scholarly journals Reliable Estimation of Minimum Embedding Dimension Through Statistical Analysis of Nearest Neighbors

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
David Chelidze
Keyword(s):  
Time Series ◽  
Data Analysis ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Surrogate Data ◽  
Original Method ◽  
Random Time ◽  
Embedding Dimension ◽  
False Nearest Neighbors ◽  
Coordinate Embedding

False nearest neighbors (FNN) is one of the essential methods used in estimating the minimally sufficient embedding dimension in delay-coordinate embedding of deterministic time series. Its use for stochastic and noisy deterministic time series is problematic and erroneously indicates a finite embedding dimension. Various modifications to the original method have been proposed to mitigate this problem, but those are still not reliable for noisy time series. Here, nearest-neighbor statistics are studied for uncorrelated random time series and contrasted with the corresponding deterministic and stochastic statistics. New composite FNN metrics are constructed and their performance is evaluated for deterministic, correlates stochastic, and white random time series. In addition, noise-contaminated deterministic data analysis shows that these composite FNN metrics are robust to noise. All FNN results are also contrasted with surrogate data analysis to show their robustness. The new metrics clearly identify random time series as not having a finite embedding dimension and provide information about the deterministic part of correlated stochastic processes. These metrics can also be used to differentiate between chaotic and random time series.

Statistical Characterization of Nearest Neighbors to Reliably Estimate Minimum Embedding Dimension

2014 ◽  
Author(s):  
David Chelidze
Keyword(s):  
Time Series ◽  
Nearest Neighbor ◽  
Nearest Neighbors ◽  
Surrogate Data ◽  
Original Method ◽  
Random Time ◽  
Embedding Dimension ◽  
Statistical Characterization ◽  
False Nearest Neighbors ◽  
Coordinate Embedding

False nearest neighbors (FNN) is one of the essential methods used in estimating the minimally sufficient embedding dimension in delay coordinate embedding of deterministic time series. Its use for stochastic and noisy deterministic time series is problematic and erroneously indicates a finite embedding dimension. Various modifications to the original method have been proposed to mitigate this problem, but those are still not reliable for noisy time series. Nearest neighbor statistics are studied for uncorrelated random time series and contrasted with the deterministic statistics. A new FNN metric is constructed and its performance is evaluated for deterministic, stochastic, and random time series. The results are also contrasted with surrogate data analysis and show that the new metric is robust to noise. It also clearly identifies random time series as not having a finite embedding dimension and provides information about the deterministic part of stochastic processes. The new metric can also be used for differentiating between chaotic and random time series.

scholarly journals A New Adaptive Local Linear Prediction Method and Its Application in Hydrological Time Series

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Dunxian She ◽  
Xiaohua Yang
Keyword(s):  
Time Series ◽  
Linear Prediction ◽  
Nearest Neighbor ◽  
Prediction Method ◽  
Nearest Neighbors ◽  
New Method ◽  
Embedding Dimension ◽  
Optimal Parameters ◽  
Local Linear ◽  
Two Parameters

The embedding dimension and the number of nearest neighbors are very important parameters in the prediction of a chaotic time series. In order to reduce the uncertainties in the determination of the forgoing two parameters, a new adaptive local linear prediction method is proposed in this study. In the new method, the embedding dimension and the number of nearest neighbors are combined as a parameter set and change adaptively in the process of prediction. The generalized degree of freedom is used to help select the optimal parameters. Real hydrological time series are taken to examine the performance of the new method. The prediction results indicate that the new method can choose the optimal parameters of embedding dimension and the nearest neighbor number adaptively in the prediction process. And the nonlinear hydrological time series perhaps could be modeled better by the new method.

