invariant manifolds of partial functional differential equations this paper is concerned with the existence smoothness and attractivity of invariant manifolds for evolutionary processes on general banach spaces when the nonlinear perturbation has a small global lipschitz constant and locally ck smooth near the trivial solution such a nonlinear perturbation arises in many applications through the usual cut off procedure but the requirement in the existing literature that the nonlinear perturbation is globally ck smooth and has a globally small lipschitz constant is hardly met in those systems for which the phase space does not allow a smooth cut off function our general results are illustrated by and applied to partial functional differential equations for which the phase space c r 0 x where r 0 and x being a banach space has no smooth inner product structure and for which the validity of variation of constants formula is still an interesting open problem

perron type theorems for functional differential equations with infinite delay in a banach space for functional differential equations in a banach space we obtain some results on the asymptotic behavior of solutions which correspond to perron type theorems for differential equations without delay or with finite delay

the zd garch model a new way to study heteroscedasticity this paper proposes a first order zero drift garch zd garch 1 1 model to study conditional heteroscedasticity and heteroscedasticity together unlike the classical garch model zd garch 1 1 model is always non stationary regardless of the sign of the lyapunov exponent gamma 0 but interestingly when gamma 0 0 it is stable with its sample path oscillating randomly between zero and infinity over time furthermore this paper studies the generalized quasi maximum likelihood estimator gqmle of zd garch 1 1 model and establishes its strong consistency and asymptotic normality based on the gqmle an estimator for gamma 0 a test for stability and a portmanteau test for model checking are all constructed simulation studies are carried out to assess the finite sample performance of the proposed estimators and tests applications demonstrate that a stable zd garch 1 1 model is more appropriate to capture heteroscedasticity than a non stationary garch 1 1 model which suffers from an inconsistent qmle of the drift term

delay times of sequential procedures for multiple time series regression models we consider a multiple regression model in which the explanatory variables are specified by time series to sequentially test for the stability of the regression parameters in time we introduce a detector which is based on the first excess time of a cusum type statistic over a suitably constructed threshold function the aim of this paper is to study the delay time associated with this detector as our main result we derive the limit distribution of the delay time and provide thereby a theory that extends the benchmark average run length concept utilized in most of the sequential monitoring literature to highlight the applicability of the limit results in finite samples we present a monte carlo simulation study and an application to macroeconomic data

topsis for modm abstract in this study we extend topsis to solve a multiple objective decision making problem the principle of compromise of topsis for multiple criteria decision making is that the chosen solution should have the shortest distance from the positive ideal solution as well as the longest distance from the negative ideal solution thus we reduce a k dimensional objective space to a two dimensional objective space by a first order compromise procedure we then use membership functions of fuzzy set theory to represent the satisfaction level for both criteria we obtain a single objective programming problem by using the max min operator for the second order compromise operation to illustrate the procedure the bow river valley water quality management problem is solved by use of topsis

self weighted lad based inference for heavy tailed threshold autoregressive models abstract the least squares estimator of the threshold autoregressive tar model may not be consistent when its tail is less than or equal to 2 neither theory nor methodology can be applied to model fitting in this case this paper is to develop a systematic procedure of statistical inference for the heavy tailed tar model we first investigate the self weighted least absolute deviation estimation for the model it is shown that the estimated slope parameters are n consistent and asymptotically normal and the estimated thresholds are n consistent each of which converges weakly to the smallest minimizer of a compound poisson process based on this theory the wald test statistic is considered for testing the linear restriction of slope parameters and a procedure is given for inference of threshold parameters we finally construct a sign based portmanteau test for model checking simulations are carried out to assess the performance of our procedure and a real example is given

stable manifolds for delay equations and parameter dependence abstract we establish the existence of lipschitz stable invariant manifolds for semiflows generated by a delay equation x l t x t f t x t assuming that the linear equation x l t x t admits a nonuniform exponential dichotomy and that f is a sufficiently small lipschitz perturbation we also show that the stable invariant manifolds are lipschitz in the parameter

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 bootstrapped spectral test for adequacy in weak arma models this paper proposes a cramer von mises cm test statistic to check the adequacy of weak arma models without posing a martingale difference assumption on the error terms the asymptotic null distribution of the cm test is obtained moreover this cm test is consistent and has nontrivial power against the local alternative of order n 1 2 due to the unknown dependence of error terms and the estimation effects a new block wise random weighting method is constructed to bootstrap the critical values of the test statistic the new method is easy to implement and its validity is justified the theory is illustrated by a small simulation study and an application to s p 500 stock index

