on ciric generalization of mappings with a contractive iterate at a point in g metric spaces main results of this paper are fixed point theorems for mappings with a generalized contractive iterate at a point in g metric spaces which are generalizations of the well known results in metric spaces

brief robust h filtering for uncertain impulsive stochastic systems under sampled measurements this paper is concerned with the problem of robust h filtering for uncertain impulsive stochastic systems under sampled measurements the parameter uncertainties are assumed to be time varying norm bounded the aim is to design a stochastically stable filter using the locally sampled measurements which ensures both the robust stochastic stability and a prescribed level of h performance for the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given an example is provided to demonstrate the effectiveness of the proposed approach

an improvement on delay and its time derivative dependent robust stability of time delayed linear systems with uncertainty in this paper an improvement on the stability result in the above paper by jin hoon see ibid vol 46 2001 is given based on a modified lyapunov function it is shown that our result is much less conservative than that in the paper especially when the size of derivative of the time delay increases for comparison we give two examples

time frequency discriminant analysis of meg signals abstract this paper introduces a novel statistical method that can identify relevant time frequency features in brain signals to distinguish between groups the feature of interest is the spectrum which characterizes the distribution of a given signal s variance or power across frequency oscillations brain signals are generally nonstationary in that the distribution of the signals power across frequency changes over time the classical fourier analysis is not formally suitable for time series signals with time varying spectra this paper utilizes the slex smooth localized complex exponentials basis function to capture the transient features of brain signals the slex basis consists of a set of localized orthogonal fourier like waveforms with a built in mechanism for representing localized spectral features the best basis is first chosen that maximizes group dissimilarity in the time varying spectra however not all spectral features extracted from the best basis may be useful for discrimination and classification purpose a thresholding scheme is further developed to remove irrelevant features from the best basis to improve accuracy for classification in simulations the proposed slex thresholding discriminant method was able to consistently identify the most discriminant time frequency features and was able to correctly classify signals at a high rate the method was then applied to magnetoencephalographic data from a standard paired click paradigm discrimination between individuals with schizophrenia and a healthy comparison group confirmed the utility of the method

consistent classification of nonstationary time series using stochastic wavelet representations consider the situation when we have training data containing many time series having known group membership and testing data with unknown group membership the goals are to find timescale features using training data that can best separate the groups and to use these highly discriminant features to classify test data we propose a method for classification using a bias corrected nondecimated wavelet transform wavelets are ideal for identifying highly discriminant local time and scale features the observed signals will be treated as realizations of locally stationary wavelet processes under which we define and rigorously estimate the evolutionary wavelet spectrum timescale decomposition of variance the evolutionary wavelet spectrum which contains the second moment information on the signals is used as the classification signature for each test time series we compute the empirical wavelet spectrum and its divergence from the wavelet spectrum of each group the test time series is then assigned

coupled fixed point results for ψ φ weakly contractive mappings in ordered g metric spaces in this paper we establish coupled coincidence and common coupled fixed point theorems for j f weakly contractive mappings in ordered g metric spaces presented theorems extend generalize and improve many existing results in the literature an example is given

sequential change point detection methods for nonstationary time series we present two new spectral based methods for detection of changes in autocorrelation structure in a continuous valued time series in an online process monitoring setting our methods are based on the idea that changes in the autocorrelation structure are reflected by changes in the fourier or wavelet based spectrum and can be detected by comparing estimated spectra of adjacent blocks of the series to be effective for slowly changing spectral structure the methods are extended to allow information from more than one past block to be used in determining whether a change has occurred in such a way as to minimize computational burden through simulation we evaluate the performance of our methods and find that they can provide reliable and timely detection of changes in covariance structure in an online monitoring framework we illustrate the methods using electroencephalogram traces brain waves and run time computer performance metrics

lattice filter based multivariate autoregressive spectral estimation with joint model order and estimation bandwidth adaptation the problem of parametric autoregressive model based estimation of a time varying spectral density function of a multivariate nonstationary process is considered it is shown that estimation results can be considerably improved if identification of the autoregressive model is carried out using the two sided doubly exponentially weighted lattice algorithm which combines results yielded by two one sided lattice algorithms running forward in time and backward in time respectively it is also shown that the model order and the most appropriate estimation bandwidth can be efficiently selected using the suitably modified akaike s final prediction error criterion