ON THE RELIABILITY OF THE SURROGATE DATA TEST FOR NONLINEARITY IN THE ANALYSIS OF NOISY TIME SERIES

2001 ◽  
Vol 11 (07) ◽  
pp. 1881-1896 ◽  
Author(s):  
D. KUGIUMTZIS
Keyword(s):  
Time Series ◽  
Null Hypothesis ◽  
Volterra Series ◽  
Simulated Data ◽  
Real Data ◽  
Surrogate Data ◽  
Largest Lyapunov Exponent ◽  
Real World Data ◽  
Original Time ◽  
False Nearest Neighbors

In the analysis of real world data, the surrogate data test is often performed in order to investigate nonlinearity in the data. The null hypothesis of the test is that the original time series is generated from a linear stochastic process possibly undergoing a nonlinear static transform. We argue against reported rejection of the null hypothesis and claims of evidence of nonlinearity based on a single nonlinear statistic. In particular, two schemes for the generation of surrogate data are examined, the amplitude adjusted Fourier transform (AAFT) and the iterated AAFT (IAFFT) and many nonlinear discriminating statistics are used for testing, i.e. the fit with the Volterra series of polynomials and the fit with local average mappings, the mutual information, the correlation dimension, the false nearest neighbors, the largest Lyapunov exponent and simple nonlinear averages (the three point autocorrelation and the time reversal asymmetry). The results on simulated data and real data (EEG and exchange rates) suggest that the test depends on the method and its parameters, the algorithm generating the surrogate data and the observational data of the examined process.

Forecasting Volatility in Financial Markets

2010 ◽  
Vol 439-440 ◽  
pp. 679-682
Author(s):  
Hong Zhang ◽  
Shu Fang Li
Keyword(s):  
Financial Markets ◽  
Nearest Neighbors ◽  
September 11 ◽  
Experimental Results ◽  
Nearest Neighbour ◽  
Embedding Dimension ◽  
Traditional Methods ◽  
Modified Method ◽  
Forecasting Volatility ◽  
False Nearest Neighbors

In this paper, we analyze the stock of Tsingtao Brewery Co Ltd for the 8-year period, from July 31, 2001, to September 11, 2009, a total of 2003 trading days. Using the False Nearest Neighbors method, we obtain the embedding dimension m in the k-nearest neighbour Algorithm. In order to investigate the validity of this method, we apply the modified method to the daily adjusted opening values of the Tsingtao Brewery Co Ltd. We find that the prediction of experimental results is more accurate than traditional methods.

LONG RANGE TIME SERIES FORECASTING BY UPSAMPLING AND USING CROSS-CORRELATION BASED SELECTION OF NEAREST NEIGHBOR

2006 ◽  
Vol 20 (08) ◽  
pp. 1261-1278 ◽  
Author(s):  
SYED RAHAT ABBAS ◽  
MUHAMMAD ARIF
Keyword(s):  
Time Series ◽  
Long Range ◽  
Euclidean Distance ◽  
Cross Correlation ◽  
Nearest Neighbor ◽  
Time Series Forecasting ◽  
Embedding Dimension ◽  
Auto Correlation Function ◽  
Original Time ◽  
Selection Of

Long range or multistep-ahead time series forecasting is an important issue in various fields of business, science and technology. In this paper, we have proposed a modified nearest neighbor based algorithm that can be used for long range time series forecasting. In the original time series, optimal selection of embedding dimension that can unfold the dynamics of the system is improved by using upsampling of the time series. Zeroth order cross-correlation and Euclidian distance criterion are used to select the nearest neighbor from up-sampled time series. Embedding dimension size and number of candidate vectors for nearest neighbor selection play an important role in forecasting. The size of embedding is optimized by using auto-correlation function (ACF) plot of the time series. It is observed that proposed algorithm outperforms the standard nearest neighbor algorithm. The cross-correlation based criteria shows better performance than Euclidean distance criteria.

False-nearest-neighbors algorithm and noise-corrupted time series

1997 ◽  
Vol 55 (5) ◽  
pp. 6162-6170 ◽  
Author(s):  
Carl Rhodes ◽  
Manfred Morari
Keyword(s):  
Time Series ◽  
Nearest Neighbors ◽  
False Nearest Neighbors
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