gel estimation for heavy tailed garch models with robust empirical likelihood inference abstract we construct a generalized empirical likelihood estimator for a garch 1 1 model with a possibly heavy tailed error the estimator imbeds tail trimmed estimating equations allowing for over identifying conditions asymptotic normality efficiency and empirical likelihood based confidence regions for very heavy tailed random volatility data we show the implied probabilities from the tail trimmed continuously updated estimator elevate weight for usable large values assign large but not maximum weight to extreme observations and give the lowest weight to non leverage points we derive a higher order expansion for gel with imbedded tail trimming gelitt which reveals higher order bias and efficiency properties available when the garch error has a finite second moment higher order asymptotics for gel without tail trimming requires the error to have moments of substantially higher order we use first order asymptotics and higher order bias to justify the choice of the number of trimmed observations in any given sample we also present robust versions of generalized empirical likelihood ratio wald and lagrange multiplier tests and an efficient and heavy tail robust moment estimator with an application to expected shortfall estimation finally we present a broad simulation study for gel and gelitt and demonstrate profile weighted expected shortfall for the russian ruble us dollar exchange rate we show that tail trimmed cue gmm dominates other estimators in terms of bias mse and approximate normality

estimation risk for the var of portfolios driven by semi parametric multivariate models abstract joint estimation of market and estimation risks in portfolios is investigated when the individual returns follow a semi parametric multivariate dynamic model and the asset composition is time varying under ellipticity of the conditional distribution asymptotic theory for the estimation of the conditional value at risk var is developed an alternative method the filtered historical simulation which does not rely on ellipticity is also studied asymptotic confidence intervals for the conditional var which allow for simultaneous quantification of the market and estimation risks are derived the particular case of minimum variance portfolios is analyzed in more detail potential usefulness feasibility and drawbacks of the two approaches are illustrated via monte carlo experiments and an empirical study based on stock returns

a modified topsis with a different ranking index abstract as a tool for decision analysis the topsis technique for order preference by similarity to ideal solution attempts to choose alternative that should simultaneously have the closest distance from the positive ideal solution pis and the farthest distance from the negative ideal solution nis although the ranking index of topsis is reasonable it contains a flaw that is this ranking index is irrespective of the weights of separations of an alternative from the pis and the nis in other words no matter what weights the decision maker assigns to these two separations the ranking results would not differ as if he has no preference for these two separations this flaw will certainly limit the applicability of topsis by treating the separations of an alternative from the pis and the nis as a cost criterion and a benefit criterion respectively we reduced the original mcdm multi criteria decision making problem to a new mcdm problem with these two criteria only by proposing w and w as the weights of the cost criterion and the benefit criterion respectively we defined a new ranking index experimental results showed that if the number of alternatives exceeds two or if the relative importance of the two separations should be considered the proposed ranking index would be a better choice finally two numerical examples of a real life case are given for illustration in summary the proposed ranking index is intelligible and intrinsically superior to the original ranking index in seeking compromised solutions

least absolute deviations estimation for arch and garch models hall yao 2003 showed that for arch garch i e autoregressive conditional heteroscedastic generalised autoregressive conditional heteroscedastic models with heavy tailed errors the conventional maximum quasilikelihood estimator suffers from complex limit distributions and slow convergence rates in this paper three types of absolute deviations estimator have been examined and the one based on logarithmic transformation turns out to be particularly appealing we have shown that this estimator is asymptotically normal and unbiased furthermore it enjoys the standard convergence rate of n 1 2 regardless of whether the errors are heavy tailed or not simulation lends further support to our theoretical results

estimating multivariate volatility models equation by equation summary the paper investigates the estimation of a wide class of multivariate volatility models instead of estimating an m multivariate volatility model a much simpler and numerically efficient method consists in estimating m univariate generalized auto regressive conditional heteroscedasticity type models equation by equation in the first step and a correlation matrix in the second step strong consistency and asymptotic normality of the equation by equation estimator are established in a very general framework including dynamic conditional correlation models the equation by equation estimator can be used to test the restrictions imposed by a particular multivariate generalized auto regressive conditional heteroscedasticity specification for general constant conditional correlation models we obtain the consistency and asymptotic normality of the two step estimator comparisons with the global method in which the model parameters are estimated in one step are provided monte carlo experiments and applications to financial series illustrate the interest of the approach

lade based inference for arma models with unspecified and heavy tailed heteroscedastic noises this article develops a systematic procedure of statistical inference for the auto regressive moving average arma model with unspecified and heavy tailed heteroscedastic noises we first investigate the least absolute deviation estimator lade and the self weighted lade for the model both estimators are shown to be strongly consistent and asymptotically normal when the noise has a finite variance and infinite variance respectively the rates of convergence of the lade and the self weighted lade are n 1 2 which is faster than those of least square estimator lse for the arma model when the tail index of generalized auto regressive conditional heteroskedasticity garch noises is in 0 4 and thus they are more efficient in this case since their asymptotic covariance matrices cannot be estimated directly from the sample we develop the random weighting approach for statistical inference under this nonstandard case we further propose a novel sign based portmanteau test for model adequacy simulat

consistency and asymptotic normality of the quasi maximum likelihood estimator in igarch 1 1 and covariance stationary garch 1 1 models this paper provides a proof of the consistency and asymptotic normality of the quasi maximum likelihood estimator in garch 1 1 and igarch 1 1 models in contrast to the case of a unit root in the conditional mean the presence of a unit root in the conditional variance does not affect the limiting distribution of the estimators in both models estimators are normally distributed in addition a consistent estimator of the covariance matrix is available enabling the use of standard test statistics for inference

