the fractional unit root distribution asymptotic distributions are derived for the ordinary least squares estimate of a first order autoregression model when the series is fractionally integrated the fractional unit root distribution is introduced to describe the limiting distribution the unit root distribution is shown to be an atypical member of this family because its density is nonzero over the entire real line for 1 2 copyright 1990 by the econometric society

the inverse nodal problem and the ambarzumyan problem for the p laplacian we study the issues of the reconstruction and stability of the inverse nodal problem for the one dimensional p laplacian eigenvalue problem a key step is the application of a modified prufer substitution to derive a detailed asymptotic expansion for the eigenvalues and nodal lengths two associated ambarzumyan problems are also solved

on maximum likelihood estimation of the differencing parameter of fractionally integrated noise with unknown mean abstract there are two approaches to maximum likelihood ml estimation of the parameter of fractionally integrated noise approximate frequency domain ml fox and taqqu 1986 and exact time domain ml sowell 1992b if the mean of the process is known then a clear finite sample mean squared error ranking of the estimators emerges the exact time domain estimator is superior we show in this paper however that the finite sample efficiency of approximate frequency domain ml relative to exact time domain ml rises dramatically when the mean is unknown and so must be estimated the intuition for our result is straightforward the frequency domain ml estimator is invariant to the true but unknown mean of the process while the time domain ml estimator is not feasible time domain estimation must therefore be based upon de meaned data but the long memory associated with fractional integration makes precise estimation of the mean difficult we conclude that the frequency domain estimator is an attractive and efficient alternative for situations in which large sample sizes render time domain estimation impractical

some nodal properties for a quasilinear differential equation involving the p laplacian abstract in this paper we study a quasilinear differential equation u x p 2 u x w x u x q 2 u x 0 in 0 b where q p 1 a theorem related to some oscillation properties depending on the initial parameters is developed on the basis of this result we also show that the identical zero set of solutions will determine the function w x uniquely under some minor assumption essentially the main methods using in this work are the scaling argument and prufer type substitutions

on the number of zeros of nonoscillatory solutions to half linear ordinary differential equations involving a parameter in this paper the following half linear ordinary differential equation is considered ha x sgn x p t x sgn x 0 t a where a 0 is a constant a 0 is a parameter and p t is a continuous function on oo a 0 and p t 0 for t e a the main purpose is to show that precise information about the number of zeros can be drawn for some special type of solutions x t a of h such that 0 it is shown that if 1 and if h is strongly nonoscillatory then there exists a sequence n n 1 such that 0 0 1 n n as n and x t with a an has exactly n 1 zeros in the interval a and x a n 0 and x t with a n 1 n has exactly n 1 zeros in a and x a n 0 for the proof of the theorem we make use of the generalized prufer transformation which consists of the generalized sine and cosine functions

econometric analysis of multivariate realised qml estimation of the covariation of equity prices under asynchronous trading estimating the covariance between assets using high frequency data is challenging due to market microstructure effects and asynchronous trading in this paper we develop a multivariate realised quasi likelihood qml approach carrying out inference as if the observations arise from an asynchronously observed vector scaled brownian model observed with error under stochastic volatility the resulting realised qml estimator is positive semi definite uses all available data is consistent and asymptotically mixed normal the quasi likelihood is computed using a kalman filter and optimised using a relatively simple em algorithm which scales well with the number of assets we derive the theoretical properties of the estimator and prove that it achieves the efficient rate of convergence we show how to make itobtain the non parametric efficiency bound for this problem the estimator is also analysed usingmonte carlo methods and applied to equity data with varying levels of liquidity

on estimation of a regression model with long memory stationary errors we consider estimation of a regression model with long memory stationary errors first we estimate the regression parameters by the least squares estimator lse and next those describing the correlation structure of the error terms by using the residuals obtained from the lse certain regularity conditions introduced to develop the asymptotic theory no longer hold in this model in this situation we derive asymptotic properties of the preceding estimation procedure

