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

tightness of products of random matrices and stability of linear stochastic systems soit n la distribution d un produit de n matrices aleatoire i i d on etudie la compacite et la convergence de la suite n n on l applique aux equations differentielles stochastiques lineaires

asymptotic analysis of the lyapunov exponent and rotation number of the random oscillator and application we construct asymptotic expansions for the exponential growth rate lyapunov exponent and rotation number of the random oscillator when the noise is large small rapidly varying or slowly varying we then apply our results to problems in the stability of the random oscillator the spectrum of the one dimensional random schr6dinger operator and wave propagation in a one dimensional random medium

a dimension formula for bernoulli convolutions we present a dynamical approach to the study of the singularity of infinitely convolved bernoulli measuresv for the golden section we introducev as the transverse measure of the maximum entropy measure on the repelling set invariant for contracting maps of the square the fat baker s transformation our approach strongly relies on the markov structure of the underlying dynamical system indeed if golden mean the fat baker s transformation has a very simple markov coding the ambiguity of order two of this coding which appears when projecting on the line due to passages for the central overlapping zone can be expressed by means of products of matrices of order two this product has a markov distribution inherited by the markov structure of the map the dimension of the projected measure is therefore associated to the growth of this product our dimension formula appears in a natural way as a version of the furstenberg guivarch formula our technique provides an explicit dimension formula and most important provides a formalism well suited for the multifractal analysis of this measure as we will show in a forthcoming paper

estimation of states and parameters for linear systems with nonlinearly parameterized perturbations we consider systems that can be described by a linear part with a nonlinear perturbation where the perturbation is parameterized by a vector of unknown constant parameters under a set of technical assumptions about the perturbation and its relationship to the outputs we present a modular design technique for estimating the system states and the unknown parameters the design consists of a high gain observer that estimates the states of the system together with the full perturbation and a parameter estimator constructed by the designer to invert a nonlinear equation we illustrate the technique on a simulated dc motor with friction

tightness of products of i i d random matrices ii in this paper we prove a necessary and sufficient condition for tightness of products of i i d finite dimensional random real matrices we give an example illustrating the use of our theorem and treat in more details the case of 2 x 2 real matrices

feedback stabilization of single input nonlinear systems abstract nonlinear geometric techniques partial feedback linearization and center manifold theory allow to reduce the design of a feedback stabilizing control for single input nonlinear systems into a lower dimensional stabilization problem the reduced order control system is explicitly constructed

convergence in distribution of products of d d random matrices abstract in this paper we present limit theorems on the convergence in distribution of products of i i d matrices based on easily verifiable conditions on the support of the distribution

a formula connecting sample and moment stability of linear stochastic systems given the linear stochastic system dot x a xi t x x in mathbb r d xi t some nice diffusion sample and moment stability of x equiv 0 are studied via the sample lyapunov exponent lambda and the lyapunov exponent of the pth mean g p of a solution generalizing a result of molchanov for the undamped linear oscillator it is shown that g p is a smooth convex function of p in mathbb r with g 0 0 and g 0 lambda for trace a 0 a second zero of g at p d is detected this allows one to draw simple but quite complete conclusions about the relation between sample and moment stability

a nonlinear autoregressive conditional duration model with applications to financial transaction data abstract this paper presents a new model that improves upon several inadequacies of the original autoregressive conditional duration acd model considered in engle and russell econometrica 66 5 1998 1127 1162 we propose a threshold autoregressive conditional duration tacd model to allow the expected duration to depend nonlinearly on past information variables conditions for the tacd process to be ergodic and existence of moments are established strong evidence is provided to suggest that fast transacting periods and slow transacting periods of nyse stocks have quite different dynamics based on the improved model we identify multiple structural breaks in the transaction duration data considered and those break points match nicely with real economic events

recurrent random walks in nonnegative matrices ii in this paper we continue the study undertaken in our earlier paper m1 one of the main results here can be described as follows letx0 x1 be a sequence of iid random affine maps from r d into itself let us write w n x n x n 1 x0 andz n x0x1 x n where composition of maps is the rule of multiplication by the attractora u u r d we mean the setau y r d p wnu n i o 0 for every openn containingy it is shown that the attractora u under mild conditions is the support of a stationary probability measure when the random walk z n has at least one recurrent state