solving multi period project selection problems with fuzzy goal programming based on topsis and a fuzzy preference relation project portfolio managers are multi objective decision makers dms who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multi period planning horizon however project portfolio decisions are complex multi objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences we propose a goal programming gp approach for project portfolio selection that embraces conflicting fuzzy goals with imprecise priorities a fuzzy goal with an aspiration level and a predefined membership function is defined for each objective the impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations this leads to type ii fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets the proposed model is based on the technique for order preference by similarity to ideal solution topsis and fuzzy preference relations topsis is used to reduce the multi objective problem into a bi objective problem the resulting bi objective problem is solved with fuzzy gp fgp the fuzzy preference relations are used to help dms express their preferences with respect to the membership values of the fuzzy goals the proposed approach is used to solve a real life problem characterized as a fuzzy multi objective project selection with multi period planning horizon mops mpph the performance of the proposed approach is compared with a competing method in the literature we show that our approach generates high quality solutions with minimal computational efforts

stationarity of garch processes and of some nonnegative time series abstract two time series models are considered garch processes and generalized multivariate autoregressive equations x n 1 a n 1 x n b n 1 with nonnegative i i d coefficients in each case a necessary and sufficient condition ensuring the existence of a strictly stationary solution is given

multi attribute decision making a simulation comparison of select methods abstract several methods have been proposed for solving multi attribute decision making problems madm a major criticism of madm is that different techniques may yield different results when applied to the same problem the problem considered in this study consists of a decision matrix input of n criteria weights and ratings of l alternatives on each criterion the comparative performance of some methods has been investigated in a few mostly field studies in this simulation experiment we investigate the performance of eight methods electre topsis multiplicative exponential weighting mew simple additive weighting saw and four versions of ahp original vs geometric scale and right eigenvector vs mean transformation solution simulation parameters are the number of alternatives criteria and their distribution the solutions are analyzed using twelve measures of similarity of performance similarities and differences in the behavior of these methods are investigated dissimilarities in weights produced by these methods become stronger in problems with few alternatives however the corresponding final rankings of the alternatives vary across methods more in problems with many alternatives although less significant the distribution of criterion weights affects the methods differently in general all ahp versions behave similarly and closer to saw than the other methods electre is the least similar to saw except for closer matching the top ranked alternative followed by mew topsis behaves closer to ahp and differently from electre and mew except for problems with few criteria a similar rank reversal experiment produced the following performance order of methods saw and mew best followed by topsis ahps and electre it should be noted that the electre version used was adapted to the common madm problem and therefore it did not take advantage of the method s capabilities in handling problems with ordinal or imprecise information

inconsistency of the mle and inference based on weighted ls for larch models this paper considers a class of finite order autoregressive linear arch models the model captures the leverage effect allows the volatility to be arbitrarily close to zero and to reach its minimum for non zero innovations and is appropriate for long memory modeling when infinite orders are allowed however the quasi maximum likelihood estimator is in general inconsistent a self weighted least squares estimator is proposed and is shown to be asymptotically normal a score test for conditional homoscedasticity and diagnostic portmanteau tests are developed their performance is illustrated via simulation experiments it is also investigated whether stock market returns exhibit some of the characteristic features of the linear arch model

robust score and portmanteau tests of volatility spillover abstract this paper presents a variety of tests of volatility spillover that are robust to heavy tails generated by large errors or garch type feedback the tests are couched in a general conditional heteroskedasticity framework with idiosyncratic shocks that are only required to have a finite variance if they are independent we negligibly trim test equations or components of the equations and construct heavy tail robust score and portmanteau statistics trimming is either simple based on an indicator function or smoothed in particular we develop the tail trimmed sample correlation coefficient for robust inference and prove that its gaussian limit under the null hypothesis of no spillover has the same standardization irrespective of tail thickness further if spillover occurs within a specified horizon our test statistics obtain power of one asymptotically we discuss the choice of trimming portion including a smoothed p value over a window of extreme observations a monte carlo study shows our tests provide significant improvements over extant garch based tests of spillover and we apply the tests to financial returns data finally based on ideas in patton 2011 we construct a heavy tail robust forecast improvement statistic which allows us to demonstrate that our spillover test can be used as a model specification pre test to improve volatility forecasting

tests for conditional ellipticity in multivariate garch models tests are proposed for the assumption that the conditional distribution of a multivariate garch process is elliptic these tests are of kolmogorov smirnov and cramer von mises type and make use of the common geometry underlying the characteristic function of any spherically symmetric distribution the asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions it is shown that both the finite sample and the asymptotic null distribution depend on the unknown distribution of the euclidean norm of the innovations therefore a conditional monte carlo procedure is used to actually carry out the tests the validity of this resampling scheme is formally justified results on the behavior of the new tests in finite samples are included along with comparisons with other tests