the fredholm alternative at the first eigenvalue for the one dimensionalp laplacian abstract in this work we study the range of the operatoru u p 2 u 1 u p 2 u u 0 u t 0 p 1 we prove that all functionsh c1 0 t satisfying t0 h t sinp pt t dt 0 lie in the range but that ifp 2 andh 0 the solution set is bounded here sin pt t is a first eigenfunction associated to 1 we also show that in this case the associated energy functionalu 1 p t0 u p 1 p t0 u p t0 huis unbounded from below if 1 2 onw1 p0 0 t 1corresponds precisely to the best constant in thelp poincare inequality moreover we show that unlike the linear casep 2 forp 2 the range contains a nonempty open set inl 0 t

temporal aggregation of garch processes the authors derive low frequency say weekly models implied by high frequency say daily arma models with symmetric garch errors they show that low frequency models exhibit conditional heteroskedasticity of the garch form as well the parameters in the conditional variance equation of the low frequency model depend upon mean variance and kurtosis parameters of the corresponding high frequency model moreover strongly consistent estimators of the parameters in the high frequency model can be derived from low frequency data the common assumption in applications that rescaled innovations are independent is disputable since it depends upon the available data frequency copyright 1993 by the econometric society

fitting a two phase threshold multiplicative error model abstract the recent literature on financial time series analysis has devoted considerable attention to nonnegative time series such as financial durations realized volatility and squared returns the class of models referred to as the multiplicative error models mem is particularly suited to model such nonnegative time series we develop a lack of fit test for fitting a two phase threshold model for the conditional mean function in an mem the proposed testing procedure can also be applied to a class of autoregressive conditional heteroscedastic threshold models we evaluate the test in a simulation study the testing procedure is illustrated by using two data examples

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

marginalization and contemporaneous aggregation in multivariate garch processes abstract we first of all show that contemporaneous aggregation of independent univariate garch processes yields a weak garch process as introduced by drost and nijman 1993 subsequently we analyze the dependence of the parameters in the aggregate on the parameters in the underlying models and show that the variance parameters after aggregation depend on the underlying variance and kurtosis parameters then we generalize the results by showing that a linear combination of variables generated by a multivariate garch process will also be weak garch finally we derive the marginal weak garch processes implied by several multivariate garch processes

modeling returns volatility realized garch incorporating realized risk measure abstract this study applies realized garch models by introducing several risk measures of intraday returns into the measurement equation to model the daily volatility of e mini s p 500 index futures returns besides using the conventional realized measures realized volatility and realized kernel as our benchmarks we also use generalized realized risk measures realized absolute deviation and two realized tail risk measures realized value at risk and realized expected shortfall the empirical results show that realized garch models using the generalized realized risk measures provide better volatility estimation for the in sample and substantial improvement in volatility forecasting for the out of sample in particular the realized expected shortfall performs best for all of the alternative realized measures our empirical results reveal that future volatility may be more attributable to present losses risk measures the results are robust to different sample estimation windows

multivariate realised kernels consistent positive semi definite estimators of the covariation of equity prices with noise and non synchronous trading we propose a multivariate realised kernel to estimate the ex post covariation of log prices we show this new consistent estimator is guaranteed to be positive semi definite and is robust to measurement noise of certain types and can also handle non synchronous trading it is the first estimator which has these three properties which are all essential for empirical work in this area we derive the large sample asymptotics of this estimator and assess its accuracy using a monte carlo study we implement the estimator on some us equity data comparing our results to previous work which has used returns measured over 5 or 10 minutes intervals we show the new estimator is substantially more precise

properties of a simple bilinear stochastic model estimation and predictability we analyze the properties of arguably the simplest bilinear stochastic multiplicative process proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise by construction it has no linear predictability zero two point correlation but a certain nonlinear predictability non zero three point correlation it can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series we present a rather exhaustive study of the process including its ability to produce fat tailed distributions from gaussian innovations the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super exponential sensitivity of the inversion of the innovations in the presence of a large impulse our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts which overall illuminates the properties of the process in conclusion notwithstanding its remarkable simplicity the bilinear stochastic process exhibits remarkably rich and complex behavior which makes it a serious candidate for the modeling of financial time series among others

the detection and estimation of long memory in stochastic volatility abstract we propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility lmsv model the lmsv model is constructed by incorporating an arfima process in a standard stochastic volatility scheme strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the gaussian likelihood the finite sample properties of the spectral likelihood estimator are analyzed by means of a monte carlo study an empirical example with a long time series of stock prices demonstrates the superiority of the lmsv model over existing short memory volatility models

asymptotic filtering theory for univariate arch models this paper builds on this earlier work by deriving the asymptotic distribution of the measurement error this allows us to approximate the measurement accuracy of arch conditional variance estimates and compare the efficiency achieved by different arch models we are also able to characterize the relative importance of different kinds of misspecification for example we show that misspecifying conditional means adds only trivially at least asymptotically to measurement error while other factors for example capturing the leverage effect accommodating thick tailed residuals and correctly modelling the variability of the conditional variance process are potentially much more important third we are able to characterize a class of asymptotically optimal arch conditional variance estimates

the method of simulated quantiles we introduce an inference method based on quantiles matching which is useful for situations where the density function does not have a closed form but it is simple to simulate and or moments do not exist functions of theoretical quantiles which depend on the parameters of the assumed probability law are matched with sample quantiles which depend on observations since the theoretical quantiles may not be available analytically the optimization is based on simulations we illustrate the method with the estimation of stable distributions a thorough monte carlo study and an illustration to 22 nancial indexes show

wkb approach to zero distribution of solutions of linear second order differential equations given a second order linear differential equation y z s z y z 0 the distribution of zeros of its solutions is defined by v y z 0 z where z stands for the dirac delta at the point z some techniques of approximation of the restriction of v to r directly from s z are considered in particular for the wkb method error bounds are provided and some related results established in the second part formulas for the appropriate scaling in the holonomic case are given as an illustration we obtain the asymptotic distribution of the real zeros of some families of polynomials

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

multiscale local change point detection with applications to value at risk this paper offers a new approach to modeling and forecasting of non stationary time series with applications to volatility modeling for financial data the approach is based on the assumption of local homogeneity for every time point there exists a historical interval of homogerzeity in which the volatility parameter can be well approximated by a constant the proposed procedure recovers this interval from the data using the local change point lcp analysis afterward the estimate of the volatility can be simply obtained by local averaging the approach carefully addresses the question of choosing the tuning parameters of the procedure using the so called propagation condition the main result claims a new oracle inequality in terms of the modeling bias which measures the quality of the local constant approximation this result yields the optimal rate of estimation for smooth and piecewise constant volatility functions then the new procedure is applied to some data sets and a comparison with a standard garch model is also provided finally we discuss applications of the new method to the value at risk problem the numerical results demonstrate a very reasonable performance of the new method

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

characteristics of the volatility in the korea composite stock price index abstract we empirically analyze the time series of the korea composite stock price index kospi from march of 1992 to february of 2007 using methods from the hydrodynamic turbulence to this end we focus on characteristics of the return and volatility which are respectively the price change and a measure of the financial market fluctuation over a time interval with these we show that the non gaussian probability distribution of the return can be modeled by the convolution of the conditional probability distribution of the return given the volatility and the distribution of the volatility per se from this model we suggest that the non gaussian characteristic of the return results from the fluctuation of the volatility that is a large return is partly if not entirely due to the market fluctuation in a long time scale influencing the fluctuation in a short time scale via net information flow we further show that the volatility has a multi fractal property which resembles the multifractality of the energy dissipation in the turbulence

