bipolar fuzzy graphs in this paper we introduce the notion of bipolar fuzzy graphs describe various methods of their construction discuss the concept of isomorphisms of these graphs and investigate some of their important properties we then introduce the notion of strong bipolar fuzzy graphs and study some of their properties we also discuss some propositions of self complementary and self weak complementary strong bipolar fuzzy graphs

types of arcs in a fuzzy graph the concept of connectivity plays an important role in both theory and applications of fuzzy graphs depending on the strength of an arc this paper classifies arcs of a fuzzy graph into three types namely a strong b strong and d arcs the advantage of this type of classification is that it helps in understanding the basic structure of a fuzzy graph completely we analyze the relation between strong paths and strongest paths in a fuzzy graph and obtain characterizations for fuzzy bridges fuzzy trees and fuzzy cycles using the concept of a strong b strong and d arcs an arc of a fuzzy tree is a strong if and only if it is an arc of its unique maximum spanning tree also we identify different types of arcs in complete fuzzy graphs

notes on bipolar fuzzy graphs in this note we show by examples that definitions 3 1 5 6 and 5 7 example 5 8 propositions 5 9 and 5 10 and partial proof of propositions 5 11 and 5 12 in a previous paper by akram muhammad akram bipolar fuzzy graphs inform sci 181 2011 5548 5564 contain some flaws and then provide the correct versions finally we introduce a generalized bipolar fuzzy graph

long term dependence with asymmetric conditional heteroscedasticity in stock returns abstract this paper studies the long term dependence and the possible asymmetric behavior of the financial time series both can be modeled using a fractionally integrated autoregressive moving average time series model with threshold type conditional heteroscedasticity denoted as an arfima tgarch model into which a bayesian approach is introduced to conduct the parameter estimation with these parameters we apply the arfima tgarch model to describe the daily stock returns of six markets from the empirical results we find that the returns of these markets exhibit mildly long memory processes and reveal an asymmetric response to the negative and positive news

rbf methods in a stochastic volatility framework for greeks computation abstract in this paper we aim to apply a new proposed meshless approach for heston pde resolution in mathematical finance most classical models may be reformulated as partial differential equations pde which are commonly solved by finite difference and monte carlo methods alternatively bio inspired methods may be considered to select parameters and to solve said pdes in particular we focus on heston model pde and we solve it via radial basis functions rbf methods moreover some considerations on the computation of model parameters through learning approaches have been discussed we aim to price a vanilla call option focusing on the derivation of the formulae for its greeks profiles eventually we conclude rbfs are an accurate alternative method to price derivatives in a stochastic volatility framework especially since they allow for a fast and precise computation of greeks

modeling maxima with autoregressive conditional frechet model abstract this paper introduces a novel dynamic generalized extreme value gev framework for modeling the time varying behavior of maxima in financial time series specifically an autoregressive conditional frechet acf model is proposed in which the maxima are modeled by a frechet distribution with time varying scale parameter volatility and shape parameter tail index conditioned on past information the acf provides a direct and accurate modeling of the time varying behavior of maxima and furthermore offers a new angle to study the tail risk dynamics in financial markets probabilistic properties of acf are studied and a maximum likelihood estimator is used for model estimation with its statistical properties investigated simulations show the flexibility of acf and confirm the reliability of its estimators two real data examples on cross sectional stock returns and high frequency foreign exchange returns are used to demonstrate the acf modeling approach where significant improvement over the static gev has been observed for market tail risk monitoring and conditional var estimation empirical result of acf is consistent with the findings of the dynamic peak over threshold pot literature that the tail index of financial markets varies through time

can the random walk model be beaten in out of sample density forecasts evidence from intraday foreign exchange rates abstract it has been documented that random walk outperforms most economic structural and time series models in out of sample forecasts of the conditional mean dynamics of exchange rates in this paper we study whether random walk has similar dominance in out of sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance we first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out of sample setting and provide simulation evidence on its finite sample performance then we conduct a comprehensive empirical analysis on the out of sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates euro dollar and yen dollar it is found that some sophisticated time series models that capture time varying higher order conditional moments such as markov regime switching models have better density forecasts for exchange rates than random walk or modified random walk with garch and student t innovations this finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out of sample applications involving the probability density

