existence and multiplicity of solutions for an elliptic system with nonlinear boundary conditions abstract in this paper we prove the existence and multiplicity of solutions for the elliptic system u u v v in with nonlinear coupling at the smooth boundary given by u h u v h v on where is a bounded domain of r n with smooth boundary is the outer normal derivative the proofs are done under suitable assumptions on the hamiltonian and based on the local linking theorem and a multiple critical points theorem of the critical point theory

least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity summary we consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity its asymptotic normality is established when the second moments of errors and innovations are finite several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach a diagnostic tool consisting of two portmanteau tests is designed to check whether or not the estimated models are adequate the simulation experiments give further support to our model and the results for the absolute returns of the dow jones industrial average index daily closing price demonstrate their usefulness in modelling time series exhibiting the features of long memory conditional heteroscedasticity and heavy tails

a nonlinear long memory model with an application to us unemployment two important empirical features of us unemployment are that shocks to the series seem rather persistent and that it seems to rise faster during recessions than that it falls during expansions to jointly capture these features of long memory and nonlinearity we put forward a new time series model and evaluate its empirical performance we find that the model describes the data rather well and that it outperforms related competitive models on various measures of fit

maximum likelihood estimation of linear continuous time long memory processes with discrete time data summary we develop a new class of time continuous autoregressive fractionally integrated moving average carfima models which are useful for modelling regularly spaced and irregularly spaced discrete time long memory data we derive the autocovariance function of a stationary carfima model and study maximum likelihood estimation of a regression model with carfima errors based on discrete time data and via the innovations algorithm it is shown that the maximum likelihood estimator is asymptotically normal and its finite sample properties are studied through simulation the efficacy of the approach proposed is demonstrated with a data set from an environmental study

maximum likelihood estimation of the differencing parameter for invertible short and long memory autoregressive integrated moving average models in practical applications of box jenkins autoregressive integrated moving average arima models the number of times that the observed time series must be differenced to achieve approximate stationarity is usually determined by careful but mostly informal analysis of the differenced series for many time series some differencing seems appropriate but taking the first or the second difference may be too strong as an alternative hosking and granger and joyeux proposed the use of fractional differences for 1 2 1 2 can be estimated by an approximate maximum likelihood method we thus obtain a unified approach to fitting traditional box jenkins arima processes as well as stationary and non stationary fractional arima processes a confidence interval for d can be given tests such as for unit roots in the autoregressive parameter or for stationarity follow immediately the resulting confidence intervals for the arma parameters take into account the additional uncertainty due to estimation of d a simple algorithm for calculating the estimate of d and the arma parameters is given simulations and two data examples illustrate the results

on critical point theory for indefinite functionals in the presence of symmetries we consider functionals which are not bounded from above or from below even modulo compact perturbations and which exhibit certain symmetries with respect to the action of a compact lie group we develop a method which permits us to prove the existence of multiple critical points for such functionals the proofs are carried out directly in an infinite dimensional hilbert space and they are based on minimax arguments the applications given here are to hamiltonian systems of ordinary differential equations where the existence of multiple time periodic solutions is established for several classes of hamiltonians symmetry properties of these hamiltonians such as time translation invariancy or evenness are exploited introduction many variational problems which arise from physics or mathematical physics are indefinite in the sense that the functionals involved are not bounded from below or from above however some of these functionals defined in an appropriate function space are semidefinite in the sense that they are bounded from below or from above if perturbed with a weakly continuous functional this paper deals with functionals which are not semidefinite usually problems involving indefinite functionals are more difficult to handle and only very recently a method has been developed which permits us to treat such problems directly in an infinite dimensional function space 7 in 7 some theorems have been proved which establish the existence of at least one nontrivial critical point for such functionals in many physical situations there are problems which have symmetries with respect to the action of some lie group in this case we expect the existence of many critical points this has been established for semidefinite functionals cf e g 8 and 3 for even functionals 9 for a zp action with p prime numbers 15 16 10 and 6 for an s action in this paper we develop a method which allows us to estimate the number of critical points of indefinite functionals in the presence of symmetries more precisely received by the editors july 16 1980 and in revised form june 26 1981 1980 mathematics subject classification primary 58e05 70h05 secondary 34c25