inverse nodal problems for the sturm liouville operator with a constant delay we study inverse nodal problems for non self adjoint second order differential operator with a constant delay the uniqueness theorem is proved for this inverse problem and a constructive procedure for the solution of the inverse nodal problems is provided we show that the space of delay differential operators characterized by q l1 a 0 2 a 0 under a certain metric is homeomorphic to the partition set of the space of quasinodal sequences which is all admissible sequences x xnj n 2 j 1 n 1 which form sequences that converge to q and individually as a consequence the inverse nodal problem when defined on the partition set of admissible sequence induced by the same equivalence relation is stable

testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression abstract broad classes of diagnostics for serial correlation and or dynamic conditional heteroskedasticity of regression disturbances are considered the classes include statistics with good power against strongly dependent alternatives along with the usual ones that test against weak dependence and many others limiting null distributions are obtained under mild conditions on the dependence structure of the alternative against which the test is derived on moments of the disturbances and on the regressors the various test statistics have a similar overall structure and while tests against strongly dependent alternatives entail more computation than ones against weakly dependent alternatives the difference can be slight if the fast fourier transform is used

autoregressive conditional duration a new model for irregularly spaced transaction data this paper proposes a new statistical model for the analysis of data which arrive at irregular intervals the model treats the time between events as a stochastic process and proposes a new class of point processes with dependent arrival rates the conditional intensity is developed and compared with other self exciting processes because the model focuses on the expected duration between events it is called the autoregressive conditional duration acd model asymptotic properties of the quasi maximum likelihood estimator are developed as a corollary to arch model results strong evidence is provided for duration clustering for the financial transaction data analyzed both deterministic time of day effects and stochastic effects are important the model is applied to the arrival times of trades and therefore is a model of transaction volume and also to the arrival of other events such as price changes models for the volatility of prices are estimated with price based durations and examined from a market microstructure point of view

notes on financial econometrics the first part of the discussion reviews recent successes in modeling of discrete time financial data and argues that a direct approach is better suited than stochastic volatility the second part reviews recent work on estimating continuous time models with emphasis on simulation based techniques and joint estimation of the risk neutral and objective probability distributions

neglecting parameter changes in garch models if a garch model is estimated on a time series that contains parameter changes in the conditional volatility process and these parameter changes are not accounted for a distinct error in the estimation occurs the sum of the estimated autoregressive parameters of the conditional variance converges to one in finite samples the sum of the estimated autoregressive parameters is heavily biased towards one this paper shows that this convergence holds for all common estimators of garch simulations of the garch model show that the effect occurs for realistic parameter changes and sample sizes for financial volatility data

a nodal inverse problem for second order sturm liouville operators with indefinite weights in this paper we study an inverse problem for weighted second order sturm liouville equations we show that the zeros of any subsequence of eigenfunctions or a dense set of nodes are enough to determine the weight we impose weaker hypotheses for positive weights and we generalize the proof to include indefinite weights moreover the parameters in the boundary conditions can be determined numerically by using a shooting method

forecasting volatility in shanghai and shenzhen markets based on multifractal analysis abstract this paper analyzes the multifractality in shanghai and shenzhen stock markets using multifractal spectrum analysis and multifractal detrended fluctuation analysis we find that the main source of multifractality is long range correlations of large and small fluctuations then we introduce a multifractal volatility measure mv and find that by taking mv as daily conditional volatility the simulated series displayed similar stylized facts to the original daily return series by capturing the dynamics of mv using the arfima model we find that the out of sample forecasting performance of the arfima mv model is better than some garch class models and the arfima rv model under some criteria of loss function