modelling price dynamics a hybrid truncated levy flight garch approach abstract arch and garch stochastic processes are widely used in finance and are generally accepted as good approximations when modelling the price dynamics with gaussian conditional probability it can be seen that certain aspects of the empirical data for asset price changes seems to more closely fit a truncated levy flight or garch model but each with individual shortfalls in this paper therefore we combine the garch process with a conditional truncated levy distribution in order to build a hybrid model that most notably describes the price change and associated volatility probability density distributions and scaling behaviour over different time horizons

dynamic theory of quasilinear parabolic equations i abstracts evolution equations on etablit les fondements abstraits pour une theorie dynamique generale pour des problemes aux valeurs limites et initiales quasilineaires

diffraction problems for quasilinear reaction diffusion systems abstract the aim of this paper is to investigate existence uniqueness and qualitative properties of the weak and piecewise classical solutions of the diffraction problem for weakly coupled reaction diffusion systems monotony and stability with respect to the time variable of the weak solutions is proved as an application is considered a model reaction diffusion system describing an enzyme sensor for concentration of phenol in the chemical industry

large deviation estimates for exceedance times of perpetuity sequences and their dual processes in a variety of problems in pure and applied probability it is relevant to study the large exceedance probabilities of the perpetuity sequence yn b1 a1b2 a1 an 1 bnyn b1 a1b2 a1 an 1 bn where ai bi 0 r ai bi 0 r estimates for the stationary tail distribution of yn yn have been developed in the seminal papers of kesten acta math 131 1973 207 248 and goldie ann appl probab 1 1991 126 166 specifically it is well known that if m supnynm supnyn then p m u cmu p m u cmu as u u while much attention has been focused on extending such estimates to more general settings little work has been devoted to understanding the path behavior of these processes in this paper we derive sharp asymptotic estimates for the normalized first passage time tu logu 1inf n yn u tu log u 1inf n yn u we begin by showing that conditional on tu tu tu tu as u u for a certain positive constant we then provide a conditional central limit theorem for tu tu and study p tu g p tu g as u u for sets g 0 g 0 if g 0 g 0 then we show that p tu g ui g c g p tu g ui g c g as u u for a certain large deviation rate function ii and constant c g c g on the other hand if g g then we show that the tail behavior is actually quite complex and different asymptotic regimes are possible we conclude by extending our results to the corresponding forward process understood in the sense of letac in random matrices and their applications brunswick maine 1984 1986 263 273 amer math soc namely to the reflected process m n max anm n 1 bn 0 mn max anmn 1 bn 0 n z n z using siegmund duality we relate the first passage times of yn yn to the finite time exceedance probabilities of m n mn yielding a new result concerning the convergence of m n mn to its stationary distribution

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

on the extremes of a class of non linear processes with heavy tailed innovations the aim of this paper is to look at the limiting form of certain empirical point processes induced by a particular class of non linear processes generated by heavy tailed innovations such asymptotic results will be highly useful in obtaining the weak limiting behavior of various functionals of the underlying process including the asymptotic distribution of upper and lower order statistics in particular we investigate the maximum limiting distribution and its corresponding extremal index the results are applied to the study of the extremal properties of bilinear processes

expectation propagation for likelihood free inference many models of interest in the natural and social sciences have no closed form likelihood function which means that they cannot be treated using the usual techniques of statistical inference in the case where such models can be efficiently simulated bayesian inference is still possible thanks to the approximate bayesian computation abc algorithm although many refinements have been suggested abc inference is still far from routine abc is often excruciatingly slow due to very low acceptance rates in addition abc requires introducing a vector of summary statistics s y the choice of which is relatively arbitrary and often require some trial and error making the whole process laborious for the user we introduce in this work the ep abc algorithm which is an adaptation to the likelihood free context of the variational approximation algorithm known as expectation propagation the main advantage of ep abc is that it is faster by a few orders of magnitude than standard algorithms while producing

value at risk estimation with wavelet based extreme value theory evidence from emerging markets abstract this paper introduces wavelet based extreme value theory evt for univariate value at risk estimation wavelets and evt are combined for volatility forecasting to estimate a hybrid model in the first stage wavelets are used as a threshold in generalized pareto distribution and in the second stage evt is applied with a wavelet based threshold this new model is applied to two major emerging stock markets the istanbul stock exchange ise and the budapest stock exchange bux the relative performance of wavelet based evt is benchmarked against the riskmetrics ewma arma garch generalized pareto distribution and conditional generalized pareto distribution models the empirical results show that the wavelet based extreme value theory increases predictive performance of financial forecasting according to number of violations and tail loss tests the superior forecasting performance of the wavelet based evt model is also consistent with basel ii requirements and this new model can be used by financial institutions as well

