The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Boris Podobnik - One of the best experts on this subject based on the ideXlab platform.
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detrended cross correlation analysis for non Stationary Time Series with periodic trends
EPL, 2011Co-Authors: Davor Horvatic, H E Stanley, Boris PodobnikAbstract:Noisy signals in many real-world systems display long-range autocorrelations and long-range cross-correlations. Due to periodic trends, these correlations are difficult to quantify. We demonstrate that one can accurately quantify power-law cross-correlations between different simultaneously recorded Time Series in the presence of highly non-Stationary sinusoidal and polynomial overlying trends by using the new technique of detrended cross-correlation analysis with varying order l of the polynomial. To demonstrate the utility of this new method —which we call DCCA-l(n), where n denotes the scale— we apply it to meteorological data.
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detrended cross correlation analysis a new method for analyzing two non Stationary Time Series
Research Papers in Economics, 2007Co-Authors: Boris Podobnik, Eugene H StanleyAbstract:Here we propose a method, based on detrended covariance which we call detrended cross-correlation analysis (DXA), to investigate power-law cross-correlations between different simultaneously-recorded Time Series in the presence of non-stationarity. We illustrate the method by selected examples from physics, physiology, and finance.
Pushpendra Singh - One of the best experts on this subject based on the ideXlab platform.
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novel fourier quadrature transforms and analytic signal representations for nonlinear and non Stationary Time Series analysis
arXiv: Signal Processing, 2018Co-Authors: Pushpendra SinghAbstract:The Hilbert transform (HT) and associated Gabor analytic signal (GAS) representation are well-known and widely used mathematical formulations for modeling and analysis of signals in various applications. In this study, like the HT, to obtain quadrature component of a signal, we propose the novel discrete Fourier cosine quadrature transforms (FCQTs) and discrete Fourier sine quadrature transforms (FSQTs), designated as Fourier quadrature transforms (FQTs). Using these FQTs, we propose sixteen Fourier-Singh analytic signal (FSAS) representations with following properties: (1) real part of eight FSAS representations is the original signal and imaginary part is the FCQT of the real part, (2) imaginary part of eight FSAS representations is the original signal and real part is the FSQT of the real part, (3) like the GAS, Fourier spectrum of the all FSAS representations has only positive frequencies, however unlike the GAS, the real and imaginary parts of the proposed FSAS representations are not orthogonal to each other. The Fourier decomposition method (FDM) is an adaptive data analysis approach to decompose a signal into a set of small number of Fourier intrinsic band functions which are AM-FM components. This study also proposes a new formulation of the FDM using the discrete cosine transform (DCT) with the GAS and FSAS representations, and demonstrate its efficacy for improved Time-frequency-energy representation and analysis of nonlinear and non-Stationary Time Series.
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the fourier decomposition method for nonlinear and non Stationary Time Series analysis
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2017Co-Authors: Pushpendra Singh, Shiv Dutt Joshi, R K Patney, Kaushik SahaAbstract:for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-Stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-Stationary Time Series. The proposed FDM decomposes any data into a small number of ‘Fourier intrinsic band functions’ (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a Time Series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-Stationary Time Series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a Time–frequency–energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
P H Algoet - One of the best experts on this subject based on the ideXlab platform.
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weakly convergent nonparametric forecasting of Stationary Time Series
arXiv: Statistics Theory, 2008Co-Authors: Gusztav Morvai, Sidney Yakowitz, P H AlgoetAbstract:The conditional distribution of the next outcome given the infinite past of a Stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but they all demand prohibitive amounts of input data. In this paper we consider real-valued Time Series and construct conditional distribution estimates that make much more efficient use of the input data. The estimates are consistent in a weak sense, and the question whether they are pointwise consistent is still open. For finite-alphabet processes one may rely on a universal data compression scheme like the Lempel-Ziv algorithm to construct conditional probability mass function estimates that are consistent in expected information divergence. Consistency in this strong sense cannot be attained in a universal sense for all Stationary processes with values in an infinite alphabet, but weak consistency can. Some applications of the estimates to on-line forecasting, regression and classification are discussed.