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

a tikhonov regularization for the inverse nodal problem for p laplacian abstract we apply the tikhonov regularization method to reconstruct potentials of a p laplacian eigenvalue problem using only zeros of one eigenfunction with explicit error bounds this is an inverse problem on a class of nonlinear equations when p 2 the study is motivated by our previous work on sturm liouville operators chen et al 2011 6

the distribution of realized exchange rate volatility using high frequency data on deutschemark and yen returns against the dollar we construct model free estimates of daily exchange rate volatility and correlation that cover an entire decade our estimates termed realized volatilities and correlations are not only model free but also approximately free of measurement error under general conditions which we discuss in detail hence for practical purposes we may treat the exchange rate volatilities and correlations as observed rather than latent we do so and we characterize their joint distribution both unconditionally and conditionally noteworthy results include a simple normality inducing volatility transformation high contemporaneous correlation across volatilities high correlation between correlation and volatilities pronounced and persistent dynamics in volatilities and correlations evidence of long memory dynamics in volatilities and correlations and remarkably precise scaling laws under temporal aggregation

regular and pathological eigenvalue behavior for the equation λu vuon the semiaxis we study the behavior of the eigenvalue distribution functionn for the equation u vuon r u 0 0 typically n o 1 2 and moreover 1 2n 1 v dxas 0 we obtain criteria for each of these relations examples are presented where lim 0 1 2n does exist but is not equal to 1 v dx

filtering and forecasting with misspecified arch models i getting the right variance with the wrong model this paper investigates the properties of the conditional covariance estimates generated by a misspecified arch model for example suppose that we observe a diffusion process at discrete time intervals of length h for each h we use a garch 1 1 model to estimate the instantaneous conditional covariance matrix of the diffusion under mild regularity conditions the difference between these conditional covariance estimates and the true conditional covariance converges to zero in probability as h 0 many other arch models for example exponential arch have similar consistency properties this may well account for the success of arch models in short term forecasting using high frequency data since even misspecified arch models can produce good estimates of volatility

arch models as diffusion approximations abstract this paper investigates the convergence of stochastic difference equations e g arch to stochastic differential equations as the length of the discrete time intervals between observations goes to zero these results are applied to the garch 1 1 model of bollerslev 1986 and to the ar 1 exponential arch model of nelson 1989 in their continuous time limits the conditional variance processes in these models have stationary distributions that are inverted gamma and lognormal respectively in addition a class of diffusion approximations based on the exponential arch model is developed

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

forecasting s p 100 volatility the incremental information content of implied volatilities and high frequency index returns the information content of implied volatilities and intraday returns is compared in the context of forecasting index volatility over horizons from 1 to 20 days forecasts of two measures of realized volatility are obtained after estimating arch models using daily index returns daily observations of the vix index of implied volatility and sums of squares of 5 min index returns the in sample estimates show that nearly all relevant information is provided by the vix index and hence there is not much incremental information in high frequency index returns for out of sample forecasting the vix index provides the most accurate forecasts for all forecast horizons and performance measures considered the evidence for incremental forecasting information in intraday returns is insignificant

a multiple indicators model for volatility using intra daily data many ways exist to measure and model financial asset volatility in principle as the frequency of the data increases the quality of forecasts should improve yet there is no consensus about a true or best measure of volatility in this paper we propose to jointly consider absolute daily returns daily high low range and daily realized volatility to develop a forecasting model based on their conditional dynamics as all are non negative series we develop a multiplicative error model that is consistent and asymptotically normal under a wide range of specifications for the error density function the estimation results show significant interactions between the indicators we also show that one month ahead forecasts match well both in and out of sample the market based volatility measure provided by an average of implied volatilities of index options as measured by vix

incorporating overnight and intraday returns into multivariate garch volatility models abstract we propose and evaluate mixed frequency multivariate garch models for forecasting low frequency weekly volatility based on high frequency intraday returns at 5 minute intervals and on the overnight returns the low frequency conditional volatility matrix is modeled as a weighted sum of an intraday and an overnight component the components are specified as multivariate garch processes of the bekk type adapted to the mixed frequency data setting and may enter the model as two separate components or as a single one the models may further be extended by a nonparametrically estimated slowly varying long run volatility matrix we evaluate the models in and out of sample using the 5 minute and overnight returns on four djia stocks axp ge hd and ibm from january 1988 to november 2014 and find that they systematically dominate a variety of models that only use lower frequency data weekly daily or close to open and open to close returns