linear siso systems with extremely sensitive zero structure if a system with regular system pencil and relative degree greater than one is perturbed the relative degree will typically decrease and new finite zeros will appear these new zeros are singularly perturbed this paper applies a new canonical parameterization to systems with singular system pencils such systems have undefined relative degree in singular systems new zeros also appear under small perturbation but they are not necessarily singularly perturbed rather these zeros may appear at any frequency

sequential detection of markov targets with trajectory estimation the problem of detection and possible estimation of a signal generated by a dynamic system when a variable number of noisy measurements can be taken is here considered assuming a markov evolution of the system in particular the pair signal observation forms a hidden markov model hmm a sequential procedure is proposed wherein the detection part is a sequential probability ratio test sprt and the estimation part relies upon a maximum a posteriori probability map criterion gated by the detection stage the parameter to be estimated is the trajectory of the state evolution of the system itself a thorough analysis of the asymptotic behavior of the test in this new scenario is given and sufficient conditions for its asymptotic optimality are stated i e for almost sure minimization of the stopping time and for first order minimization of any moment of its distribution an application to radar surveillance problems is also examined

feedback control of two time scale nonlinear systems this article concerns a class of two time scale single input single output nonlinear systems for such systems combination of singular perturbation and geometric methods is employed to synthesize well conditioned static state feedback laws that induce a well characterized input output behaviour and guarantee stability of the closed loop system the developed control laws are applied to two nonlinear chemical processes with time scale multiplicity and their performance is evaluated through simulations

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

convergence in distribution of products of random matrices a semigroup approach on considere le probleme de la convergence faible de la suite des puissances de convolution d une mesure de probabilite dans le contexte general d un semigroupe non compact

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

on the multifractal analysis of bernoulli convolutions i large deviation results we show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved bernoulli measures for the golden mean in this first part we establish some large deviation results for random products of matrices using perturbation theory of quasicompact operators

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

stationarity of stable power garch processes we present conditions for strict stationarity of power garch processes whose innovations are described by a heavy tailed and possibly asymmetric stable paretian distribution the results generalize those of bougerol and picard j econom 52 1992 115 who derived analogous conditions for standard i e power two garch processes with finite variance innovations

anderson localization for bernoulli and other singular potentials we prove exponential localization in the anderson model under very weak assumptions on the potential distribution in one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment in particular this solves the longstanding problem of localization for bernoulli potentials i e potentials that take only two values in dimensions greater than one we prove localization at high disorder for potentials with holder continuous distributions and for bounded potentials whose distribution is a convex combination of a holder continuous distribution with high disorder and an arbitrary distribution these include potentials with singular distributions we also show that for certain bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component

direct singular perturbation analysis of high gain and cheap control problems a new and direct approach to the analysis and design of high gain feedback and cheap control problems is developed transformation of such singular problems to singular perturbation models of conventional type early at the onset of analysis or design allows a direct application of the readily available singular perturbation literature the approach permits a simple characterization of a multivariable root loci under a high gain feedback and b asymptotic behavior of optimal closed loop poles state and control trajectories performance index and optimal transfer function as the control cost coefficient in the performance index goes to zero

large deviations for products of random two dimensional matrices we establish large deviation type estimates for i i d products of two dimensional random matrices with finitely supported probability distribution the estimates are stable under perturbations and require no irreducibility assumptions in consequence we obtain a uniform local modulus of continuity for the corresponding lyapunov exponent regarded as a function of the support of the distribution this in turn has consequences on the modulus of continuity of the integrated density of states and on the localization properties of random jacobi operators

fractionally integrated generalized autoregressive conditional heteroskedasticity abstract the new class of fractionally integrated generalized autoregressive conditionally heteroskedastic figarch processes is introduced the conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations unlike i d processes for the mean maximum likelihood estimates mle of the figarch parameters are argued to be t 1 2 consistent the small sample behavior of an approximate mle procedure is assessed through a simulation study which also documents how the estimation of a standard garch model tends to produce integrated or igarch like estimates an empirical example with daily deutschmark u s dollar exchange rates illustrates the practical relevance of the new figarch specification