self weighted and local quasi maximum likelihood estimators for arma garch igarch models the limit distribution of the quasi maximum likelihood estimator qmle for parameters in the arma garch model remains an open problem when the process has infinite 4th moment we propose a self weighted qmle and show that it is consistent and asymptotically normal under only a fractional moment condition based on this estimator the asymptotic normality of the local qmle is established for the arma model with garch finite variance and igarch errors using the self weighted and the local qmles we construct wald statistics for testing linear restrictions on the parameters and their limiting distributions are given in addition we show that the tail index of the igarch process is always 2 which is independently of interest

risk parameter estimation in volatility models abstract this paper introduces the concept of risk parameter in conditional volatility models of the form t t 0 t and develops statistical procedures to estimate this parameter for a given risk measure r the risk parameter is expressed as a function of the volatility coefficients 0 and the risk r t of the innovation process a two step method is proposed to successively estimate these quantities an alternative one step approach relying on a reparameterization of the model and the use of a non gaussian qml is proposed asymptotic results are established for smooth risk measures as well as for the value at risk var asymptotic comparisons of the two approaches for var estimation suggest a superiority of the one step method when the innovations are heavy tailed for standard garch models the comparison only depends on characteristics of the innovations distribution not on the volatility parameters monte carlo experiments and an empirical study illustrate the superiority of the one step approach for financial series

regime switching for dynamic correlations we propose a new model for the variance between multiple time series the regime switching dynamic correlation we decompose the covariances into correlations and standard deviations and the correlation matrix follows a regime switching model it is constant within a regime but different across regimes the transitions between the regimes are governed by a markov chain this model does not suffer from a curse of dimensionality and it allows analytic computation of multi step ahead conditional expectations of the variance matrix when combined with the armach model taylor modelling financial time series wiley new york and schwert j finance 44 5 1989 1115 for the standard deviations we also present an empirical application which illustrates that our model can have a better fit of the data than the dynamic conditional correlation model proposed by engle j business econ statist 20 3 2002 339

conditional heteroscedastic time series models abstract under the traditional linear time series or regression setting the conditional variance of one step ahead prediction is time invariant experience in conjunction with data analysis however suggests that the variability of a process might well depend on the available information this reality has motivated extensive research to relax the constant variance assumption imposed by the traditional linear time series model and several classes of generalized parametric models designed specifically for handling nonhomogeneity of a process have been proposed recently in particular the random coefficient autoregressive rca models were widely investigated by time series analysts and the autoregressive conditional heteroscedastic arch models were investigated by econometricians the interesting fact is that the arch processes can be regarded as special cases of the rca model in this article i first give the relationship between these two types of models and show that the special feature of these t

weighted least absolute deviations estimation for an ar 1 process with arch 1 errors the weighted least absolute deviations estimator is studied for an ar 1 process with arch 1 errors e t unlike for the quasi maximum likelihood estimator the estimator s limiting distribution is shown to be normal even when e e 4 t furthermore the estimator can be applied to examine the symmetry of the density of e t and to estimate the quantity e log 1 2 e t which are of crucial importance for conducting asymptotic inference for quasi maximum likelihood estimators and weighted least absolute deviations estimators

residual based rank specification tests for ar garch type models this paper derives the asymptotic distribution for a number of rank based and classical residual specification tests in ar garch type models we consider tests for the null hypotheses of no linear and quadratic serial residual autocorrelation residual symmetry and no structural breaks we also apply our method to backtesting value at risk for these tests we show that generally no size correction is needed in the asymptotic test distribution when applied to ar garch residuals obtained through gaussian quasi maximum likelihood estimation to be precise we give exact expressions for the limiting null distribution of the test statistics applied to standardized residuals and find that standard critical values often though not always lead to conservative tests for this result we give simple necessary and sufficient conditions simulations show that our asymptotic approximations work well for a large number of ar garch models and parameter values we also show that the rank based tests often though not always have superior power properties over the classical tests even if they are conservative an empirical application illustrates the relevance of these tests to the ar garch models for weekly stock market return indices of some major and emerging countries

flow invariance for nonlinear partial differential delay equations several fundamental results on existence flow invariance regularity and linearized stability of solutions to the nonlinear partial differential delay equation u t bu t f u t t 0 uo with b c x x x w accretive are developed for a general banach space x in contrast to existing results with the history response f globally defined and at least lipschitz on bounded sets the results are tailored for situations with f defined on possibly thin subsets of the initial history space e only and are applied to place several classes of population models in their natural l 1 setting the main result solves the open problem of a subtangential condition for flow invariance of solutions in the fully nonlinear case paralleling those known for the cases of a no delay b ordinary delay equations with b 0 and c the semilinear case