a nodal inverse problem for a quasi linear ordinary differential equation in the half line abstract in this paper we study an inverse problem for a quasi linear ordinary differential equation with a monotonic weight in the half line first we find the asymptotic behavior of the singular eigenvalues and we obtain a weyl type asymptotics imposing an appropriate integrability condition on the weight then we investigate the inverse problem of recovering the coefficients from nodal data we show that any dense subset of nodes of the eigenfunctions is enough to recover the weight

the econometrics of ultra high frequency data ultra high frequency data is defined to be a full record of transactions and their associated characteristics the transaction arrival times and accompanying measures can be analyzed as marked point processes the acd point process developed by engle and russell 1998 is applied to ibm transactions arrival times to develop semiparametric hazard estimates and conditional intensities combining these intensities with a garch model of prices produces ultra high frequency measures of volatility both returns and variances are found to be negatively influenced by long durations as suggested by asymmetric information models of market micro structure

lobby index as a network centrality measure we study the lobby index l index for short as a local node centrality measure for complex networks the l index is compared with degree a local measure betweenness and eigenvector centralities two global measures in the case of a biological network yeast interaction protein protein network and a linguistic network moby thesaurus ii in both networks the l index has a poor correlation with betweenness but correlates with degree and eigenvector centralities although being local the l index carries more information about its neighbors than degree centrality also it requires much less time to compute when compared with eigenvector centrality results show that the l index produces better results than degree and eigenvector centrality for ranking purposes

econometric analysis of realized volatility and its use in estimating stochastic volatility models summary the availability of intraday data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets called realized volatility to study the stochastic properties of returns here under the assumption of a rather general stochastic volatility model we derive the moments and the asymptotic distribution of the realized volatility error the difference between realized volatility and the discretized integrated volatility which we call actual volatility these properties can be used to allow us to estimate the parameters of stochastic volatility models without recourse to the use of simulation intensive methods

maximum likelihood estimation of stationary univariate fractionally integrated time series models abstract to estimate the parameters of a stationary univariate fractionally integrated time series the unconditional exact likelihood function is derived this allows the simultaneous estimation of all the parameters of the model by exact maximum likelihood issues involved in obtaining maximum likelihood estimates are discussed particular attention is given to efficient procedures to evaluate the likelihood function obtaining starting values and the small sample properties of the estimators limitations of previous estimation procedures are also discussed

lobby index in networks abstract we propose a new node centrality measure in networks the lobby index which is inspired by hirsch s h index it is shown that in scale free networks with exponent the distribution of the l index has power tail with exponent 1 properties of the l index and extensions are discussed

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

chasing volatility a persistent multiplicative error model with jumps abstract persistence and unpredictable large increments characterize the volatility of financial returns we propose the multiplicative error model with volatility jumps mem j to describe and predict the probability and the size of these extreme events under the mem j the conditional density of the realized measure is a countably infinite mixture of gamma and kappa distributions with closed form conditional moments we derive stationarity conditions and the asymptotic theory for the maximum likelihood estimation estimates of the volatility jump component confirm that the probability of jumps dramatically increases during the financial crises the mem j improves over other models with fat tails

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

thesaurus as a complex network abstract a thesaurus is one out of many possible representations of term or word connectivity the terms of a thesaurus are seen as the nodes and their relationship as the links of a directed graph the directionality of the links retains all the thesaurus information and allows the measurement of several quantities this has lead to a new term classification according to the characteristics of the nodes for example nodes with no links in no links out etc using an electronic available thesaurus we have obtained the incoming and outgoing link distributions while the incoming link distribution follows a stretched exponential function the lower bound for the outgoing link distribution has the same envelope of the scientific paper citation distribution proposed by tsallis and albuquerque eur phys j b 13 2000 777 however a better fit is obtained by simpler function which is the solution of ricatti s differential equation we conjecture that this differential equation is the continuous limit of a stochastic growth model of the thesaurus network we also propose a new manner to arrange a thesaurus using the inversion method