on the invariance of the lagrange multiplier test with respect to certain changes in the alternative hypothesis this paper examines some implications of the observation that the same lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses a characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification and the consequences for finite sample power properties are examined by monte carlo experiments

financial time series modeling using the hurst exponent abstract this study aims to enhance the understanding of logarithmic asset returns in particular more emphasis is given to the long memory property of financial returns a well documented stylized fact however in the presence of structural breaks other studies suggest that statistical tools such as the autocorrelation function acf can wrongly indicate long memory we propose an insensitive to structural breaks method to test for dependence between distant observations furthermore a model which combines memory in returns and memory in absolute returns is developed in two stages first return series are segmented with respect to changes in the volatility and then the two parameters of the model are estimated to assess the capabilities of the model historical prices of the standard and poor 500 index s p500 financial time stocks exchange 100 index ftse100 deutsche boerse ag german stock index dax and crude oil are used 1 given the estimated parameters and the volatility within each regime 10000 vectors are generated and compared to the original data in terms of the kolmogorov smirnov k s statistical test the obtained results suggest that long memory is present and provide evidence that the additional memory information captured by the model improves financial returns modeling

bayes inference in regression models with arma p q errors we develop practical and exact methods of analyzing arma p 4 regression error models in a bayesian framework by using the gibbs sampling and metropolis hastings algorithms and we prove that the kernel of the proposed markov chain sampler converges to the true density the procedures can be applied to pure arma time series models and to determine features of the likelihood function by choosing appropriate diffuse priors our results are unconditional on the initial observations we also show how the algorithm can be further simplified for the important special cases of stationary ar p and invertible ma q models recursive transformations developed in this paper to diagonalize the covariance matrix of the errors should prove useful in frequentist estimation examples with simulated and actual economic data are presented kpj ourls gibbs sampling metropolis hastings algorithm data augmentation time series arma processes markov chain bayesian statistics

likelihood based estimation of latent generalized arch structures garch models are commonly used as latent processes in econometrics financial economics and macroeconomics yet no exact likelihood analysis of these models has been provided so far in this paper we outline the issues and suggest a markov chain monte carlo algorithm which allows the calculation of a classical estimator via the simulated em algorithm or a bayesian solution in o t computational operations where t denotes the sample size we assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 uk sectorial stock returns and compare it to existing approximate solutions

a top bottom price approach to understanding financial fluctuations abstract the presence of sequences of top and bottom tb events in financial series is investigated for the purpose of characterizing such switching points they clearly mark a change in the trend of rising or falling prices of assets to the opposite tendency are of crucial importance for the players decision and also for the market stability previous attempts to characterize switching points have been based on the behavior of the volatility and on the definition of microtrends the approach used herein is based on the smoothing of the original data with a gaussian kernel the events are identified by the magnitude of the difference of the extreme prices by the time lag between the corresponding events waiting time and by the time interval between events with a minimal magnitude return time results from the analysis of the inter day dow jones industrial average index djia from 1928 to 2011 are discussed q gaussian functions with power law tails are found to provide a very accurate description of a class of measures obtained from the series statistics

impact of foreign exchange rate on oil companies risk in stock market during the recent years the importance of effective risk management has become extremely crucial value at risk var is a standard downside measure to explain the behavior of financial series as the garch models have been successfully applied in modeling the volatility structure of securities and other financial assets the var of garch models has turned into an important quantity to study in addition to garch family models the markov regime switching garch mrs garch models are a widely used approach to model financial volatility with potential structural breaks in this paper we evaluated the performance of the mrs garch models with the traditional arma garch family models for estimating var of the stock return of operating companies in the oil industry srocoi in irans stock market under the normal student t and ged distributions our findings showed that the mrs garch models outperform the arma garch family models to capture the characteristics of the srocois volatility additionally we evaluated impact of the foreign exchange rate fluctuations on the var of srocois that were calculated from the optimal models under two regimes usingardl model the results further demonstrated that foreign exchange rate fluctuations have significant and different impacts on the var of srocois across regimes we modeled srocois in irans stock market using mrs garch and arma garch family models mrs garch models under student t and ged distributions have better performance to capture srocois we estimated in sample and out of sample var of srocois from optima models we evaluated impact of the foreign exchange rate fluctuations on the var of srocois foreign exchange rate significantly effect on the var of srocois in different regimes

