter Period ◽  
Statistical Methodology ◽  
Summer Period ◽  
Short Term ◽  
Efficient Prediction ◽  
Climatic Time Series

Flooding normally occurs during periods of excessive precipitation or thawing in the winter period (ice jam). Flooding is typically accompanied by an increase in river discharge. This paper presents a statistical model for the prediction and explanation of the water discharge time series using an example from the Schoharie Creek, New York (one of the principal tributaries of the Mohawk River). It is developed with a view to wider application in similar water basins. In this study a statistical methodology for the decomposition of the time series is used. The Kolmogorov-Zurbenko filter is used for the decomposition of the hydrological and climatic time series into the seasonal and the long and the short term component. We analyze the time series of the water discharge by using a summer and a winter model. The explanation of the water discharge has been improved up to 81%. The results show that as water discharge increases in the long term then the water table replenishes, and in the seasonal term it depletes. In the short term, the groundwater drops during the winter period, and it rises during the summer period. This methodology can be applied for the prediction of the water discharge at multiple sites.

scholarly journals Revisiting Climate Region Definitions via Clustering

2009 ◽  
Vol 22 (7) ◽  
pp. 1787-1800 ◽  
Author(s):  
Robert Lund ◽  
Bo Li
Keyword(s):  
Time Series ◽  
Clustering Methods ◽  
Distance Metric ◽  
Climatic Zones ◽  
Time Series Clustering ◽  
Climate Region ◽  
Covariate Effects ◽  
Weather Stations ◽  
Climatic Time Series ◽  
Natural Way

Abstract This paper introduces a new distance metric that enables the clustering of general climatic time series. Clustering methods have been frequently used to partition a domain of interest into distinct climatic zones. However, previous techniques have neglected the time series (autocorrelation) component and have also handled seasonal features in a suboptimal way. The distance proposed here incorporates the seasonal mean and autocorrelation structures of the series in a natural way; moreover, trends and covariate effects can be considered. As an important by-product, the methods can be used to statistically assess whether two stations can serve as reference stations for one another. The methods are illustrated by partitioning 292 weather stations within the state of Colorado into six different zones.

scholarly journals Chaotic Patterns in Aeroelastic Signals

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
F. D. Marques ◽  
R. M. G. Vasconcellos
Keyword(s):  
Time Series ◽  
State Space ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Separated Flow ◽  
Direct Analysis ◽  
Surrogate Data ◽  
The State ◽  
Aeroelastic System ◽  
Value Decomposition

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

scholarly journals APPLICATION OF CHAOS GAME REPRESENTATION TO NONLINEAR TIME SERIES ANALYSIS

Fractals ◽  
2006 ◽  
Vol 14 (01) ◽  
pp. 27-35 ◽  
Author(s):  
TOMOYA SUZUKI ◽  
TOHRU IKEGUCHI ◽  
MASUO SUZUKI
Keyword(s):  
Time Series ◽  
Real Time ◽  
Dna Sequences ◽  
Surrogate Data ◽  
Nonlinear Time Series Analysis ◽  
Conditional Probabilities ◽  
Fractal Structures ◽  
Chaos Game Representation ◽  
Chaos Game ◽  
Game Representation

Iterative function systems are often used for investigating fractal structures. The method is also referred as Chaos Game Representation (CGR), and is applied for representing characteristic structures of DNA sequences visually. In this paper, we proposed an original way of plotting CGR to easily confirm the property of the temporal evaluation of a time series. We also showed existence of spurious characteristic structures of time series, if we carelessly applied the CGR to real time series. We revealed that the source of spurious identification came from non-uniformity of the frequency histograms of the time series, which is often the case of analyzing real time series. We also showed how to avoid such spurious identification by applying the method of surrogate data and introducing conditional probabilities of the time series.

scholarly journals Quantifying Statistical Interdependence by Message Passing on Graphs—Part I: One-Dimensional Point Processes

2009 ◽  
Vol 21 (8) ◽  
pp. 2152-2202 ◽  
Author(s):  
J. Dauwels ◽  
F. Vialatte ◽  
T. Weber ◽  
A. Cichocki
Keyword(s):  
Time Series ◽  
Message Passing ◽  
Point Processes ◽  
Pairwise Alignment ◽  
Surrogate Data ◽  
Map Estimation ◽  
One Dimensional ◽  
Novel Approach ◽  
Average Similarity ◽  
Stochastic Event

We present a novel approach to quantify the statistical interdependence of two time series, referred to as stochastic event synchrony (SES). The first step is to extract “events” from the two given time series. The next step is to try to align events from one time series with events from the other. The better the alignment, the more similar the two time series are considered to be. More precisely, the similarity is quantified by the following parameters: time delay, variance of the timing jitter, fraction of noncoincident events, and average similarity of the aligned events. The pairwise alignment and SES parameters are determined by statistical inference. In particular, the SES parameters are computed by maximum a posteriori (MAP) estimation, and the pairwise alignment is obtained by applying the max-product algorithm. This letter deals with one-dimensional point processes; the extension to multidimensional point processes is considered in a companion letter in this issue. By analyzing surrogate data, we demonstrate that SES is able to quantify both timing precision and event reliability more robustly than classical measures can. As an illustration, neuronal spike data generated by the Morris-Lecar neuron model are considered.

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