non standard inference for augmented double autoregressive models with null volatility coefficients abstract this paper considers an augmented double autoregressive dar model which allows null volatility coefficients to circumvent the over parameterization problem in the dar model since the volatility coefficients might be on the boundary the statistical inference methods based on the gaussian quasi maximum likelihood estimation gqmle become non standard and their asymptotics require the data to have a finite sixth moment which narrows the applicable scope in studying heavy tailed data to overcome this deficiency this paper develops a systematic statistical inference procedure based on the self weighted gqmle for the augmented dar model except for the lagrange multiplier test statistic the wald quasi likelihood ratio and portmanteau test statistics are all shown to have non standard asymptotics the entire procedure is valid as long as the data are stationary and its usefulness is illustrated by simulation studies and one real example

semiparametric inference in a garch in mean model abstract a new semiparametric estimator for an empirical asset pricing model with general nonparametric risk return tradeoff and garch type underlying volatility is introduced based on the profile likelihood approach it does not rely on any initial parametric estimator of the conditional mean function and it is under stated conditions consistent asymptotically normal and efficient i e it achieves the semiparametric lower bound a sampling experiment provides finite sample comparisons with the parametric approach and the iterative semiparametric approach with parametric initial estimate of conrad and mammen 2008 an application to daily stock market returns suggests that the risk return relation is indeed nonlinear

a modified weighted topsis to identify influential nodes in complex networks abstract identifying influential nodes in complex networks is still an open issue although various centrality measures have been proposed to address this problem such as degree betweenness and closeness centralities they all have some limitations recently technique for order performance by similarity to ideal solution topsis as a tradeoff between the existing metrics has been proposed to rank nodes effectively and efficiently it regards the centrality measures as the multi attribute of the complex network and connects the multi attribute to synthesize the evaluation of node importance of each node however each attribute plays an equally important part in this method which is not reasonable in this paper we improve the method to ranking the node s spreading ability a new method named as weighted technique for order performance by similarity to ideal solution weighted topsis is proposed in our method we not only consider different centrality measures as the multi attribute to the network but also propose a new algorithm to calculate the weight of each attribute to evaluate the performance of our method we use the susceptible infected recovered sir model to do the simulation on four real networks the experiments on four real networks show that the proposed method can rank the spreading ability of nodes more accurately than the original method

asymptotic normality of the quasi maximum likelihood estimator for multidimensional causal processes strong consistency and asymptotic normality of the quasi maximum likelihood estimator qmle are given for a general class of multidimensional causal processes for particular cases already studied in the literature for instance univariate or multivariate garch arch arma garch processes the assumptions required for establishing these results are often weaker than existing conditions the qmle asymptotic behavior is also given for numerous new examples of univariate or multivariate processes for instance tarch or nlarch processes

optimal predictions of powers of conditionally heteroscedastic processes in conditionally heteroskedastic models the optimal prediction of powers or logarithms of the absolute process has a simple expression in terms of the volatility process and an expectation involving the independent process a standard procedure for estimating this prediction is to estimate the volatility by gaussian quasi maximum likelihood qml in a first step and to use empirical means based on rescaled innovations to estimate the expectation in a second step this paper proposes an alternative one step procedure based on an appropriate non gaussian qml estimation of the model and establishes the asymptotic properties of the two approaches their performances are compared for finite order garch models and for the infinite arch for the standard garch p q and the asymmetric power garch p q it is shown that the are of the estimators only depends on the prediction problem and some moments of the independent process an application to indexes of major stock exchanges is proposed

parameter dependence of stable manifolds under nonuniform hyperbolicity abstract for a nonautonomous linear equation v a t v in a banach space with a nonuniform exponential dichotomy we show that the nonlinear equation v a t v f t v has stable invariant manifolds v which are lipschitz in the parameter provided that f is a sufficiently small lipschitz perturbation since any linear equation with nonzero lyapunov exponents has a nonuniform exponential dichotomy the above assumption is very general we emphasize that passing from a classical uniform exponential dichotomy to a general nonuniform exponential dichotomy requires a substantially new approach

sign based portmanteau test for arch type models with heavy tailed innovations this paper proposes a sign based portmanteau test for diagnostic checking of arch type models estimated by the least absolute deviation approach under the strict stationarity condition the asymptotic distribution is obtained the new test is applicable for very heavy tailed innovations with only finite fractional moments simulations are undertaken to assess the performance of the sign based test as well as a comparison with other two portmanteau tests a real empirical example for exchange rates is given to illustrate the practical usefulness of the test

inference in arch and garch models with heavy tailed errors arch and garch models directly address the dependency of conditional second moments and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present these include financial time series which can be particularly heavy tailed however little is known about properties of arch or garch models in the heavy tailed setting and no methods are available for approximating the distributions of parameter estimators there in this paper we show that for heavy tailed errors the asymptotic distributions of quasi maximum likelihood parameter estimators in arch and garch models are nonnormal and are particularly difficult to estimate directly using standard parametric methods standard bootstrap methods also fail to produce consistent estimators to overcome these problems we develop percentile t subsample bootstrap approximations to estimator distributions studentizing is employed to approximate scale and the subsample bootstrap is used to estimate shape the good performance of this approach is demonstrated both theoretically and numerically