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

discrimination and classification of nonstationary time series using the slex model statistical discrimination for nonstationary random processes is important in many applications our goal was to develop a discriminant scheme that can extract local features of the time series is consistent and is computationally efficient here we propose a discriminant scheme based on the slex smooth localized complex exponential library the slex library forms a collection of fourier type bases that are simultaneously orthogonal and localized in both time and frequency domains thus the slex library has the ability to extract local spectral features of the time series the first step in our procedure which is the feature extraction step based on work by saito is to find a basis from the slex library that can best illuminate the difference between two or more classes of time series in the next step we construct a discriminant criterion that is related to the kullback leibler divergence between the slex spectra of the different classes the discrimination criterion is based on estimates of the

common fixed point theorems for contractive maps two common fixed point theorems have been proved by using minimal type commutativity and contractive conditions the last theorem extends known results on compatible maps to a wider class of mappings

on multiple regression models with nonstationary correlated errors summary we consider the estimation of parameters of a multiple regression model with non stationary errors we assume the nonstationary errors satisfy a time dependent auto regressive process and describe a method for estimating the parameters of the regressors and the time dependent autoregressive parameters the parameters are rescaled as in nonparametric regression to obtain the asymptotic sampling properties of the estimators the method is illustrated with an example taken from global temperature anomalies

wavelet threshold estimators for data with correlated noise wavelet threshold estimators for data with stationary correlated noise are constructed by applying a level dependent soft threshold to the coefficients in the wavelet transform a variety of threshold choices is proposed including one based on an unbiased estimate of mean squared error the practical performance of the method is demonstrated on examples including data from a neurophysiological context the theoretical properties of the estimators are investigated by comparing them with an ideal but unattainable bench mark that can be considered in the wavelet context as the risk obtained by ideal spatial adaptivity and more generally is obtained by the use of an oracle that provides information that is not actually available in the data it is shown that the level dependent threshold estimator performs well relative to the bench mark risk and that its minimax behaviour cannot be improved on in order of magnitude by any other estimator the wavelet domain structure of both short and long range dependent noise is considered and in both cases it is shown that the estimators have near optimal behaviour simultaneously in a wide range of function classes adapting automatically to the regularity properties of the underlying model the proofs of the main results are obtained by considering a more general multivariate normal decision theoretic problem

slex analysis of multivariate nonstationary time series we develop a procedure for analyzing multivariate nonstationary time series using the slex library smooth localized complex exponentials which is a collection of bases each basis consisting of waveforms that are orthogonal and time localized versions of the fourier complex exponentials under the slex framework we build a family of multivariate models that can explicitly characterize the time varying spectral and coherence properties every model has a spectral representation in terms of a unique slex basis before selecting a model we first decompose the multivariate time series into nonstationary components with uncorrelated nonredundant spectral information the best slex model is selected using the penalized log energy criterion which we derive in this article to be the kullback leibler distance between a model and the slex principal components of the multivariate time series the model selection criterion takes into account all of the pairwise cross correlation simultaneously in the multivar

clustering of biological time series by cepstral coefficients based distances clustering of stationary time series has become an important tool in many scientific applications like medicine finance etc time series clustering methods are based on the calculation of suitable similarity measures which identify the distance between two or more time series these measures are either computed in the time domain or in the spectral domain since the computation of time domain measures is rather cumbersome we resort to spectral domain methods a new measure of distance is proposed and it is based on the so called cepstral coefficients which carry information about the log spectrum of a stationary time series these coefficients are estimated by means of a semiparametric model which assumes that the log likelihood ratio of two or more unknown spectral densities has a linear parametric form after estimation the estimated cepstral distance measure is given as an input to a clustering method to produce the disjoint groups of data simulated examples show that the method yields good results even when the processes are not necessarily linear these cepstral based clustering algorithms are applied to biological time series in particular the proposed methodology effectively identifies distinct and biologically relevant classes of amino acid sequences with the same physicochemical properties such as hydrophobicity

optimal data based kernel estimation of evolutionary spectra complex demodulation of evolutionary spectra is formulated as a two dimensional kernel smoother in the time frequency domain first a tapered fourier transform y sub v f t is calculated then the log spectral estimate is smoothed as the characteristic widths of the kernel smoother increase the bias from the temporal and frequency averaging increases while the variance decreases the demodulation parameters such as the order length and bandwidth of spectral taper and the kernel smoother are determined by minimizing the expected error for well resolved evolutionary spectra the optimal taper length is a small fraction of the optimal kernel halfwidth the optimal frequency bandwidth w for the spectral window scales as w sup 2 approximately lambda tau where tau is the characteristic time and lambda sub f is the characteristic frequency scalelength in contrast the optimal halfwidths for the second stage kernel smoother scales as h approximately 1 tau lambda sub f sup 1 p 2 where p is the order of the kernel smoother the ratio of the optimal frequency halfwidth to the optimal time halfwidth is determined

validating stationarity assumptions in time series analysis by rolling local periodograms we propose a simple and powerful procedure to validate the assumption of weak stationarity in time series analysis our focus is on processes with a slowly varying autocovariance structure the procedure evaluates the supremum over time of the l2 distance between the local sample spectral density local periodogram calculated using a segment of observations falling within a rolling window and an estimator of the spectral density obtained using the entire time series at hand large sample properties of a basic deviation process are investigated and critical values of a supremum type test are obtained using an appropriate bootstrap procedure the finite sample size and power properties of the procedure are investigated by means of simulations real data examples demonstrate the ability of the procedure to detect possible changes in the autocovariance structure of a time series and to understand their nature

multiscale clustering of nonparametric regression curves abstract in a wide range of modern applications one observes a large number of time series rather than only a single one it is often natural to suppose that there is some group structure in the observed time series when each time series is modeled by a nonparametric regression equation one may in particular assume that the observed time series can be partitioned into a small number of groups whose members share the same nonparametric regression function we develop a bandwidth free clustering method to estimate the unknown group structure from the data more precisely speaking we construct multiscale estimators of the unknown groups and their unknown number which are free of classical bandwidth or smoothing parameters in the theoretical part of the paper we analyze the statistical properties of our estimators our theoretical results are derived under general conditions which allow the data to be dependent both in time series direction and across different time series the technical analysis of the paper is complemented by simulated and real data examples

semiparametric estimation by model selection for locally stationary processes over recent decades increasingly more attention has been paid to the problem of how to fit a parametric model of time series with time varying parameters a typical example is given by autoregressive models with time varying parameters we propose a procedure to fit such time varying models to general non stationary processes the estimator is a maximum whittle likelihood estimator on sieves the results do not assume that the observed process belongs to a specific class of time varying parametric models we discuss in more detail the fitting of time varying ar p processes for which we treat the problem of the selection of the order p and we propose an iterative algorithm for the computation of the estimator a comparison with model selection by akaike s information criterion is provided through simulations

entropy based algorithms for best basis selection adapted waveform analysis uses a library of orthonormal bases and an efficiency functional to match a basis to a given signal or family of signals it permits efficient compression of a variety of signals such as sound and images the predefined libraries of modulated waveforms include orthogonal wavelet packets and localized trigonometric functions and have reasonably well controlled time frequency localization properties the idea is to build out of the library functions an orthonormal basis relative to which the given signal or collection of signals has the lowest information cost the method relies heavily on the remarkable orthogonality properties of the new libraries all expansions in a given library conserve energy and are thus comparable several cost functionals are useful one of the most attractive is shannon entropy which has a geometric interpretation in this context

wavelet processes and adaptive estimation of the evolutionary wavelet spectrum this article defines and studies a new class of non stationary random processes constructed from discrete non decimated wavelets which generalizes the cramer fourier representation of stationary time series we define an evolutionary wavelet spectrum ews which quantifies how process power varies locally over time and scale we show how the ews may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time localized autocovariance we illustrate our theory with a pedagogical example based on discrete non decimated haar wavelets and also a real medical time series example

delay dependent robust stability criteria for uncertain systems with interval time varying delay this paper proposes an approach for the robust stability of uncertain systems with interval time varying delay the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology unlike existing methodologies the proposed approach involves neither free weighting matrices nor any model transformation it can however lead to much less conservative stability criteria than the existing ones for the systems under consideration numerical examples show that the proposed criteria improve the existing results significantly with much less computational effort

narrowband acoustic doppler volume backscattering signal ii spectral centroid estimation for pt i see ibid vol 50 p 2644 2655 2002 this paper proposes a novel algorithm to estimate the time varying spectral centroid of the narrowband doppler volume backscattering signal it is constructed in a semi parametric way that is modeling parametrically the local narrowband evolutionary spectrum using an ar 2 and nonparametrically adapting its time varying coefficients using the wavelet shrinkage the improved performance is gained by the underlying linear prediction function of the ar 2 and the minimax optimality of the unknown smoothness adaptation of the wavelet shrinkage procedure

thick pen transformation for time series traditional visualisation of time series data often consists of plotting the time series values against time and connecting the dots we propose an alternative multiscale visualisation technique motivated by the scale space approach in computer vision in brief our method also connects the dots but uses a range of pens of varying thicknesses for this purpose the resulting multiscale map termed the thick pen transform tpt corresponds to viewing the time series from a range of distances we formally prove that the tpt is a discriminatory statistic for two gaussian time series with distinct correlation structures further we show interesting possible applications of the tpt to measuring cross dependence in multivariate time series classifying time series and testing for stationarity in particular we derive the asymptotic distribution of our test statistic and argue that the test is applicable to both linear and nonlinear processes under low moment assumptions various other aspects of the methodology including other possible applications are also discussed

delay dependent delay independent stability of linear systems with multiple time varying delays delay dependent delay independent uniform asymptotic stability and uniform stability criteria for linear systems with multiple time varying delays are established respectively in this note the results are derived based on a new type stability theorem for retarded dynamical systems and a new analysis technique for estimating the derivative of a lyapunov function along the solution of a system at certain specific instants four remarks together with an illustrative example are given to compare the obtained results with and to show their superiority to those in the literature

mean square exponential stability analysis of impulsive stochastic switched systems with mixed delays abstract in this paper a class of impulsive stochastic switched systems with mixed delays is considered on the basis of some integro differential inequalities and stochastic analysis techniques some general criteria for mean square exponential stability are obtained an example is given to illustrate the theory

adaptive drift estimation for nonparametric diffusion model we consider a nonparametric diffusion process whose drift and diffusion coefficients are nonparametric functions of the state variable the goal is to estimate the unknown drift coefficient we apply a locally linear smoother with a data driven bandwidth choice the procedure is fully adaptive and nearly optimal up to a log log factor the results about the quality of estimation are nonasymptotic and do not require any ergodic or mixing properties of the observed process

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

almost sure exponential stability of recurrent neural networks with markovian switching this paper presents new stability results for recurrent neural networks with markovian switching first algebraic criteria for the almost sure exponential stability of recurrent neural networks with markovian switching and without time delays are derived the results show that the almost sure exponential stability of such a neural network does not require the stability of the neural network at every individual parametric configuration next both delay dependent and delay independent criteria for the almost sure exponential stability of recurrent neural networks with time varying delays and markovian switching parameters are derived by means of a generalized stochastic halanay inequality the results herein include existing ones for recurrent neural networks without markovian switching as special cases finally simulation results in three numerical examples are discussed to illustrate the theoretical results

a smoothness priors time varying ar coefficient modeling of nonstationary covariance time series a smoothness priors time varying ar coefficient model approach for the modeling of nonstationary in the covariance time series is shown smoothness priors in the form of a difference equation constraint excited by an independent white noise are imposed on each ar coefficient the unknown white noise variances are hyperparameters of the ar coefficient distribution the critical computation is of the likelihood of the hyperparameters of the bayesian model this computation is facilitated by a state space representation kalman filter implementation the best difference equation order best ar model order best hyperparameter model locally in time is selected using the minimum aic method also an instantaneous spectral density is defined in terms of the instantaneous ar model coefficients and a smoothed estimate of the instantaneous time series variance an earthquake record is analyzed the changing spectral analysis of the original data and of simulations from a time varying ar coefficient model of that data are shown

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

on common fixed points in g metric spaces using e a property in this paper we introduce some new types of pairs of mappings f g on g metric spaces called g weakly commuting of type g f and g r weakly commuting of type g f we obtain also several common fixed point results by using the e a property

robustness analysis of global exponential stability of recurrent neural networks in the presence of time delays and random disturbances in recent years the global stability of recurrent neural networks rnns has been investigated extensively it is well known that time delays and external disturbances can derail the stability of rnns in this paper we analyze the robustness of global stability of rnns subject to time delays and random disturbances given a globally exponentially stable neural network the problem to be addressed here is how much time delay and noise the rnn can withstand to be globally exponentially stable in the presence of delay and noise the upper bounds of the time delay and noise intensity are characterized by using transcendental equations for the rnns to sustain global exponential stability moreover we prove theoretically that for any globally exponentially stable rnns if additive noises and time delays are smaller than the derived lower bounds arrived at here then the perturbed rnns are guaranteed to also be globally exponentially stable three numerical examples are provided to substantiate the theoretical results

detecting gradual changes in locally stationary processes in a wide range of applications the stochastic properties of the observed time series change over time the changes often occur gradually rather than abruptly the properties are approximately constant for some time and then slowly start to change in such situations it is frequently of interest to locate the time point where the properties start to vary in contrast to the analysis of abrupt changes methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions in this paper we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework we set up a general procedure which allows to deal with a wide variety of stochastic properties including the mean auto covariances and higher order moments the theoretical part of the paper establishes the convergence rate of the new estimator in addition we examine its finite sample performance by means of a simulation study and illustrate the methodology by applications to temperature and financial return data

positive solution and its asymptotic behaviour of stochastic functional kolmogorov type system abstract in general population systems are often subject to environmental noise this paper considers the stochastic functional kolmogorov type system d x t diag x 1 t x n t f x t d t g x t d w t under the traditionally diagonally dominant condition we study existence and uniqueness of the global positive solution of this stochastic system and its asymptotic bound properties and moment average boundedness in time these properties are natural requirements from the biological point of view as the special cases we also discuss some stochastic lotka volterra systems

discrimination and clustering for multivariate time series abstract minimum discrimination information provides a useful generalization of likelihood methodology for classification and clustering of multivariate time series discrimination between different classes of multivariate time series that can be characterized by differing covariance or spectral structures is of importance in applications occurring in the analysis of geophysical and medical time series data for discrimination between such multivariate series kullback leibler discrimination information and the chernoff information measure are developed for the multivariate non gaussian case asymptotic error rates and limiting distributions are given for a generalized spectral disparity measure that includes the foregoing criteria as special cases applications to problems of clustering and classifying earthquakes and mining explosions are given

asymptotic theory for time series with changing mean and variance abstract the paper develops point estimation and asymptotic theory with respect to a semiparametric model for time series with moving mean and unconditional heteroscedasticity these two features are modelled nonparametrically whereas autocorrelations are described by a short memory stationary parametric time series model we first study the usual least squares estimate of the coefficient of the first order autoregressive model based on constant but unknown mean and variance allowing for both the latter to vary over time in a general way we establish its probability limit and a central limit theorem for a suitably normed and centred statistic giving explicit bias and variance formulae as expected mean variation is the main source of inconsistency and heteroscedasticity the main source of inefficiency though we discuss circumstances in which the estimate is consistent for and asymptotically normal about the autoregressive coefficient albeit inefficient we then consider standard implicitly defined whittle estimates of a more general class of short memory parametric time series model under otherwise more restrictive conditions when the mean is correctly assumed to be constant estimates that ignore the heteroscedasticity are again found to be asymptotically normal but inefficient allowing a slowly time varying mean we resort to trimming out of low frequencies to achieve the same outcome returning to finite order autoregression nonparametric estimates of the varying mean and variance are given asymptotic justification and forecasting formulae developed finite sample properties are studied by a small monte carlo simulation and an empirical example is also included

common fixed point results for noncommuting mappings without continuity in generalized metric spaces using the setting of a generalized metric space a fixed point theorem is proved for one map and several fixed point theorems are proved for two maps these results generalize several well known comparable results in the literature

robustness analysis for parameter matrices of global exponential stability time varying delay systems abstract this paper analyzes the robustness of global exponential stability time varying delay systems subjected to parameter uncertainty given a globally exponentially stable time varying delay systems the problem to be addressed herein is how much parameter uncertainty the systems can withstand to be globally exponentially stable we characterize the upper bounds of the parameter uncertainty for the systems to sustain global exponential stability moreover we prove theoretically that for globally exponentially stable systems if additive parameter uncertainty is smaller than the derived upper bounds arrived at here then the perturbed systems are guaranteed to also be globally exponentially stable a numerical example is provided to illustrate the theoretical result

automatic statistical analysis of bivariate nonstationary time series we propose a new method for analyzing bivariate nonstationary time series the proposed method is a statistical procedure that automatically segments the time series into approximately stationary blocks and selects the span to be used to obtain the smoothed estimates of the time varying spectra and coherence it is based on the smooth localized complex exponential slex transform which forms a library of orthogonal complex valued transforms that are simultaneously localized in time and frequency we show that the smoothed slex periodograms are consistent estimators report simulation results and apply the method to a two channel electroencephalogram dataset recorded during an epileptic seizure

discrimination of locally stationary time series based on the excess mass functional discrimination of time series is an important practical problem with applications in various scientific fields we propose and study a novel approach to this problem our approach is applicable to cases where time series in different categories have a different shape although based on the idea of feature extraction our method is not distance based and as such does not require aligning the time series instead features are measured for each time series and discrimination is based on these individual measures an ar process with a time varying variance is used as an underlying model our method then uses shape measures or better measures of concentration of the variance function as a criterion for discrimination it is this concentration aspect or shape aspect that makes the approach intuitively appealing we provide some mathematical justification for our proposed methodology as well as a simulation study and an application to the problem of discriminating earthquakes and explosions

wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra we derive minimax rates for estimation in anisotropic smoothness classes this rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension it is shown that this basis is superior to its one scale multiresolution analog if different degrees of smoothness in different directions are present as an important application we introduce a new adaptive wavelet estimator of the time dependent spectrum of a locally stationary time series using this model which was resently developed by dahlhaus we show that the resulting estimator attains nearly the rate which is optimal in gaussian white noise simultaneously over a wide range of smoothness classes moreover by our new approach we overcome the difficulty of how to choose the right amount of smoothing i e how to adapt to the appropriate resolution for reconstructing the local structure of the evolutionary spectrum in the time frequency plane

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

statistical inference for time varying arch processes in this paper the class of arch oo models is generalized to the nonstationary class of arch oo models with time varying coefficients for fixed time points a stationary approximation is given leading to the notation locally stationary arch oo process the asymptotic properties of weighted quasi likelihood estimators of time varying arch p processes p oo are studied including asymptotic normality in particular the extra bias due to nonstationarity of the process is investigated moreover a taylor expansion of the nonstationary arch process in terms of stationary processes is given and it is proved that the time varying arch process can be written as a time varying volterra series

smoothing spline anova for time dependent spectral analysis in this article we propose a smoothing spline anova model ss anova to estimate and to make inference on the time varying log spectrum of a locally stationary process the time varying spectrum is assumed to be smooth in both time and frequency this assumption essentially turns a time frequency spectral estimation problem into a 2 dimensional surface estimation problem a smooth localized complex exponential slex basis is used to calculate the initial periodograms and a ss anova is fitted to the log periodograms this approach allows the time and frequency domains to be modeled in a unified approach and jointly estimated inference procedures such as confidence intervals and hypothesis tests proposed for the ss anova can be adopted for the time varying spectrum because of the smoothness assumption of the underlying spectrum once we have the estimates on a time frequency grid we can calculate the estimate at any given time and frequency this leads to a high computational efficiency because for

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

an efficient estimator for locally stationary gaussian long memory processes this paper addresses the estimation of locally stationary long range dependent processes a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency a time varying parametric formulation of these models is introduced and a whittle likelihood technique is proposed for estimating the parameters involved large sample properties of these whittle estimates such as consistency normality and efficiency are established in this work furthermore the finite sample behavior of the estimators is investigated through monte carlo experiments as a result from these simulations we show that the estimates behave well even for relatively small sample sizes

robust stabilization of uncertain systems with delays in control input a matrix inequality approach this paper presents a new stabilization criterion for dynamic systems with parametric uncertainties and delays in control input based on the lyapunov method the stabilization criterion is derived in terms of matrix inequalities which can be easily solved by efficient convex optimization algorithms numerical examples are included to show the effectiveness of the proposed method

testing for smooth structural changes in time series models via nonparametric regression checking parameter stability of econometric models is a long standing problem almost all existing structural change tests in econometrics are designed to detect abrupt breaks little attention has been paid to smooth structural changes which may be more realistic in economics we propose a consistent test for smooth structural changes as well as abrupt structural breaks with known or unknown change points the idea is to estimate smooth time varying parameters by local smoothing and compare the fitted values of the restricted constant parameter model and the unrestricted time varying parameter model the test is asymptotically pivotal and does not require prior information about the alternative a simulation study highlights the merits of the proposed test relative to a variety of popular tests for structural changes in an application we strongly reject the stability of univariate and multivariate stock return prediction models in the postwar and post oil shocks periods

on robust stability criterion for dynamic systems with time varying delays and nonlinear perturbations in this paper we propose a new delay dependent stability criterion for dynamic systems with time varying delays and nonlinear perturbations based on the lyapunov method a sufficient delay dependent criterion for asymptotic stability is derived in terms of linear matrix inequality lmi numerical examples are given to show the effectiveness of our result

clustering high dimensional time series based on parallelism this article considers the problem of clustering high dimensional time series based on trend parallelism the underlying process is modeled as a nonparametric trend function contaminated by locally stationary errors a special class of nonstationary processes for each group where the parallelism holds i semiparametrically estimate its representative trend function and vertical shifts of group members and establish their central limit theorems an information criterion consisting of in group similarities and number of groups is then proposed for the purpose of clustering i prove its theoretical consistency and propose a splitting coalescence algorithm to reduce the computational burden in practice the method is illustrated by both simulation and a real data example

estimating the population local wavelet spectrum with application to non stationary functional magnetic resonance imaging time series functional magnetic resonance imaging fmri is a dynamic four dimensional imaging modality however in almost all fmri analyses the time series elements of this data are assumed to be second order stationary in this paper we examine using time series spectral methods whether such stationary assumptions can be made and whether estimates of non stationarity can be used to gain understanding into fmri experiments a non stationary version of replicated stationary time series analysis is proposed that takes into account the replicated time series that are available from nearby voxels in a region of interest roi these are used to investigate non stationarities in both the roi itself and the variations within the roi the proposed techniques are applied to simulated data and to an anxiety inducing fmri experiment

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

fitting time series models to nonstationary processes a general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation the asymptotic properties of the estimate are derived under the assumption of possible model misspecification for autoregressive processes with time varying coefficients the estimate is compared to the least squares estimate furthermore the behavior of estimates is explained when a stationary model is fitted to a nonstationary process

parameter dependent stability and stabilization of uncertain time delay systems a new robust delay dependent stability test is introduced that determines the asymptotic stability of linear systems with state delays the parameters of the system are not exactly given they are known to reside in a given polytope the test provides an efficient sufficient condition for the stability of the system over the uncertainty polytope this condition is parameter dependent and it therefore improves previous results that were derived using a single lyapunov krasovskii functional the stability test is readily extended to provide a criterion for robust stabilization via state feedback

compatible maps and invariant approximations the existence of invariant best approximations for compatible maps is proved our results unify and generalize various known results to a more general class of noncommuting mappings

improved delay dependent robust stability criteria for uncertain time delay systems abstract this paper deals with the robust stability analysis for uncertain systems with time varying delay new delay dependent robust stability criteria of uncertain time delay systems are proposed by exploiting appropriate lyapunov functional candidate these developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism due to the introduction of a method to estimate the upper bound of the derivative of lyapunov functional candidate without ignoring the additional useful terms numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method

bootstrapping locally stationary processes summary we propose a non parametric method to bootstrap locally stationary processes which combines a time domain wild bootstrap approach with a non parametric frequency domain approach the method generates pseudotime series which mimic asymptotically correct the local second and to the necessary extent the fourth order moment structure of the underlying process thus it can be applied to approximate the distribution of several statistics that are based on observations of the locally stationary process we prove a bootstrap central limit theorem for a general class of statistics that can be expressed as functionals of the preperiodogram the latter being a useful tool for inferring properties of locally stationary processes some simulations and a real data example shed light on the finite sample properties and illustrate the ability of the bootstrap method proposed

generalized meir keeler type contractions on g metric spaces in this manuscript we introduce generalized meir keeler type contractions over g metric spaces moreover we show that every orbitally continuous generalized meir keeler type contraction has a unique fixed point on complete g metric spaces we illustrate our results by some given examples

