Non-stationary Correlation Research Articles

Optimal and Sub-Optimal Spectrum Sensing of OFDM Signals in Known and Unknown Noise Variance

We consider spectrum sensing of OFDM signals in an AWGN channel. For the case of completely known noise and signal powers, we set up a vector-matrix model for an OFDM signal with a cyclic prefix and derive the optimal Neyman-Pearson detector from first principles. The optimal detector exploits the inherent correlation of the OFDM signal incurred by the repetition of data in the cyclic prefix, using knowledge of the length of the cyclic prefix and the length of the OFDM symbol. We compare the optimal detector to the energy detector numerically. We show that the energy detector is near-optimal (within 1 dB SNR) when the noise variance is known. Thus, when the noise power is known, no substantial gain can be achieved by using any other detector than the energy detector. For the case of completely unknown noise and signal powers, we derive a generalized likelihood ratio test (GLRT) based on empirical second-order statistics of the received data. The proposed GLRT detector exploits the non-stationary correlation structure of the OFDM signal and does not require any knowledge of the noise power or the signal power. The GLRT detector is compared to state-of-the-art OFDM signal detectors, and shown to improve the detection performance with 5 dB SNR in relevant cases.

IMPROVED AND EXTENDED END-OF-SAMPLE INSTABILITY TESTS USING A FEASIBLE QUASI-GENERALIZED LEAST SQUARES PROCEDURE

This paper extends the Andrews (2002, Econometrica 71, 1661–1694) and Andrews and Kim (2006, Journal of Business & Economic Statistics 24, 379–394) ordinary least squares–based end-of-sample instability tests for linear regression models. The author proposes to quasi-difference the data first using a consistent estimate of the sum of the autoregressive coefficients of the error process and then test for the end-of-sample instability. For the cointegration model, the feasible quasi-generalized least squares (FQGLS) version of the Andrews and Kim (2006) P test is considered and is shown, by simulations, to be more robust to serial correlation in the error process and to have power no less than Andrews and Kim’s original test. For the linear time trend model, the FQGLS version of the Andrews (2002) S test is considered with the error process allowed to be nonstationary up to one unit root, and the new test is shown to be robust to potentially nonstationary serial correlation. A simulation study also shows that the finite-sample properties of the proposed test can be further improved when the Andrews (1993, Econometrica 61,139–165) or Andrews and Chen (1994, Journal of Business & Economic Statistics 12, 187–204) median unbiased estimate of the sum of the autoregressive coefficients is used.

On the non-reducibility of non-stationary correlation functions to stationary ones under a class of mean-operator transformations

Some special functional equations involving means and related to a problem of reducibility of some classes of correlation functions are considered. We show some characterizations of the reducibility problem under several choices of the mean operators and different weak regularity assumptions imposed on the involving functions. We find that mean-generated correlation functions are completely irreducible, in the sense that, for this broad class of correlation functions, there does not exist a non-trivial solution associated to the Perrin–Senoussi problem.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on 1/6/2010orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Interdecadal modulation of the relationship between ENSO, IPO and precipitation: insights from tree rings in Australia

Australian climate-proxy reconstructions based on tree rings from tropical and subtropical forests have not been achieved so far due to the rarity of species producing anatomically distinct annual growth rings. Our study identifies the Australian Red Cedar (Toona ciliata) as one of the most promising tree species for tree-ring research in Australasia because this species exhibits distinct annual tree rings, a prerequisite for high quality tropical dendroclimatology. Based on these preliminary studies, we were able, for the first time in subtropical and tropical Australia, to develop a statistically robust, precisely dated and annually resolved chronology back to AD1854. We show that the variability in ring widths of T. ciliata is mainly dependent on annual precipitation. The developed proxy data series contains both high- and low-frequency climate signals which can be associated with the El Niño Southern Oscillation (ENSO) and the Interdecadal Pacific Oscillation (IPO). A comparison of different data sets (Brisbane precipitation, tree rings, coral luminescence record from the Great Barrier Reef, ENSO and IPO) revealed non-stationary correlation patterns throughout the twentieth century but little instability between the new tree-ring chronology and Brisbane precipitation.

Detection of non-stationary higher-order spike correlation

Event Abstract Back to Event Detection of non-stationary higher-order spike correlation Precise spike coordination in the spiking activities of a neuronal population is discussed as an indication of coordinated network activity in form of a cell assembly relevant for information processing. Supportive evidence for its relevance in behavior was provided by the existence of excess spike synchrony occurring dynamically in relation to behavioral context [e.g. Riehle et. al., Science (278) 1950-1953, 1997]. This finding was based on the null-hypothesis of full independence. However, one can assume that neurons jointly involved in assemblies express higher-order correlation (HOC) between their activities. Previous work on HOC assumed stationary condition. Here we aim at analyzing simultaneous spike trains for time-dependent HOCs to trace active assemblies. We suggest to estimate the dynamics of HOCs by means of a state-space analysis with a log-linear observation model. A log-linear representation of the parallel spikes provides a well-defined measure of HOC based on information geometry (Amari, IEEE Trans. Inf. Theory (47) 1701-1711, 2001). We developed a nonlinear recursive filtering/smoothing algorithm for the time-varying log-linear model by applying a log-quadratic approximation to its posterior distribution. The time-scales of each parameter and their covariation are automatically optimized via the EM-algorithm under the maximum likelihood principle. To obtain the most predictive model, we compare the goodness-of-fit of hierarchical log-linear models with different order of interactions using the Akaike information criterion (AIC; Akaike, IEEE Trans. Autom. Control (19) 716-723, 1974). While inclusion of increasingly higher-order interaction terms improves model accuracy, estimation of higher-order parameters suffers from large variances due to the paucity of synchronous spikes in the data. This bias-variance trade-off is optimally resolved with the model that minimizes the AIC. Complexity of the model is thus selected based on the sample size of the data and the prominence of the higher-order structure. Application of the proposed method to simultaneous recordings of neuronal activity is expected to provide us with new insights into the dynamics of assembly activities, their composition, and behavioral relevance. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). Detection of non-stationary higher-order spike correlation. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.019 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 29 Jan 2009; Published Online: 29 Jan 2009. Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Google Google Scholar PubMed Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Identification of Modal Parameters from Nonstationary Ambient Vibration Data Using Correlation Technique

Identification of modal parameters is considered from response data of structural systems under nonstationary ambient vibration. It is shown theoretically that by assuming the ambient excitation to be nonstationary white noise in the form of a product model, the nonstationary response signals can be converted into free-vibration data via the correlation technique. The practical problem of insufficient data samples available for evaluating nonstationary correlation can be approximately resolved by first extracting the amplitude-modulating function from the response and then transforming the nonstationary responses into stationary ones. Modal-parameter identification can then be performed using the Ibrahim time-domain technique, which is effective at identifying closely spaced modes. The theory proposed can be further extended by using the filtering concept to cover the case of nonstationary color excitations. Numerical simulations confirm the validity of the proposed method for identification of modal parameters from nonstationary ambient response data.

Longitudinal Models for Non-Stationary Exponential Data

In many manufacturing studies, longitudinal failure time data comprise repeated exponential responses, and a set of multi-dimensional covariates for a large number of independent components or objects. When the covariates collected along with exponential failure times are time dependent, the responses of an object exhibit non-stationary correlations. We examine the effects of the covariates by taking this non-stationary correlation structure into account. First, we develop Gaussian type non-stationary AR(1), MA(1), and exchangeable correlation structures for the repeated exponential failure times; and then exploit the suitable auto-correlation structure to obtain consistent, efficient estimates for the effects of the covariates by using a generalized quasi-likelihood (GQL) estimating equation approach. The finite sample estimation performance of the GQL approach is examined through a simulation study.

On a Unified Generalized Quasi-likelihood Approach for Familial-Longitudinal Non-Stationary Count Data

In this paper, conditional on random family effects, we consider an auto-regres- sion model for repeated count data and their corresponding time-dependent covariates, collected from the members of a large number of independent families. The count responses, in such a set up, unconditionally exhibit a non-stationary familial-longitudinal correlation structure. We then take this two-way correlation structure into account, and develop a generalized quasilikelihood (GQL) approach for the estimation of the regression effects and the familial correlation index para- meter, whereas the longitudinal correlation parameter is estimated by using the well-known method of moments. The performance of the proposed estimation approach is examined through a simula- tion study. Some model mis-specification effects are also studied. The estimation methodology is illustrated by analysing real life healthcare utilization count data collected from 36 families of size four over a period of 4 years.