gap bifurcation for nonlinear perturbations of hill s equation keywords bifurcation nonlinear hill s equation testfunctions reference ana article 1990 002view record in web of science record created on 2008 12 10 modified on 2016 08 08

an integrodifferential model for phase transitions stationary solutions in higher space dimensions we study the existence and stability of stationary solutions of an integrodifferential model for phase transitions which is a gradient flow for a free energy functional with general nonlocal integrals penalizing spatial nonuniformity as such this model is a nonlocal extension of the allencahn equation which incorporates long range interactions we find that the set of stationary solutions for this model is much larger than that of the allencahn equation

existence and gap bifurcation of multiple solutions to certain nonlinear eigenvalue problems in this paper we study i a class of operator equations in an abstract hilbert space and ii the l2 theory of certain nonlinear schrodinger equations which can be viewed as special cases of i in order to describe the type of abstract nonlinear eigenvalue problems to be discussed consider a real hilbert space h with scalar product and norm ii 11 and let s be a not necessarily bounded positive self adjoint linear operator in li we write s in the form

on unified model selection for stationary and nonstationary short and long memory autoregressive processes summary the question of model choice for the class of stationary and nonstationary fractional and nonfractional autoregressive processes is considered this class is defined by the property that the dth difference for 2 d oo is a stationary autoregressive process of order p0 00 a version of the akaike information criterion aic for determining an appropriate autoregressive order when d and the autoregressive parameters are estimated simultaneously by a maximum likelihood procedure beran 1995 is derived and shown to be of the same general form as for a stationary autoregressive process but with d treated as an additional estimated parameter moreover as in the stationary case this criterion is shown not to provide a consistent estimator of p0 the corresponding versions of the bic of schwarz 1978 and the hic of hannan quinn 1979 are shown to yield consistent estimators of po the results provide a unified treatment of fractional and nonfractional stationary and integrated nonstationary autoregressive models

generalized arma models with martingale difference errors the analysis of non gaussian time series has been studied extensively and has many applications many successful models can be viewed as special cases or variations of the generalized autoregressive moving average garma models of benjamin et al 2003 where a link function similar to that used in generalized linear models is introduced and the conditional mean under the link function assumes an arma structure under such a model the transformed time series under the same link function assumes an arma form as well unfortunately unless the link function is an identity function the error sequence defined in the transformed arma model is usually not a martingale difference sequence in this paper we extend the garma model in such a way that the resulting arma model in the transformed space has a martingale difference sequence as its error sequence the benefit of such an extension are four folds it has easily verifiable conditions for stationarity and ergodicity its gaussian pseudo likelihood estimator is consistent standard time series model building tools are ready to use and its mle s asymptotic distribution can be established we also proposes two new classes of non gaussian time series models under the new framework the performance of the proposed models is demonstrated with simulated and real examples

determination of changes in streamflow variance by means of a wavelet based test 1 changes in the variance of streamflow over time may possibly be caused by land cover changes or climate changes knowledge of these possible changes in the time series structure is desirable for validation of modeling efforts detection is not always straightforward however we present the use of a wavelet based statistical test for the detection of changes in the variance of a time series applied to records of streamflow from 12 rivers in the united states from the period 1954 1999 the test is able to show during which time periods and at what wavelet scales changes in the variance are taking place it is found that the major similarities in variance change for all the streamflow time series exist when the largest time domain wavelet is used and also when a wavelet of the second largest frequency scale is used sampling considerations prevent exact localization of the time and frequency of the change s results of the test indicate that for the data analyzed in this study a change in the variance of the streamflow time series most likely did take place over the time period examined

existence of solutions for semilinear elliptic equations with indefinite linear part we study equations on rn lu w x u p 1 ulu f u where l is an indefinite schrodinger operator 0 w x 0 as and subcritical nonlinearities we prove existence of solutions u h1 rn via an inversion to a dual variational problem