fitting an error distribution in some heteroscedastic time series models this paper addresses the problem of fltting a known distribution to the innovation distribution in a class of stationary and ergodic time series models the asymptotic null distribution of the usual kolmogorov smirnov test based on the residuals generally depends on the underlying model parameters and the error distribution to overcome the dependence on the underlying model parameters we propose that tests be based on a vector of certain weighted residual empirical processes under the null hypothesis and under minimal moment conditions this vector of processes is shown to converge weakly to a vector of independent copies of a gaussian process whose covariance function depends only on the fltted distribution and not on the model under certain local alternatives the proposed test is shown to have nontrivial asymptotic power the monte carlo critical values of this test are tabulated when fltting standard normal and double exponential distributions the results obtained are shown to be applicable to garch and arma garch models the often used models in econometrics and flnance a simulation study shows that the test has satisfactory size and power for flnite samples at these models the paper also contains an asymptotic uniform expansion result for a general weighted residual empirical process useful in heteroscedastic models under minimal moment conditions a result of independent interest

asymptotics of cholesky garch models and time varying conditional betas this paper proposes a new model with time varying slope coefficients our model called char is a cholesky garch model based on the cholesky decomposition of the conditional variance matrix introduced by pourahmadi 1999 in the context of longitudinal data we derive stationarity and invertibility conditions and prove consistency and asymptotic normality of the full and equation by equation qml estimators of this model we then show that this class of models is useful to estimate conditional betas and compare it to the approach proposed by engle 2016 finally we use real data in a portfolio and risk management exercise we find that the char model outperforms a model with constant betas as well as the dynamic conditional beta model of engle 2016

generalized autoregressive conditional heteroskedasticity a natural generalization of the arch autoregressive conditional heteroskedastic process introduced in engle 1982 to allow for past conditional variances in the current conditional variance equation is proposed stationarity conditions and autocorrelation structure for this new class of parametric models are derived maximum likelihood estimation and testing are also considered finally an empirical example relating to the uncertainty of the inflation rate is presented

bootstrapping the portmanteau tests in weak auto regressive moving average models this paper uses a random weighting rw method to bootstrap the critical values for the ljung box monti portmanteau tests and weighted ljung box monti portmanteau tests in weak arma models unlike the existing methods no user chosen parameter is needed to implement the rw method as an application these four tests are used to check the model adequacy in power garch models simulation evidence indicates that the weighted portmanteau tests have the power advantage over other existing tests a real example on s p 500 index illustrates the merits of our testing procedure as one extension work the block wise rw method is also studied

lipschitzian semigroups and abstract functional differential equations abstract the paper is devoted to studying an abstract functional differential equation by a nonlinear semigroup approach we first prove in details the equivalence of the well posedness of an abstract functional differential equation and an associated abstract cauchy problem in the sense of strong solutions secondly a sufficient condition is derived for well posedness of the abstract functional differential equation thirdly we present principles of linearized stability for the abstract functional differential equation finally the results obtained are applied to a reaction diffusion equation with delays

global self weighted and local quasi maximum exponential likelihood estimators for arma garch igarch models this paper investigates the asymptotic theory of the quasi maximum exponential likelihood estimators qmele for arma garch models under only a fractional moment condition the strong consistency and the asymptotic normality of the global self weighted qmele are obtained based on this self weighted qmele the local qmele is showed to be asymptotically normal for the arma model with garch finite variance and igarch errors a formal comparison of two estimators is given for some cases a simulation study is carried out to assess the performance of these estimators and a real example on the world crude oil price is given

parameter estimation for arma models with infinite variance innovations abstract we consider a standard arma process of the form phi b xt theta b zt where the innovations zt belong to the domain of attraction of a stable law so that neither the zt nor the xt have a finite variance our aim is to estimate the coefficients of phi and theta since maximum likelihood estimation is not a viable possibility due to the unknown form of the marginal density of the innovation sequence we adopt the so called whittle estimator based on the sample periodogram of the x sequence despite the fact that the periodogram does not a priori seem like a logical object to study in this non l situation we show that our estimators are consistent obtain their asymptotic distributions and show that they converge to the true values faster than in the usual l2 case

self weighted least absolute deviation estimation for infinite variance autoregressive models summary how to undertake statistical inference for infinite variance autoregressive models has been a long standing open problem to solve this problem we propose a self weighted least absolute deviation estimator and show that this estimator is asymptotically normal if the density of errors and its derivative are uniformly bounded furthermore a wald test statistic is developed for the linear restriction on the parameters and it is shown to have non trivial local power simulation experiments are carried out to assess the performance of the theory and method in finite samples and a real data example is given the results are entirely different from other published results and should provide new insights for future research on heavy tailed time series