connectivity index of a fuzzy graph and its application to human trafficking abstract connectivity is a high priority concept in fuzzy graphs the stability of a fuzzy graph is determined by the strength of connectedness of each pair of its nodes this paper introduces two measures of connectivity called as connectivity index and average connectivity index of fuzzy graphs several results related to these parameters are obtained these measures can be used to determine the potential flow of a fuzzy graph certain special types of nodes called cen crn and neutral nodes are also introduced and algorithms for finding these nodes are provided applications of these concepts in two different type of networks are provided

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

solutions for quasilinear nonsmooth evolution systems in l p we prove that nonsmooth quasilinear parabolic systems admit a local solution in l p strongly differentiable with respect to time over a bounded three dimensional polyhedral space domain the proof rests essentially on new elliptic regularity results for polyhedral laplace interface problems for anisotropic materials these results are based on sharp pointwise estimates for green s function which are also of independent interest to treat the nonlinear problem we then apply a classical theorem of sobolevskii for abstract parabolic equations and recently obtained resolvent estimates for elliptic operators and interpolation results as applications we have in mind primarily reaction diffusion systems the treatment of such equations in an l p context seems to be new and allows by gauss theorem the proper definition of the normal component of currents across the boundary

fuzzy pogroupoids in this paper we show that for given a pogroupoid x the associated poset x is c2 1 free if and only if the relation is transitive for any fuzzy subset of x also we determine the set c x of fuzzy subsets such that x y y x for all x y x furthermore with a given finite poset x or the associated pogroupoid x we may then associate a polynomial whose coefficients count the number of congruence classes mod x of fuzzy subsets of x along with another polynomial invariant of interest

exact predictive densities for linear models with arch disturbances abstract it is shown how exact predictive densities may be formed in the arch linear model by means of monte carlo integration with importance sampling several improvements in computational efficiency over earlier implementations of this procedure are developed including use of the exact likelihood function rather than an asymptotic approximation to construct the importance sampling distribution and antithetic acceleration of convergence a numerical approach to the formulation of posterior odds ratios and the combination of non nested models is also introduced these methods are applied to daily quotations of closing stock prices forecasts are formulated using linear models arch linear models and an integrated model constructed from the posterior probabilities of the respective models the use of the exact predictive density in a decision theoretic context is illustrated by deriving the optimal day to day portfolio adjustments of a trader with constant relative risk aversion

bayesian analysis of arma garch models a markov chain sampling approach abstract we develop a markov chain monte carlo method for a linear regression model with an arma p q garch r s error to generate a monte carlo sample from the joint posterior distribution we employ a markov chain sampling with the metropolis hastings algorithm as illustration we estimate an arma garch model of simulated time series data

monte carlo inference in econometric models with symmetric stable disturbances the paper develops markov chain monte carlo methods to perform exact posterior analysis in models with symmetric stable paretian disturbances it is shown how posterior moments and marginal densities of functions of parameters can be computed methodically by combining a gibbs sampler with metropolis independence chains the new method is shown to perform satisfactorily in constructed examples the method is also applied to a set of monthly real exchange rates and the question of difference versus trend stationarity is taken up jointly with the problem of inference about the parameter of the stable distribution

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

interval estimation of value at risk based on garch models with heavy tailed innovations arch and garch models are widely used to model financial market volatilities in risk management applications considering a garch model with heavy tailed innovations we characterize the limiting distribution of an estimator of the conditional value at risk var which corresponds to the extremal quantile of the conditional distribution of the garch process we propose two methods the normal approximation method and the data tilting method for constructing confidence intervals for the conditional var estimator and assess their accuracies by simulation studies finally we apply the proposed approach to an energy market data set

managing distribution changes in time series prediction when a problem is modeled statistically a single distribution model is usually postulated that is assumed to be valid for the entire space nonetheless this practice may be somewhat unrealistic in certain application areas in which the conditions of the process that generates the data may change as far as we are aware however no techniques have been developed to tackle this problem this article proposes a technique for modeling and predicting this change in time series with a view to improving estimates and predictions the technique is applied among other models to the hypernormal distribution recently proposed when tested on real data from a range of stock market indices the technique produces better results that when a single distribution model is assumed to be valid for the entire period of time studied moreover when a global model is postulated it is highly recommended to select the hypernormal distribution parameter in the same likelihood maximization process