augmented garch p q process and its diffusion limit abstract a family of parametric garch models defined in terms of an auxiliary process and referred to as the augmented garch process is proposed the strict stationarity of the augmented garch process is characterized and this process is shown to contain many existing parametric garch models the augmented garch process can serve as a general alternative for lagrange multiplier test of many existing garch specifications the diffusion limit of the augmented garch process is shown to contain many bivariate diffusion processes that are commonly used for modeling stochastic volatility in the finance literature this convergence result generalizes that of nelson 1990a to cover a substantially larger class of garch 1 1 models and also extends to the garch p q specification the augmented garch process can be used as a direct approximation to the stochastic volatility models or as the score generator in the efficient method of moments gallant and tauchen 1996 estimation of these models

kotani theory for one dimensional stochastic jacobi matrices we consider families of operators h on l2 given by h u n u n 1 u n 1 v n u n wherev is a stationary bounded ergodic sequence we prove analogs of kotani s results including that for a e ac h is the essential closure of the set ofe where e the lyaponov index vanishes and the result that ifv is non deterministic then ac is empty

localization for off diagonal disorder and for continuous schrodinger operators we extend the proof of localization by delyon levy and souillard to accommodate the anderson model with off diagonal disorder and the continuous schrodinger equation with a random potential

central limit theorem in negative curvature we prove a central limit theorem for the distance of the brownian point on the universal cover of a compact negatively curved riemannian manifold the technical point is a contraction property for the leafwise brownian motion along the stable foliation

on the control of regularly e perturbed nonlinear systems abstract this paper deals with the control of regularly c perturbed nonlinear systems on the basis of a nominal control law i e designed with respect to the unperturbed plant an iterative procedure is proposed for achieving at a fixed order of approximation the requirements specified oh the dynamics of the feedback control system the sufficient conditions ensuring the applicability of the procedure are verified when dealing with feedback linearization problems some working examples developed in the paper illustrate the efficiency of such a design strategy

theoremes limite pour les systemes lineaires a coefficients markoviens nous montrons un theoreme central limite et une estimee des grandes deviations pour les solutions d equations differentielles stochastiques lineaires a coefficients markoviens ces resultats sont obtenus dans le cadre general des processus markoviens multiplicatifs ils s appliquent alors par exemple au flot derive d un flot stochastique sur une variete compacte et aux produits de matrices aleatoires en dependance markovienne

zeros of discretized continuous systems expressed in the euler operator an asymptotic analysis the structure of the zeros of siso continuous time systems which are discretized via a zero order hold and expressed in the euler operator is studied in particular it is shown that when state space descriptions of linear siso continuous time systems with relative degree spl ges 2 are discretized then the zero dynamics of the resulting discrete system is singularly perturbed and shows a separation of time scale the part of the zero dynamics associated with the fast time scale is shown to correspond to the zeros introduced by the sampling process sampling zeros an asymptotic formula for this part of the zero dynamics is given and implications of the result to control design based on pole zero cancellation is discussed

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

limit theorems for products of positive random matrices let s be the set of q times q matrices with positive entries such that each column and each row contains a strictly positive element and denote by s circ the subset of these matrices all entries of which are strictly positive consider a random ergodic sequence x n n geq1 in s the aim of this paper is to describe the asymptotic behavior of the random products x n x n ldots x 1 n geq 1 under the main hypothesis p bigcup n geq 1 x n in s circ 0 we first study the behavior in direction of row and column vectors of x n then adding a moment condition we prove a law of large numbers for the entries and lengths of these vectors and also for the spectral radius of x n under the mixing hypotheses that are usual in the case of sums of real random variables we get a central limit theorem for the previous quantities the variance of the gaussian limit law is strictly positive except when x n n geq 1 is tight this tightness property is fully studied when the x n n geq 1 are independent

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

an integral manifold approach to tracking control for a class of non minimum phase linear systems using output feedback in this paper the tracking control problem for a class of siso non minimum phase linear systems containing n dominant slow modes and m parasitic fast modes using output feedback is considered it is assumed that the reduced order slow model obtained by neglecting the parasitic modes is minimum phase it is shown that by using the integral manifolds approach it is possible to design a corrected control so that the full order system restricted to the pth order corrected manifold is minimum phase this in principle amounts to formally defining a new output for which the corrected system is minimum phase by applying to the full order system the corrected dynamical output feedback controller that is designed for the minimum phase corrected system it is then possible for the actual output to track a class of desired trajectories with minimum accuracy of o ep where 0 e 1 is the perturbation parameter and p is an arbitrarily large positive integer moreover it is shown that the zero dynamics of the associated corrected slow subsystem is itself singularly perturbed therefore the dynamical output feedback may contain both slow and fast dynamics numerical simulations are included to demonstrate the significant improvement that is possible to achieve by employing the proposed control strategy