should annual maximum temperatures follow a generalized extreme value distribution summary motivated by the study of annual temperature extremes two new results on the limiting distribution of block maxima of random variables with varying upper bounds are obtained one gives a generalized extreme value distribution as the limit but with a different shape parameter from that obtained when the bound on the random variables does not vary the other gives a limiting distribution that is only a generalized extreme value in certain cases both results consider triangular arrays of random variables in order to mimic the property of an upper bound that changes slowly with the day of the year as seems to occur for temperature data at many locations an analysis of 140 years of daily temperatures in new york city shows mixed results in terms of the ability of the theory presented here to provide new insights into the behaviour of extreme temperatures at this location

small sample effects in time series analysis a new asymptotic theory and a new estimate on introduit un modele mathematique qui couvre les effets des petits echantillons dans l approximation de whittle 1953 on montre que l estimation du maximum de vraisemblance exacte est toujours optimale dans ce modele

coupled fixed point results for ψ φ weakly contractive condition in ordered partial metric spaces in this paper we prove some coupled fixed point theorems involving a j f weakly contractive condition for mapping having the mixed monotone property in ordered partial metric spaces these results are analogous to theorems of van luong and xuan thuan 2011 10 on the class of ordered partial metric spaces also an application is given to support our results

online bayesian inference in some time frequency representations of non stationary processes the use of bayesian inference in the inference of time frequency representations has thus far been limited to offline analysis of signals using a smoothing spline based model of the time frequency plane in this paper we introduce a new framework that allows the routine use of bayesian inference for online estimation of the time varying spectral density of a locally stationary gaussian process the core of our approach is the use of a likelihood inspired by a local whittle approximation this choice along with the use of a recursive algorithm for non parametric estimation of the local spectral density permits the use of a particle filter for estimating the time varying spectral density online we provide demonstrations of the algorithm through tracking chirps and the analysis of musical data

some new common fixed point theorems under strict contractive conditions the main purpose of this paper is to give some new common fixed point theorems under strict contractive conditions for mappings satisfying a new property

parameter dependent robust stability of uncertain time delay systems this paper presents a new delay dependent and parameter dependent robust stability criterion for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state this criterion expressed as a set of linear matrix inequalities requires no matrix variable to be fixed for the entire uncertainty polytope which produces a less conservative stability test result numerical examples are given to show the effectiveness of the proposed techniques

minimax adaptive spectral estimation from an ensemble of signals we develop a statistical method for estimating the spectrum from a data set that consists of several signals all of which are realizations of a common random process we first find estimates of the common spectrum using each signal then we construct m partial aggregates each partial aggregate is a linear combination of m 1 of the spectral estimates the weights are obtained from the data via a least squares criterion the final spectral estimate is the average of these m partial aggregates we show that our final estimator is minimax rate adaptive if at least two of the estimators per signal attain the optimal rate n 2alpha 2alpha 1 for spectra belonging to a generalized lipschitz ball with smoothness index alpha our simulation study strongly suggests that our procedure works well in practice and in a large variety of situations is preferable to the simple averaging of the m spectral estimates

technical communique delay dependent robust stability for uncertain linear systems with interval time varying delay this paper is concerned with the delay dependent robust stability problem for uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and no restriction on the derivative of the time varying delay is needed which allows the delay to be a fast time varying function the uncertainty under consideration is norm bounded and possibly time varying uncertainty based on the lyapunov krasovskii functional approach a stability criterion is derived by introducing some relaxation matrices that can be used to reduce the conservatism of the criteria numerical examples are given to demonstrate effectiveness of the proposed method

technical communique a delay partitioning approach to the stability analysis of discrete time systems this paper revisits the problem of stability analysis for linear discrete time systems with time varying delay in the state by utilizing the delay partitioning idea new stability criteria are proposed in terms of linear matrix inequalities lmis these conditions are developed based on a novel lyapunov functional in addition to delay dependence the obtained conditions are also dependent on the partitioning size we have also established that the conservatism of the conditions is a non increasing function of the number of partitions numerical examples are given to illustrate the effectiveness and advantage of the proposed methods

simultaneous inference of linear models with time varying coefficients summary the paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models using a gaussian approximation result for non stationary multiple time series we show that the constructed simultaneous confidence tubes have asymptotically correct nominal coverage probabilities our results are applied to the problem of testing whether the regression coefficients are of certain parametric forms which is a fundamental problem in the inference of functional linear models as an application we analyse an environmental data set and study the association between levels of pollutants and hospital admissions