transitive blocks and their applications in fuzzy interconnection networks abstract in any network the problem of reduction of flow is more important and frequent than the disconnection of the network problems related with maximum bandwidth paths and maximal flows are also very significant in this article the authors discuss connectivity concepts related with paths and flows in interconnection networks in a fuzzy framework some of the properties and applications of a stable structure called transitive block are discussed blocks in fuzzy graphs generalize the concept of blocks in graphs the existence of a strongest strong cycle in any fuzzy block having at least three vertices is established four characterizations previously proposed for a class of blocks in fuzzy graphs are found to be true for a larger class two subclasses of fuzzy graphs namely connectivity transitive and cyclically transitive fuzzy graphs are introduced to get a better understanding of blocks in fuzzy graphs an application of transitive blocks in interconnection networks is also proposed

maximum entropy autoregressive conditional heteroskedasticity model abstract in many applications it has been found that the autoregressive conditional heteroskedasticity arch model under the conditional normal or student s t distributions are not general enough to account for the excess kurtosis in the data moreover asymmetry in the financial data is rarely modeled in a systematic way in this paper we suggest a general density function based on the maximum entropy me approach that takes account of asymmetry excess kurtosis and also of high peakedness the me principle is based on the efficient use of available information and as is well known many of the standard family of distributions can be derived from the me approach we demonstrate how we can extract information functional from the data in the form of moment functions we also propose a test procedure for selecting appropriate moment functions our procedure is illustrated with an application to the nyse stock returns the empirical results reveal that the me approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively

a simple r estimation method for semiparametric duration models modeling nonnegative financial variables e g durations between trades traded volumes or asset volatilities is central to a number of studies across financial econometrics and despite the efforts still poses several statistical challenges among them the efficiency aspects of semiparametric estimation in this paper we concentrate on estimation problems in autoregressive conditional duration acd models with unspecified innovation densities exponential quasi likelihood estimators qmle are the usual practice in that context the efficiency of those qmles the only fisher consistent qmles unfortunately rapidly deteriorates away from the reference exponential density a phenomenon that has been emphasized earlier by drost and werker 2003 who propose various semiparametrically efficient procedures to palliate that phenomenon those procedures rely on a general semiparametric approach which typically requires kernel estimation of the underlying innovation density we propose rank based estimators r estimators as a substitute just as the qmle r estimators remain root n consistent irrespective of the underlying density and rely on the choice of a reference density under which they achieve semiparametric efficiency that density however needs not be the exponential one contrary to the semiparametric estimators proposed by drost and werker 2003 r estimators neither require tangent space calculations nor kernel based density estimation numerical results moreover indicate that r estimators based on exponential reference densities uniformly outperform the exponential qmle under such families of innovations as the weibull or burr densities a real data example about modeling the price range of the swiss stock market index concludes the paper

solving forward backward stochastic differential equations explicitly a four step scheme in this paper we investigate the nature of the adapted solutions to a class of forward backward stochastic differential equations sdes for short in which the forward equation is non degenerate we prove that in this case the adapted solution can always be sought in an ordinary sense over an arbitrarily prescribed time duration via a direct four step scheme using this scheme we further prove that the backward components of the adapted solution are determined explicitly by the forward components via the solution of a certain quasilinear parabolic pde system moreover the uniqueness of the adapted solutions over an arbitrary time duration as well as the continuous dependence of the solutions on the parameters can all be proved within this unified framework some special cases are studied separately in particular we derive a new form of the integral representation of the clark haussmann ocone type for functionals or functions of diffusions in which the conditional expectation is no longer needed

time evolution of stochastic processes with correlations in the variance stability in power law tails of distributions abstract we model the time series of the s p500 index by a combined process the ar garch process where ar denotes the autoregressive process which we use to account for the short range correlations in the index changes and garch denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long range correlations in the variance we study the ar garch process with an initial distribution of truncated levy form we find that this process generates a new probability distribution with a crossover from a levy stable power law to a power law with an exponent outside the levy range beyond the truncation cutoff we analyze the sum of n variables of the ar garch process and find that due to the correlations the ar garch process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n a feature which is observed in the probability distribution of the s p500 index we find that this power law stability depends on the characteristic scale in the correlations we also find that inclusion of short range correlations through the ar process is needed to obtain convergence to a limiting gaussian distribution for large n as observed in the data

holder regularity for certain strongly coupled parabolic systems abstract we present a shorter proof to show holder continuity of bounded solutions to a general class of quasilinear parabolic equations the proof will be extended to obtain regularity results for bounded solutions to certain strongly coupled or cross diffusion quasilinear parabolic systems

bootstrap refinements for qml estimators of the garch 1 1 parameters a b s t r a c t this paper reconsiders a block bootstrap procedure for quasi maximum likelihood estimation of garch models based on the resampling of the likelihood function as proposed by goncalves and white 2004 maximum likelihood and the bootstrap for nonlinear dynamic models journal of econometrics 119 199 219 first we provide necessary conditions and sufficient conditions in terms of moments of the innovation process for the existence of the edgeworth expansion of the garch 1 1 estimator up to the k th term second we provide sufficient conditions for higher order refinements for equally tailed and symmetric test statistics in particular the bootstrap estimator based on resampling the likelihood has the same higher order improvements in terms of error in the rejection probabilities as those in andrews 2002 higher order improvements of a computationally attractive k step bootstrap for extremum estimators econometrica 70 119 162

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

forecasting volatility of ssec in chinese stock market using multifractal analysis abstract in this paper taking about 7 years high frequency data of the shanghai stock exchange composite index ssec as an example we propose a daily volatility measure based on the multifractal spectrum of the high frequency price variability within a trading day an arfima model is used to depict the dynamics of this multifractal volatility mfv measures the one day ahead volatility forecasting performances of the mfv model and some other existing volatility models such as the realized volatility model stochastic volatility model and garch are evaluated by the superior prediction ability spa test the empirical results show that under several loss functions the mfv model obtains the best forecasting accuracy

estimating semiparametric arch models by kernel smoothing methods we investigate a class of semiparametric arch models that includes as a special case the partially nonparametric pnp model introduced by engle and ng 1993 and which allows for both flexible dynamics and flexible function form with regard to the news impact function we show that the functional part of the model satisfies a type ii linear integral equation and give simple conditions under which there is a unique solution we propose an estimation method that is based on kernel smoothing and profiled likelihood we establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model we also discuss efficiency of both the parametric part and the nonparametric part we investigate the performance of our procedures on simulated data and on a sample of s p500 index returns we find evidence of asymmetric news impact functions consistent with the parametric analysis

cycles and cocycles of fuzzy graphs abstract in this paper we show that if the fuzzy graph is a cycle then it is a fuzzy cycle if and only if is not a fuzzy tree we also examine the relationship between fuzzy bridges and cycles we introduce and examine the concepts of chords twigs 1 chains with boundary zero cycle vectors coboundary and cocycles for fuzzy graphs we show that although the set of cycle vectors fuzzy cycle vectors cocycles and fuzzy cocycles do not necessarily form vector spaces over the field z 2 of integers modulo 2 they nearly do thisallows us to introduce the concepts of fuzzy cycle rank and fuzzy cocycle rank for fuzzy graphs in a meaningful way

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

modelling high frequency economic time series abstract the minute by minute move of the hang seng index hsi data over a 4 yr period is analysed and shown to possess similar statistical features as those of other markets based on a mathematical theorem pope ching phys fluids a 5 1993 1529 we derive an analytic form for the probability distribution function pdf of index moves from fitted functional forms of certain conditional averages of the time series furthermore following a recent work by stolovitzky and ching phys lett a 255 1999 11 we show that the observed pdf can be reproduced by a langevin process with a move dependent noise amplitude the form of the langevin equation can be determined directly from the market data

quasi maximum likelihood estimation for conditional quantiles in this paper we derive the asymptotic distribution of a new class of quasi maximum likelihood estimators qmle based on a tick exponential family of densities we show that the tick exponential assumption is a necessary and sufficient condition for a qmle to be consistent for the parameters of a correctly specified model of a given conditional quantile hence the role of this family of densities in the conditional quantile estimation is analog to the role of the linear exponential family in the conditional mean estimation the tick exponential qmles are shown to be asymptotically normal with an asymptotic covariance matrix that has a novel form not seen in earlier work and which accounts for possible model misspecification for practical purposes we show that the maximization of the tick exponential quasi log likelihood can conveniently be carried out by using standard gradient based optimization techniques more importantly we provide a consistent estimator for the asymptotic covariance matrix based on the scores of the log likelihood which allows us to compute the conditional quantile confidence intervals