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weakly convergent nonparametric forecasting of Stationary Time Series
IEEE Transactions on Information Theory, 1997Co-Authors: Gusztav Morvai, Sidney Yakowitz, P H AlgoetAbstract:The conditional distribution of the next outcome given the infinite past of a Stationary process can be inferred from finite but growing segments of the past. Several schemes are known for constructing pointwise consistent estimates, but they all demand prohibitive amounts of input data. We consider real-valued Time Series and construct conditional distribution estimates that make much more efficient use of the input data. The estimates are consistent in a weak sense, and the question whether they are pointwise-consistent is still open. For finite-alphabet processes one may rely on a universal data compression scheme like the Lempel-Ziv (1978) algorithm to construct conditional probability mass function estimates that are consistent in expected information divergence. Consistency in this strong sense cannot be attained in a universal sense for all Stationary processes with values in an infinite alphabet, but weak consistency can. Some applications of the estimates to on-line forecasting, regression, and classification are discussed.
Dimitris N Politis - One of the best experts on this subject based on the ideXlab platform.
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predictive inference for locally Stationary Time Series with an application to climate data
Journal of the American Statistical Association, 2020Co-Authors: Srinjoy Das, Dimitris N PolitisAbstract:The model-free prediction principle of Politis has been successfully applied to general regression problems, as well as problems involving Stationary Time Series. However, with long Time Series, fo...
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predictive inference for locally Stationary Time Series with an application to climate data
arXiv: Methodology, 2017Co-Authors: Srinjoy Das, Dimitris N PolitisAbstract:The Model-free Prediction Principle of Politis (2015) has been successfully applied to general regression problems, as well as problems involving Stationary Time Series. However, with long Time Series, e.g. annual temperature measurements spanning over 100 years or daily financial returns spanning several years, it may be unrealistic to assume stationarity throughout the span of the dataset. In the paper at hand, we show how Model-free Prediction can be applied to handle Time Series that are only locally Stationary, i.e., they can be assumed to be as Stationary only over short Time-windows. Surprisingly there is little literature on point prediction for general locally Stationary Time Series even in model-based setups and there is no literature on the construction of prediction intervals of locally Stationary Time Series. We attempt to fill this gap here as well. Both one-step-ahead point predictors and prediction intervals are constructed, and the performance of model-free is compared to model-based prediction using models that incorporate a trend and/or heteroscedasticity. Both aspects of the paper, model-free and model-based, are novel in the context of Time-Series that are locally (but not globally) Stationary. We also demonstrate the application of our Model-based and Model-free prediction methods to speleothem climate data which exhibits local stationarity and show that our best model-free point prediction results outperform that obtained with the RAMPFIT algorithm previously used for analysis of this data.
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predictive inference for locally Stationary Time Series
2015Co-Authors: Dimitris N PolitisAbstract:The Model-free Prediction Principle of Politis (Test 22(2):183–250, 2013) has been successfully applied to both regression problems, as well as problems involving Stationary Time Series. However, with long Time Series, e.g., annual temperature measurements spanning over 100 years or daily financial returns spanning several years, it may be unrealistic to assume stationarity throughout the span of the dataset. In the paper at hand, we show how Model-free Prediction can be applied to handle Time Series that are only locally Stationary, i.e., they can be modeled as Stationary only over short Time-windows. Both one-step-ahead point predictors and prediction intervals are constructed and compared.
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high dimensional autocovariance matrices and optimal linear prediction
Electronic Journal of Statistics, 2015Co-Authors: Timothy L Mcmurry, Dimitris N PolitisAbstract:A new methodology for optimal linear prediction of a Stationary Time Series is introduced. Given a sample X1;:::;Xn, the optimal linear predictor of Xn+1 is ~ Xn+1 = 1(n)Xn +
Jari Miettinen - One of the best experts on this subject based on the ideXlab platform.