hybrid quantile regression estimation for time series models with conditional heteroscedasticity estimating conditional quantiles of financial time series is essential for risk management and many other financial applications for time series models with conditional heteroscedasticity although it is the generalized auto regressive conditional heteroscedastic garch model that has the greatest popularity quantile regression for this model usually gives rise to non smooth non convex optimization which may hinder its practical feasibility the paper proposes an easy to implement hybrid quantile regression estimation procedure for the garch model where we overcome the intractability due to the square root form of the conditional quantile function by a simple transformation the method takes advantage of the efficiency of the garch model in modelling the volatility globally as well as the flexibility of quantile regression in fitting quantiles at a specific level the asymptotic distribution of the estimator is derived and is approximated by a novel mixed bootstrapping procedure a portmanteau test is further constructed to check the adequacy of fitted conditional quantiles the finite sample performance of the method is examined by simulation studies and its advantages over existing methods are illustrated by an empirical application to value at risk forecasting

compromise solution by mcdm methods a comparative analysis of vikor and topsis the multiple criteria decision making mcdm methods vikor and topsis are based on an aggregating function representing closeness to the ideal which originated in the compromise programming method in vikor linear normalization and in topsis vector normalization is used to eliminate the units of criterion functions the vikor method of compromise ranking determines a compromise solution providing a maximum group utility for the majority and a minimum of an individual regret for the opponent the topsis method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative ideal solution but it does not consider the relative importance of these distances a comparative analysis of these two methods is illustrated with a numerical example showing their similarity and some differences 2003 elsevier b v all rights reserved

two stage non gaussian qml estimation of garch models and testing the efficiency of the gaussian qmle abstract in generalized autoregressive conditional heteroskedastic garch models the standard identifiability assumption that the variance of the iid process is equal to 1 can be replaced by an alternative moment assumption we show that for estimating the original specification based on the standard identifiability assumption efficiency gains can be expected from using a quasi maximum likelihood qml estimator based on a non gaussian density and a reparameterization based on an alternative identifiability assumption a test allowing to determine whether a reparameterization is needed that is whether the more efficient qmle is obtained with a non gaussian density is proposed

asymptotic bias for quasi maximum likelihood estimators in conditional heteroskedasticity models virtually all applications of time varying conditional variance models use a quasimaximum likelihood estimator qmle consistency of a qmle requires an identification condition that the quasi log likelihood have a unique maximum at the true conditional mean and relative scale parameters we show that the identification condition holds for a non gaussian qmle if the conditional mean is identically zero or if a symmetry condition is satisfied without symmetry an additional parameter for the location of the innovation density must be added for identification we calculate the efficiency loss from adding such a parameter under symmetry when the parameter is not needed we also show that there is no efficiency loss for the conditional variance parameters of a garch process

moment condition tests for heavy tailed time series abstract we develop an asymptotically chi squared statistic for testing moment conditions e m t 0 0 where m t 0 may be weakly dependent scalar components of m t 0 may have an infinite variance and e m t need not exist for any under the alternative score tests are a natural application and in general a variety of tests can be heavy tail robustified by our method including white noise garch affects omitted variables distribution functional form causation volatility spillover and over identification the test statistic is derived from a tail trimmed sample version of the moments evaluated at a consistent plug in t for 0 depending on the test in question and heaviness of tails t may be any consistent estimator including sub t 1 2 convergent and or asymptotically non gaussian ones since t can be assured not to affect the test statistic asymptotically we adapt bootstrap p value occupation time and covariance determinant methods for selecting the trimming fractile in any sample and apply our statistic to tests of white noise omitted variables and volatility spillover we find it obtains sharp empirical size and strong power while conventional tests exhibit size distortions

stability of delay equations via lyapunov functions abstract the importance of lyapunov functions is well known in the general setting of nonautonomous linear delay equations v l t v t we show how to characterize completely the existence of a nonuniform exponential contraction or of a nonuniform exponential dichotomy in terms of lyapunov functions this includes uniform exponential behavior as a very special case and it provides an alternative usually simpler and particularly more direct approach to verify the existence of exponential behavior or to obtain the robustness of the dynamics under sufficiently small perturbations

a new method of identifying influential nodes in complex networks based on topsis abstract in complex networks identifying influential nodes is the very important part of reliability analysis which has been a key issue in analyzing the structural organization of a network in this paper a new evaluation method of node importance in complex networks based on technique for order performance by similarity to ideal solution topsis approach is proposed topsis as a multiple attribute decision making madm technique has been an important branch of decision making since then in addition topsis is first applied to identify influential nodes in a complex network in this open issue in different types of networks in which the information goes by different ways we consider several different centrality measures as the multi attribute of complex network in topsis application topsis is utilized to aggregate the multi attribute to obtain the evaluation of node importance of each node it is not limited to only one centrality measure but considers different centrality measures because every centrality measure has its own disadvantage and limitation then we use the susceptible infected si model to evaluate the performance numerical examples are given to show the efficiency and practicability of the proposed method

extension of the topsis method for decision making problems with fuzzy data decision making problem is the process of finding the best option from all of the feasible alternatives in this paper from among multicriteria models in making complex decisions and multiple attribute models for the most preferable choice technique for order preference by similarity to ideal solution topsis approach has been dealt with in real word situation because of incomplete or non obtainable information the data attributes are often not so deterministic there for they usually are fuzzy imprecise therefore the aim of this paper is to extend the topsis method to decision making problems with fuzzy data in this paper the rating of each alternative and the weight of each criterion are expressed in triangular fuzzy numbers the normalized fuzzy numbers is calculated by using the concept of a cuts finally a numerical experiment is used to illustrate the procedure of the proposed approach at the end of this paper

periodic seasonal reg arfima garch models for daily electricity spot prices novel periodic extensions of dynamic long memory regression models with autoregressive conditional heteroscedastic errors are considered for the analysis of daily electricity spot prices the parameters of the model with mean and variance specifications are estimated simultaneously by the method of approximate maximum likelihood the methods are implemented for time series of 1 200 4 400 daily price observations in four european power markets apart from persistence heteroscedasticity and extreme observations in prices a novel empirical finding is the importance of day of the week periodicity in the autocovariance function of electricity spot prices in particular the very persistent daily log prices from the nord pool power exchange of norway are effectively modeled by our framework which is also extended with explanatory variables to capture supply and demand effects the daily log prices of the other three electricity markets eex in germany powernext in france and apx in the netherlands are less

asymptotic inference for a nonstationary double ar 1 model we investigate the nonstationary double ar 1 model y t y t 1 t y 2 t 1 where 0 a 0 the t are independent standard normal random variables and e log t 0 we show that the maximum likelihood estimator of is consistent and asymptotically normal combination of this result with that in ling 2004 for the stationary case gives the asymptotic normality of the maximum likelihood estimator of for any in the real line with a root n rate of convergence this is in contrast to the results for the classical ar 1 model corresponding to a 0

a robust goodness of fit test for generalized autoregressive conditional heteroscedastic models summary the estimation of time series models with heavy tailed innovations has been widely discussed but corresponding goodness of fit tests have attracted less attention primarily because the autocorrelation function commonly used in constructing goodness of fit tests necessarily imposes certain moment conditions on the innovations as a bounded random variable has finite moments of all orders we address the problem by first transforming the residuals with a bounded function more specifically we consider the sample autocorrelation function of the transformed absolute residuals of a fitted generalized autoregressive conditional heteroscedastic model with the corresponding residual empirical distribution function naturally employed as the transformation a robust goodness of fit test is then constructed the asymptotic distributions of the test statistic under the null hypothesis and local alternatives are derived and monte carlo experiments are conducted to examine finite sample properties the proposed test is shown to be more powerful than existing tests when the innovations are heavy tailed

the efficiency of the estimators of the parameters in garch processes we propose a class of estimators for the parameters of a garch p q sequence we show that our estimators are consistent and asymptotically normal under mild conditions the quasi maximum likelihood and the likelihood estimators are discussed in detail we show that the maximum likelihood estimator is optimal if the tail of the distribution of the innovations is polynomial even a quasi maximum likelihood estimator based on exponential density performs better than the standard normal density based quasi likelihood estimator of lee and hansen and lumsdaine

testing the nullity of garch coefficients correction of the standard tests and relative efficiency comparisons this article is concerned with testing the nullity of coefficients in generalized autoregressive conditionally heteroscedastic garch models the problem is nonstandard because the quasi maximum likelihood estimator is subject to positivity constraints this article establishes the asymptotic null and local alternative distributions of wald score and quasi likelihood ratio tests efficiency comparisons under fixed alternatives are considered two cases of special interest are tests of the null hypothesis of one coefficient equal to zero and tests of the null hypothesis of no conditional heteroscedasticity finally the proposed approach is used in the analysis of financial data and suggests reconsidering the preeminence of garch 1 1 among garch models

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

an approach to generalization of fuzzy topsis method the topsis method is a technique for establishing order preference by similarity to the ideal solution and was primarily developed for dealing with real valued data this technique is currently one of most popular methods for multiple criteria decision making mcdm in many cases it is hard to present precisely exact ratings of alternatives with respect to local criteria and as a result these ratings are seen as fuzzy values a number of papers have been devoted to fuzzy extensions of the topsis method in the literature but these extensions are not complete since the ideal solutions are usually presented as real values not by fuzzy values or as fuzzy values which are not attainable in the decision matrix in most of these papers a defuzzification of elements of the fuzzy decision matrix is used which leads inevitably to a loss of important information and may even produce the wrong results in this paper we propose a new direct approach to the fuzzy extension of the topsis method which is free of the limitations of other known approaches we show that the distances of the alternatives from the ideal solutions may be treated in some sense as modified weighted sums of local criteria it is known that using weighted sums is not the best approach to the aggregation of local criteria in many real world situations therefore here we propose the use in addition to weighted sums some other types of local criteria aggregation in the topsis method and we develop a method for the generalization of different aggregation modes providing compromised final results

adaptive estimation in time series models in a framework particularly suited for many time series models we obtain a lan result under quite natural and economical conditions this enables us to construct adaptive estimators for part of the euclidean parameter in these semiparametric models special attention is directed to group models in time series with the important subclass of models with time varying location and scale our set up is confronted with the existing literature and as examples we reconsider linear regression and arma tar and arch models