operations on fuzzy graphs abstract we define the operations of cartesian product composition union and join on fuzzy subgraphs of graphs g1 and g2 if the graph g is formed from g1 and g2 by one of these operations we determine necessary and sufficient conditions for an arbitrary fuzzy subgraph of g also to be formed by the same operation from fuzzy subgraphs of g1 and g2

an initial boundary value problem for a certain density dependent diffusion system on considere le systeme parabolique quasilineaire u t x c 1 d 1 v v e 1 a 1 v b 1 u u v t x c 2 d 2 u v e 2 a 2 u b 2 o v dans o t u x s 0 v x s sur o t u x o w 1 x v x o w 2 x sur ou r n est un domaine borne a frontiere lisse

multivariate functional coefficient regression models for nonlinear vector time series data summary vector time series data are widely found in practice in this paper we propose a multivariate functional coefficient regression model with heteroscedasticity for modeling such data the local linear smoother is employed to estimate the unknown coefficient matrices asymptotic normality 10 of the proposed estimators is established and bandwidth selection is considered to deal with cointegration widely observed in financial markets we propose an error corrected multivariate functional coefficient model simulations show that the proposed estimation procedures capture nonlinear structures of coefficients well analysis of united states interest rates illustrates the proposed methodology 15

efficient estimation in semiparametric garch models abstract it is well known that financial data sets exhibit conditional hereroskedasticity garch type models are often used to model this phenomenon since the distribution of the rescaled innovations is generally far from a normal distribution a semiparametric approach is advisable several publications observed that adaptive estimation of the euclidean parameters is not possible in the usual parametrization when the distribution of the rescaled innovations is the efficient score functions in the parametric model of the autoregression parameters are orthogonal to the tangent space generated by the nuisance parameter thus suggesting that adaptive estimation of the autoregression parameters is possible indeed we construct adaptive and hence efficient estimators in a general garch in mean type context including integrated garch models our analysis is based on a general lan theorem for time series models published elsewhere in contrast to recent literature about arch models we do not need moment condition

global existence for semilinear parabolic systems on etudie des problemes aux valeurs limites et initiales paraboliques semilineaires de la forme u t a t u f t x u du d 2m 1 u dans t 0 b t u 0 sur t 0 u t 0 u 0 sur ou est un domaine de r n

speckle suppression in sar images using the 2 d garch model a novel bayesian based speckle suppression method for synthetic aperture radar sar images is presented that preserves the structural features and textural information of the scene first the logarithmic transform of the original image is analyzed into the multiscale wavelet domain we show that the wavelet coefficients of sar images have significantly non gaussian statistics that are best described by the 2 d garch model by using the 2 d garch model on the wavelet coefficients we are capable of taking into account important characteristics of wavelet coefficients such as heavy tailed marginal distribution and the dependencies between the coefficients furthermore we use a maximum a posteriori map estimator for estimating the clean image wavelet coefficients finally we compare our proposed method with various speckle suppression methods applied on synthetic and actual sar images and we verify the performance improvement in utilizing the new strategy

regularity for the weak solutions to certain parabolic systems under certain growth condition abstract in this paper we consider the regularity of the weak solutions to a quasilinear parabolic systems which is a generalization of p laplacian of the type u t i a i u x f i x t u u i 1 n where the main part satisfies some ellipticity and f i satisfies certain growth conditions we prove boundedness of the solutions and the gradients of solutions to the systems by the means of the energy estimates and a nonlinear iteration procedure of the moser type in this paper

testing forecast optimality under unknown loss empirical tests of forecast optimality have traditionally been conducted under the assumption of mean squared error loss or some other known loss function in this article we establish new testable properties that hold when the forecaster s loss function is unknown but testable restrictions can be imposed on the data generating process trading off conditions on the data generating process against conditions on the loss function we propose flexible estimation of the forecaster s loss function in situations where the loss depends not only on the forecast error but also on other state variables such as the level of the target variable we apply our results to the problem of evaluating the federal reserve s forecasts of output growth forecast optimality is rejected if the fed s loss depends only on the forecast error however the empirical findings are consistent with forecast optimality provided that overpredictions of output growth are costlier to the fed than underpredictions particularly during per