efficiency improvements in inference on stationary and nonstationary fractional time series we consider a time series model involving a fractional stochastic component whose integration order can lie in the stationary invertible or nonstationary regions and be unknown and an additive deterministic component consisting of a generalized polynomial the model can thus incorporate competing descriptions of trending behavior the stationary input to the stochastic component has parametric autocorrelation but innovation with distribution of unknown form the model is thus semiparametric and we develop estimates of the parametric component which are asymptotically normal and achieve an m estimation efficiency bound equal to that found in work using an adaptive lam lan approach a major technical feature which we treat is the effect of truncating the autoregressive representation in order to form innovation proxies this is relevant also when the innovation density is parameterized and we provide a result for that case also our semiparametric estimates employ nonparametric series estimation which avoids some complications and conditions in kernel approaches featured in much work on adaptive estimation of time series models our work thus also contributes to methods and theory for nonfractional time series models such as autoregressive moving averages a monte carlo study of finite sample performance of the semiparametric estimates is included

global temperatures and sunspot numbers are they related abstract this paper deals with the analysis of global temperatures and sunspot numbers and the relationship between the two we use techniques based on the concept of long range dependence for the temperatures the best specification seems to be a fractionally integrated or i d model with an order of integration d of about 0 46 and an estimated time trend coefficient that suggests that temperatures have increased by about 0 57 c over the last one hundred years however for the sunspot numbers a cyclical fractional model seems to be more appropriate with a periodicity of 11 years per cycle and an order of integration of about 0 40 thus the two series display long memory and fractional integration however the fact that both series display poles in the spectrum at different frequencies implies that we fail to reject the null hypothesis of no relationship between the two variables in the long run moreover assuming that the sunspots are exogenous the results show no statistical significance of this variable on the global temperatures which is one of the main contributions of the present work

solvability of nonlinear equations in spectral gaps of the linearization keywords strongle indefinite nonlinear hill s equation reference ana article 1992 002doi 10 1016 0362 546x 92 90116 vview record in web of science record created on 2008 12 10 modified on 2016 08 08

a fractional dickey fuller test for unit roots this paper presents a new test for fractionally integrated fi processes in particular we propose a testing procedure in the time domain that extends the well known dickey fuller approach originally designed for the i 1 versus i 0 case to the more general setup of fid 0 versus fid 1 with d1 d 0 when d0 1 the proposed test statistics are based on the ols estimator or its t ratio of the coefficient on d1 yt 1 in a regression of y t on d1 yt 1 and possibly some lags ofy t when d1 is not taken to be known a priori a pre estimation of d1 is needed to implement the test we show that the choice of any t 1 2 consistent estimator of d1 0 1 suffices to make the test feasible while achieving asymptotic normality monte carlo simulations support the analytical results derived in the paper and show that proposed tests fare very well both in terms of power and size when compared with others available in the literature the paper ends with two empirical applications

fitting long memory models by generalized linear regression summary there is an increasing awareness of the importance of long memory models in statistical applications if long memory is present it has to be taken into account in order to obtain reliable tests and confidence intervals one obstacle to using models with long memory in routine statistical analysis has been the lack of easily available and sufficiently versatile statistical software here we propose a simple but flexible class of parametric models which can be used to model such behaviour we demonstrate that these models can be fitted by generalized linear regression standard statistical software packages can be used a data example is discussed

on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity abstract this article considers fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity which combines the popular generalized autoregressive conditional heteroscedastic garch and the fractional arma models the fractional differencing parameter d can be greater than 1 2 thus incorporating the important unit root case some sufficient conditions for stationarity ergodicity and existence of higher order moments are derived an algorithm for approximate maximum likelihood ml estimation is presented the asymptotic properties of ml estimators which include consistency and asymptotic normality are discussed the large sample distributions of the residual autocorrelations and the square residual autocorrelations are obtained and two portmanteau test statistics are established for checking model adequacy in particular non stationary farima p d q garch r s models are also considered some simulation results are reported as an illustration

bifurcation into gaps in the essential spectrum in this lecture bifurcation from any boundary point of the essential spectrum is studied for a class of nonlinear operators generalizing results concerning bifurcation from the lowest point of the continuous spectrum the study is motivated by a nonlinear hill s equation as a typical example for a problem with gaps in the purely continuous spectrum