on the connection between nonlinear differential algebraic equations and singularly perturbed control systems in nonstandard form considers a class of control systems represented by nonlinear differential equations depending on a small parameter the systems are not in the standard singularly perturbed form and therefore one of the challenges is to show that the control systems do represent singularly perturbed two time scale systems assumptions are introduced which guarantee that an equivalent representation for the systems can be obtained in the standard singularly perturbed form thereby justifying the two time scale property the equations for the slow dynamics are characterized by a set of differential algebraic equations which have been studied previosly in the literature the fast dynamics are characterized by differential equations both the slow and the fast dynamics are easily derived and are defined in terms of variables that define the original control system control design for the class of systems being considered is studied using the composite control approach

a new systematic design of high gain feedback for nonlinear systems with unmatched uncertainties the systematic design of a robust output tracking algorithm for a feedback linearizable system with unmatched uncertainties is presented the proposed technique is based on a backstepping procedure to construct a time varying singularly perturbed system and the underlying theoretical approach by the lyapunov theory the main result is that a dynamically parametrized state feedback is developed to cancel the output tracking error finally an illustrative example through a chemical reactor system is given to demonstrate the utilization of the approach developed in this paper

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

robust output tracking for nonlinear systems with weakly non minimum phase this paper is concerned with the problem of designing a robust output tracking controller for mimo nonlinear systems with weakly non minimum phase based on our system formulation control plants with uncertainties and or with actuator dynamics fall into the class under consideration the controller design here is divided into two phases fast feedback control and slow feedback control so that a final composite control is obtained the former is chosen to stabilize the boundary layer system whereas the latter essentially handles the mismatched uncertainties after the system is reformulated under some mild assumptions it is shown that the overall states are bounded and the tracking errors converge to a residual set whose size is a class k function of e as e 0 the residual set shrinks to the origin an interesting application to a simplified aircraft model with fast actuator dynamics which turns out to be weakly non minimum phase is given the computer simulation has verified the expected satisfac

time delay in random scattering this work treats the time delay in scattering for the schrodinger equation with a random potential the time delay is related to the energy derivative of the phase shift in the white noise limit the phase shift and time delay satisfy a system of stochastic differential equations in the high frequency limit the time delay is governed by a single stochastic differential equation in this limit the expected time delay is zero but the variance of the time delay is the square of a kinematical time multiplied by a function of the ratio of the length of the scatterer to the localization length

zero dynamics of regularly perturbed systems may be singularly abstract in this paper we present new results on the structure of the zeros of linear and nonlinear systems under perturbation in particular we show that when state space descriptions of linear or nonlinear single input single output systems with relative degree 2 are regularly perturbed then their zero dynamics may be singularly perturbed and show a separation of time scales in the siso case we give asymptotic formulas for the new high frequency zero dynamics arising from the regular perturbation

on certain large random hermitian jacobi matrices with applications to wireless communications in this paper we study the spectrum of certain large random hermitian jacobi matrices these matrices are known to describe certain communication setups in particular we are interested in an uplink cellular channel which models mobile users experiencing a soft handoff situation under joint multicell decoding considering rather general fading statistics we provide a closed form expression for the per cell sum rate of this channel in high signal to noise ratio snr when an intra cell time division multiple access tdma protocol is employed since the matrices of interest are tridiagonal their eigenvectors can be considered as sequences with second order linear recurrence therefore the problem is reduced to the study of the exponential growth of products of two by two matrices for the case where k users are simultaneously active in each cell we obtain a series of lower and upper bound on the high snr power offset of the per cell sum rate which are considerably tighter than previously known bounds

scattering of a wave packet by an interval of random medium this paper deals with the scattering theory for the one dimensional discrete schrodinger equation with a random potential having large support the main result is that a fluctuation deep within the scattering region has a very small effect on the scattering of wave packets the region of random potential is effectively opaque

random walks on three strand braids and on related hyperbolic groups we investigate the statistical properties of random walks on the simplest nontrivial braid group b3 and on related hyperbolic groups we provide a method using cayley graphs of groups allowing us to compute explicitly the probability distribution of the basic statistical characteristics of random trajectories the drift and the return probability the action of the groups under consideration in the hyperbolic plane is investigated and the distribution of a geometric invariant the hyperbolic distance is analysed it is shown that a random walk on b3 can be viewed as a magnetic random walk on the group psl 2