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separation of uncorrelated Stationary Time Series using autocovariance matrices
Journal of Time Series Analysis, 2016Co-Authors: Jari Miettinen, Katrin Illner, Klaus Nordhausen, Hannu Oja, Sara Taskinen, Fabian J TheisAbstract:In blind source separation, one assumes that the observed p Time Series are linear combinations of p latent uncorrelated weakly Stationary Time Series. To estimate the unmixing matrix, which transforms the observed Time Series back to uncorrelated latent Time Series, second-order blind identification (SOBI) uses joint diagonalization of the covariance matrix and autocovariance matrices with several lags. In this article, we find the limiting distribution of the well-known symmetric SOBI estimator under general conditions and compare its asymptotical efficiencies to those of the recently introduced deflation-based SOBI estimator. The theory is illustrated by some finite-sample simulation studies.
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separation of uncorrelated Stationary Time Series using autocovariance matrices
arXiv: Statistics Theory, 2014Co-Authors: Jari Miettinen, Katrin Illner, Klaus Nordhausen, Hannu Oja, Sara Taskinen, Fabian J TheisAbstract:Blind source separation (BSS) is a signal processing tool, which is widely used in various fields. Examples include biomedical signal separation, brain imaging and economic Time Series applications. In BSS, one assumes that the observed $p$ Time Series are linear combinations of $p$ latent uncorrelated weakly Stationary Time Series. The aim is then to find an estimate for an unmixing matrix, which transforms the observed Time Series back to uncorrelated latent Time Series. In SOBI (Second Order Blind Identification) joint diagonalization of the covariance matrix and autocovariance matrices with several lags is used to estimate the unmixing matrix. The rows of an unmixing matrix can be derived either one by one (deflation-based approach) or simultaneously (symmetric approach). The latter of these approaches is well-known especially in signal processing literature, however, the rigorous analysis of its statistical properties has been missing so far. In this paper, we fill this gap and investigate the statistical properties of the symmetric SOBI estimate in detail and find its limiting distribution under general conditions. The asymptotical efficiencies of symmetric SOBI estimate are compared to those of recently introduced deflation-based SOBI estimate under general multivariate MA$(\infty)$ processes. The theory is illustrated by some finite-sample simulation studies as well as a real EEG data example.
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deflation based separation of uncorrelated Stationary Time Series
Journal of Multivariate Analysis, 2014Co-Authors: Jari Miettinen, Klaus Nordhausen, Sara TaskinenAbstract:In this paper we assume that the observed p Time Series are linear combinations of p latent uncorrelated weakly Stationary Time Series. The problem is then to find an estimate for an unmixing matrix that transforms the observed Time Series back to uncorrelated Time Series. The so called SOBI (Second Order Blind Identification) estimate aims at a joint diagonalization of the covariance matrix and several autocovariance matrices with varying lags. In this paper, we propose a novel procedure that extracts the latent Time Series one by one. The limiting distribution of this deflation-based SOBI is found under general conditions, and we show how the results can be used for the comparison of estimates. The exact formula for the limiting covariance matrix of the deflation-based SOBI estimate is given for general multivariate MA(~) processes. Finally, a whole family of estimates is proposed with the deflation-based SOBI as a special case, and the limiting properties of these estimates are found as well. The theory is widely illustrated by simulation studies.
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statistical properties of a blind source separation estimator for Stationary Time Series
Statistics & Probability Letters, 2012Co-Authors: Jari Miettinen, Klaus Nordhausen, Hannu Oja, Sara TaskinenAbstract:Abstract In this paper, we assume that the observed p Time Series are linear combinations of p latent uncorrelated weakly Stationary Time Series. The problem is then, using the observed p -variate Time Series, to find an estimate for a mixing or unmixing matrix for the combinations. The estimated uncorrelated Time Series may then have nice interpretations and can be used in a further analysis. The popular AMUSE algorithm finds an estimate of an unmixing matrix using covariances and autocovariances of the observed Time Series. In this paper, we derive the limiting distribution of the AMUSE estimator under general conditions, and show how the results can be used for the comparison of estimates. The exact formula for the limiting covariance matrix of the AMUSE estimate is given for general MA ( ∞ ) processes.