Non-stationary correlation matrices and noise

The exact meaning of the noise spectrum of eigenvalues of the correlation matrix is discussed. In order to better understand the possible phenomena behind the observed noise, the spectrum of eigenvalues of the correlation matrix is studied under a model where most of the true eigenvalues are zero and the parameters are non-stationary. The results are compared with real observation of Brazilian assets, suggesting that, although the non-stationarity seems to be an important aspect of the problem, partially explaining some of the eigenvalues as well as part of the kurtosis of the assets, it cannot, by itself, provide all the corrections needed to make the proposed model fit the data perfectly.

Nonstationary probabilities and time correlation functions for an asymmetric exclusion process

We give the complete solution of the master equation for a system of interacting particles with finite density. We obtain the solution using a new form of the Bethe ansatz for an asymmetric simple exclusion process on the ring. We first find the one-point time correlation function for the discrete version of the process.

A translation model for non-stationary, non-Gaussian random processes

A model for simulation of non-stationary, non-Gaussian processes based on non-linear translation of Gaussian random vectors is presented. This method is a generalization of traditional translation processes that includes the capability of simulating samples with spatially or temporally varying marginal probability density functions. A formal development of the properties of the resulting process includes joint probability density function, correlation distortion and lower and upper bounds that depend on the target marginal distributions. Examples indicate the possibility of exactly matching a wide range of marginal pdfs and second order moments through a simple interpolating algorithm. Furthermore, the application of the method in simulating statistically inhomogeneous random media is investigated, using the specific case of binary translation with stationary and non-stationary target correlations.

Nonequilibrium critical dynamics in inhomogeneous systems

We study nonequilibrium dynamical properties of inhomogeneous systems, in particular at a free surface or at a defect plane. Thereby we consider nonconserved (model-A) dynamics of a system which is prepared in the high-temperature phase and quenched into the critical point. Using Monte Carlo simulations we measure single spin relaxation and autocorrelations, as well as manifold autocorrelations and persistence. We show that, depending on the decay of critical static correlations, the short time dynamics can be of two kinds. For slow decay of local correlations the usual domain growth process takes place with non-stationary and algebraic dynamical correlations. If, however, the local correlations decay sufficiently rapidly we have the so called cluster dissolution scenario, in which case short time dynamical correlations are stationary and have a universal stretched exponential form. This latter phenomenon takes place in the surface of the three-dimensional Ising model and should be observable in real ferromagnets.

OPL181 Pre-ictal desynchronization in a model of temporal lobe epilepsy: Application of non-stationary amplitude and phase correlation techniques

OPL181 Pre-ictal desynchronization in a model of temporal lobe epilepsy: Application of non-stationary amplitude and phase correlation techniques

Estimates of covariance functions for growth of Nelore cattle applying a parametric correlation structure to model within-animal correlations

A total of 20,065 weights recorded on 3016 Nelore animals were used to estimate covariance functions for growth from birth to 630 days of age, assuming a parametric correlation structure to model within-animal correlations. The model of analysis included fixed effects of contemporary groups and age of dam as quadratic covariable. Mean trends were taken into account by a cubic regression on orthogonal polynomials of animal age. Genetic effects of the animal and its dam and maternal permanent environmental effects were modelled by random regressions on Legendre polynomials of age at recording. Changes in direct permanent environmental effect variances were modelled by a polynomial variance function, together with a parametric correlation function to account for correlations between ages. Stationary and nonstationary models were used to model within-animal correlations between different ages. Residual variances were considered homogeneous or heterogeneous, with changes modelled by a step or polynomial function of age at recording. Based on Bayesian information criterion, a model with a cubic variance function combined with a nonstationary correlation function for permanent environmental effects, with 49 parameters to be estimated, fitted best. Modelling within-animal correlations through a parametric correlation structure can describe the variation pattern adequately. Moreover, the number of parameters to be estimated can be decreased substantially compared to a model fitting random regression on Legendre polynomial of age.

Spatially adaptive denoising based on nonstationary correlation assumption

Earlier techniques used for noise filtering were global filters based on the assumption of a stationary image model. Although the stationarity assumption enables the use of the Fast Fourier transform (FFT)-based algorithm, such filters tend to oversmooth edges where stationarity is not satisfied. Recently, various noise smoothing algorithms based on the nonstationary image model have been proposed to overcome this problem. In most conventional nonstationary image models, however, pixels are assumed to be uncorrelated to each other in order not to increase a computational burden too much. As a result, some detailed information is lost in the filtered results. We propose a computationally feasible adaptive noise smoothing algorithm that considers the nonstationary correlation characteristics of images. We assume that an image has a nonstationary mean and can be segmented into subimages that have individually different stationary correlations. Taking advantage of the special structure of the covariance matrix that results from the proposed image model, we derive a computationally efficient FFT-based adaptive linear minimum mean-square-error filter for cases of signal uncorrelated additive, multiplicative, and film-grain noises. The justification for the proposed image model is presented, and the effectiveness of the proposed algorithm is demonstrated experimentally.

Variance modeling for nonstationary spatial processes with temporal replications

We have previously formulated a Bayesian approach to the Sampson and Guttorp model for the nonstationary correlation function r(x, x′) of a Gaussian spatial process [Damian et al., 2001]. This model assumes that the nonstationarity can be encoded through a bijective space deformation, f, that defines a new coordinate system in which the spatial correlation function can be considered isotropic, namely r(x, x′) = ρ(∥f(x) − f(x′)∥), where ρ belongs to a known parametric family. We extend this model to incorporate spatial heterogeneity in site‐specific temporal variances. In our Bayesian framework the variances are considered (hidden) realizations of another spatial process, which we model as log‐Gaussian, with correlation structure expressed in terms of the same spatial deformation function underlying that of the observed process. We demonstrate the method in simulations and in an application.

A Stochastic Geometry Model for Functional Magnetic Resonance Images

In functional magnetic resonance imaging, spatial activation patterns are commonly estimated using a non‐parametric smoothing approach. Significant peaks or clusters in the smoothed image are subsequently identified by testing the null hypothesis of lack of activation in every volume element of the scans. A weakness of this approach is the lack of a model for the activation pattern; this makes it difficult to determine the variance of estimates, to test specific neuroscientific hypotheses or to incorporate prior information about the brain area under study in the analysis. These issues may be addressed by formulating explicit spatial models for the activation and using simulation methods for inference. We present one such approach, based on a marked point process prior. Informally, one may think of the points as centres of activation, and the marks as parameters describing the shape and area of the surrounding cluster. We present an MCMC algorithm for making inference in the model and compare the approach with a traditional non‐parametric method, using both simulated and visual stimulation data. Finally we discuss extensions of the model and the inferential framework to account for non‐stationary responses and spatio‐temporal correlation.

High-order vibrational relaxation: a nonperturbative theory

A nonperturbative theory of the multiphonon relaxation of a localized vibrational mode, caused by a high-order anharmonic interaction with the nearest atoms of the crystal lattice, is proposed. It relates the rate of the process to the positive frequency part of the time-dependent non-stationary displacement correlation function of atoms. The nonlinear integral equation for this function is derived and solved numerically. We have found that the rate exhibits a critical behavior: it sharply increases near a specific (critical) value(s) of the interaction; the corresponding dependence is characterized by the critical index k - 1, where k is the number of the created phonons.

Estimating genetic covariance functions assuming a parametric correlation structure for environmental effects.

A random regression model for the analysis of "repeated" records in animal breeding is described which combines a random regression approach for additive genetic and other random effects with the assumption of a parametric correlation structure for within animal covariances. Both stationary and non-stationary correlation models involving a small number of parameters are considered. Heterogeneity in within animal variances is modelled through polynomial variance functions. Estimation of parameters describing the dispersion structure of such model by restricted maximum likelihood via an "average information" algorithm is outlined. An application to mature weight records of beef cow is given, and results are contrasted to those from analyses fitting sets of random regression coefficients for permanent environmental effects.