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

convergence of two dimensional branching recursions abstract the asymptotic distribution of branching type recursions ln of the form l n d a l n 1 b l n 1 is investigated in the two dimensional case here l n 1 is an independent copy of ln 1 and a b are random matrices jointly independent of l n 1 l n 1 the asymptotics of ln after normalization are derived by a contraction method the limiting distribution is characterized by a fixed point equation the assumptions of the convergence theorem are checked in some examples using eigenvalue decompositions and computer algebra

singularly perturbed zero dynamics of nonlinear systems stability properties of zero dynamics are among the crucial input output properties of both linear and nonlinear systems unstable or nonminimum phase zero dynamics are a major obstacle to input output linearization and high gain designs an analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system s relative degree it manifests itself as a singular perturbation of zero dynamics conditions are given under which the zero dynamics evolve in two time scales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics the slow part is shown to be identical to the zero dynamics of the unperturbed system while the fast part represented by the so called boundary layer system describes the effects of perturbation

a goodness of fit test for arch models a goodness of fit test in the class of conditional heteroscedastic time series models is examined due to the nonstandard limiting distribution of the test we propose to bootstrap the test showing its asymptotic validity moreover we illustrate the finite sample performance of the test by a small monte carlo study

approximate decoupling and asymptotic tracking for mimo systems this paper presents an algorithm for approximate input output decoupling of nonlinear mimo systems that are either numerically ill posed or exhibit nearly singular behavior in the application of decoupling algorithms although the systems considered are regular so that the exact decoupling algorithms are applicable in this case they require inversion of an ill conditioned matrix and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros the approximate algorithms of this paper are numerically robust and provide solutions that do not cancel far off right half plane zeros this latter characteristic is especially valuable when some of the far off right half plane zeros are unstable the algorithms are inspired by and are generalizations of some examples in the flight control literature

common volatility and correlation clustering in asset returns abstract we present a new multivariate framework for the estimation and forecasting of the evolution of financial asset conditional correlations our approach assumes return innovations with time dependent covariances a cholesky decomposition of the asset covariance matrix with elements written as sines and cosines of spherical coordinates allows for modelling conditional variances and correlations and guarantees its positive definiteness at each time t as in christodoulakis and satchell christodoulakis g a satchell s e 2002 correlated arch corrarch modelling the time varying conditional correlation between financial asset returns european journal of operational research 139 2 350 369 correlation is generated by conditionally autoregressive processes thus allowing for an autocorrelation structure for correlation our approach allows for explicit out of sample forecasting and is consistent with stylized facts as time varying correlations and correlation clustering co movement between correlation coefficients correlation and volatility as well as between volatility processes co volatility the latter two are shown to depend on correlation and volatility persistence empirical evidence on a trivariate model using monthly data from dow jones industrial nasdaq composite and the 3 month us treasury bill yield supports our theoretical arguments

on the multifractal analysis of bernoulli convolutions ii dimensions we show how the formalism developed in a previous paper allows us to exhibit the multifractal nature of the infinitely convolved bernoulli measures for the golden mean in this second part we show how the hausdorff dimension of the set where the measure has a power law singularity of strength is related to the large deviation function given in part i

convergence in distribution of products of random matrices we consider a sequence a2 a2 of i i d nonnegative matrices of size d d and investigate convergence in distribution of the product mn a1 an when d 2 it is possible for mn to converge in distribution without normalization to a distribution not concentrated on the zero matrix several equivalent conditions for this to happen are given these lead to a fairly general family of examples these conditions can also be used to determine when the a s limit of 1 nlog mn equals the logarithm of the largest eigenvalue of e a1

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

strict stationarity of generalized autoregressive processes in this paper we consider the multivariate equation x n 1 a n 1 x n b n 1 with i i d coefficients which have only a logarithmic moment we give a necessary and sufficient condition for existence of a strictly stationary solution independent of the future as an application we characterize the multivariate arma equations with general noise which have such a solution

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

recurrent random walks in nonnegative matrices attractors of certain iterated function systems in this paper the structure of the set of recurrent points for random walks in finite dimensional nonnegative matrices is determined the structural results are then used in understanding attractors of certain not necessarily contractive iterated function systems

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods