generalized dynamic factor models and volatilities estimation and forecasting abstract in large panels of financial time series with dynamic factor structure on the levels or returns the volatilities of the common and idiosyncratic components often exhibit strong correlations indicating that both are exposed to the same market volatility shocks this suggests alongside the dynamic factor decomposition of returns a dynamic factor decomposition of volatilities or volatility proxies based on this observation barigozzi and hallin 2016 proposed an entirely non parametric and model free two step general dynamic factor approach which accounts for a joint factor structure of returns and volatilities and allows for extracting the market volatility shocks here we go one step further and show how the same two step approach naturally produces volatility forecasts for the various stocks under study in an applied exercise we consider the panel of asset returns of the constituents of the s p100 index over the period 2000 2009 numerical results show that the predictors based on our two step method outperform existing univariate and multivariate garch methods as well as static factor garch models in the prediction of daily high low range while avoiding the usual problems associated with the curse of dimensionality

an analysis of separable least squares data driven local coordinates for maximum likelihood estimation of linear systems in this paper we study a novel parametrization for state space systems namely separable least squares data driven local coordinates slsddlc the parametrization by slsddlc has recently been successfully applied to maximum likelihood estimation of linear dynamic systems in a simulation study the use of slsddlc has led to numerical advantages in comparison to the use of more conventional parametrizations including data driven local coordinates ddlc however an analysis of properties of slsddlc which are relevant to identification has not been performed up to now in this paper we provide insights into the geometry and topology of the slsddlc construction and show a number of results which are important for actual identification in particular for maximum likelihood estimation we also prove that the separable least squares methodology is indeed guaranteed to be applicable to maximum likelihood estimation of linear dynamic systems in typical situations

multifactorial functions in fuzzy sets theory abstract the multifactorial function is a very important new concept which can be used to many aspects in fuzzy sets theory it appeared firstly in 5 where it was used to define fuzzy perturbation function and where the stability for the solutions of fuzzy relation equations by using fuzzy perturbation was studied in 6 by means of multifactorial functions multifactorial fuzzy sets and the multifactorial degree of nearness which are two new concepts too were given and they were used to multifactorial pattern recognition and clustering analysis with fuzzy characteristics in fact generally speaking most of the mathematical models dependent on several factors should use multifactorial functions especially fuzzy decision making fuzzy games fuzzy programming and fuzzy linear programming with several objective functions should here we study properties of multifactorial functions how to generate a new multifactorial function and we introduce in detail its applications in fuzzy pattern recognition fuzzy decision making fuzzy clustering fuzzy games and fuzzy programming etc

determining the number of factors in the general dynamic factor model this article develops an information criterion for determining the number q of common shocks in the general dynamic factor model developed by forni et al as opposed to the restricted dynamic model considered by bai and ng and by amengual and watson our criterion is based on the fact that this number q is also the number of diverging eigenvalues of the spectral density matrix of the observations as the number n of series goes to infinity we provide sufficient conditions for consistency of the criterion for large n and t where t is the series length we show how the method can be implemented and provide simulations and empirics illustrating its very good finite sample performance application to real data adds a new empirical facet to an ongoing debate on the number of factors driving the u s economy

the generalized dynamic factor model consistency and rates abstract a factor model generalizing those proposed by geweke in d j aigner and a s goldberger latent variables in socio economic models north holland amsterdam 1977 sargent and sims new methods in business research federal reserve bank of minneapolis minneapolis 1977 engle and watson j amer statist assoc 76 1981 774 and stock and watson j business econom statist 20 2002 147 has been introduced in forni et al rev econ statist 80 2000 540 where consistent as the number n of series and the number t of observations both tend to infinity along appropriate paths n t n estimation methods for the common component are proposed rates of convergence associated with these methods are obtained here as functions of the paths n t n along which n and t go to infinity these results show that under suitable assumptions consistency requires t n to be at least of the same order as n whereas an optimal rate of n is reached for t n of the order of n2 if convergence to the space of common components is considered consistency holds irrespective of the path t n thus can be arbitrarily slow the optimal rate is still n but only requires t n to be of the order of n

factor analysis for non normal variables factor analysis for nonnormally distributed variables is discussed in this paper the main difference between our approach and more traditional approaches is that not only second order cross products like covariances are utilized but also higher order cross products it turns out that under some conditions the parameters factor loadings can be uniquely determined two estimation procedures will be discussed one method gives best generalized least squares bgls estimates but is computationally very heavy in particular for large data sets the other method is a least squares method which is computationally less heavy in one example the two methods will be compared by using the bootstrap method in another example real life data are analyzed

fuzzy perturbation analysis part 2 undirectional perturbation abstract in this paper the stability of the solutions of fuzzy relation equations is discussed by the method of undirectional fuzzy perturbation first a general definition of fuzzy perturbation is given from this the concept of fuzzy perturbation equation is introduced and thus stability of the solutions is defined next the degree of stability of the solutions a kind of metric of the stability is advanced three ordered quotient sets are induced by use of the degree of stability these quotient sets have a well chained characteristic

generalized dynamic factor models and volatilities consistency rates and prediction intervals abstract volatilities in high dimensional panels of economic time series with a dynamic factor structure on the levels or returns typically also admit a dynamic factor decomposition we consider a two stage dynamic factor model method recovering the common and idiosyncratic components of both levels and log volatilities specifically in a first estimation step we extract the common and idiosyncratic shocks for the levels from which a log volatility proxy is computed in a second step we estimate a dynamic factor model which is equivalent to a multiplicative factor structure for volatilities for the log volatility panel by exploiting this two stage factor approach we build one step ahead conditional prediction intervals for large n t panels of returns those intervals are based on empirical quantiles not on conditional variances they can be either equal or unequal tailed we provide uniform consistency and consistency rates results for the proposed estimators as both n and t tend to infinity we study the finite sample properties of our estimators by means of monte carlo simulations finally we apply our methodology to a panel of asset returns belonging to the s p100 index in order to compute one step ahead conditional prediction intervals for the period 2006 2013 a comparison with the componentwise garch benchmark which does not take advantage of cross sectional information demonstrates the superiority of our approach which is genuinely multivariate and high dimensional nonparametric and model free

nearest comoment estimation with unobserved factors we propose a minimum distance estimator for the higher order comoments of a multivariate distribution exhibiting a lower dimensional latent factor structure we derive the influence function of the proposed estimator and prove its consistency and asymptotic normality the simulation study confirms the large gains in accuracy compared to the traditional sample comoments the empirical usefulness of the novel framework is shown in applications to portfolio allocation under non gaussian objective functions and to the extraction of factor loadings in a dataset with mental ability scores

matchable observable linear models and direct filter tuning an approach to multivariable identification identification of linear time invariant multivariable systems can best be understood as comprising three separate problems selection of system model structure filter design and parameter estimation itself approaching the first using matchable observable models originally developed in the adaptive control literature and the second via direct or derivative free optimization effective least squares algorithms can be used for parameter estimation the accuracy robustness and moderate computational demands of the methods proposed are demonstrated via simulations with randomly generated models and applied to identification using real process data the results obtained are comparable or superior to the best results obtained using standard implementations of the algorithms described in the literature

forecasting using principal components from a large number of predictors this article considers forecasting a single time series when there are many predictors n and time series observations t when the data follow an approximate factor model the predictors can be summarized by a small number of indexes which we estimate using principal components feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both n and t grow large the estimated factors are shown to be consistent even in the presence of time variation in the factor model

on a principal varying coefficient model we propose a novel varying coefficient model vcm called principal varying coefficient model pvcm by characterizing the varying coefficients through linear combinations of a few principal functions compared with the conventional vcm pvcm reduces the actual number of nonparametric functions and thus has better estimation efficiency compared with the semivarying coefficient model svcm pvcm is more flexible but with the same estimation efficiency when the number of principal functions in pvcm and the number of varying coefficients in svcm are the same model estimation and identification are investigated and the better estimation efficiency is justified theoretically incorporating the estimation with the l 1 penalty variables in the linear combinations can be selected automatically and hence the estimation efficiency can be further improved numerical experiments suggest that the model together with the estimation method is useful even when the number of covariates is large supplementary mat

variance analysis of identified linear miso models having spatially correlated inputs with application to parallel hammerstein models this contribution concerns variance analysis of linear multi input single output models when the inputs are temporally white but where different inputs may be correlated an expression is provided for the variance of a linearly parametrized estimate of the frequency response function from one block i e from one input to the output in particular this expression reveals that the variance increases in one block when the number of estimated parameters in another block is increased but levels off when the number of parameters in the other block reaches the number of parameters in the block in question it also quantifies exactly how correlation between inputs affects the resulting accuracy and a graphical representation is provided for this purpose the results are applicable to parallel miso hammerstein models when the nonlinearities are known and generalize an existing variance expression for this type of model

risks of large portfolios the risk of a large portfolio is often estimated by substituting a good estimator of the volatility matrix however the accuracy of such a risk estimator is largely unknown we study factor based risk estimators under a large amount of assets and introduce a high confidence level upper bound h club to assess the estimation the h club is constructed using the confidence interval of risk estimators with either known or unknown factors we derive the limiting distribution of the estimated risks in high dimensionality we find that when the dimension is large the factor based risk estimators have the same asymptotic variance no matter whether the factors are known or not which is slightly smaller than that of the sample covariance based estimator numerically h club outperforms the traditional crude bounds and provides an insightful risk assessment in addition our simulated results quantify the relative error in the risk estimation which is usually negligible using 3 month daily data

alternative approximations to the distributions of instrumental variable estimators the paper considers the ols the iv and two method of moments estimators mm and mmk of the coefficients of a single equation where the explanatory variables are correlated with the disturbance term the mm and mmk estimators are generalizations of the liml and limlk estimators respectively multivariate first order approximations to the distributions are derived under normality using a parameter sequence where the number of instruments increases as the number of observations increases numerical results show these approximations are more accurate compared to large sample approximations even if the number of instruments is small the moments of the multivariate limit distributions of the mm and mmk estimators can be consistently estimated under a variety of parameter sequences including the large sample sequence the new approximate confidence regions perform well in terms of exact levels compared to traditional ones the iv estimator of the coefficient of a single explanatory endogenous variable is interpreted as a shrinkage estimator which is dominated in practical cases by the mm and mmk estimators in terms of nearness to the true value in the sense of pitman

a new kind of fuzzy relation equations based on inner transformation this paper mainly deals with a new kind of fuzzy relation equations based on inner transformation first the inner projection of a fuzzy relation and the inner transformation by a fuzzy relation are introduced and also what is a fuzzy relation equation based on inner transformation is described second the discriminative matrix and the discriminative vector are defined on the basis of them an approach of discriminating whether such a fuzzy relation equation has nonzero solution is obtained at last a procedure of solving such fuzzy relation equations is presented the solution set of a fuzzy relation equation based on inner transformation is not closed with respect to join and meet operations in general this shows that the traditional methods being used for solving email protected composite fuzzy relation equations cannot be applied into the study of this kind of fuzzy relation equations based on inner transformation

on pseudo transitive approximations of fuzzy relations abstract in the present paper we consider a generalization of the well known notion of transitive fuzzy relations this may be useful for preference relations or similarity relations describing butterfly like configurations where the widely used transitive closure is rather different from the original relation moreover the proposed concept enables us to determine relations which are transitive only for a part of the elements under consideration some examples demonstrate the usefulness of our approach

arbitrage factor structure and mean variance analysis on large asset markets we examine the implications of arbitrage in a market with many assets the absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous hence there exist unique portfolios that represent these functionals these portfolios span the mean variance efficient set we resolve the question of when a market with many assets permits so much diversification that risk free investment opportunities are available ross 12 14 showed that if there is a factor structure then the mean returns are approximately linear functions of factor loadings we define an approximate factor structure and show that this weaker restriction is sufficient for ross result if the covariance matrix of the asset returns has only k unbounded eigenvalues then there is an approximate factor structure and it is unique the corresponding k eigenvectors converge and play the role of factor loadings hence only a principal component analysis is needed in empirical work

an lft approach to parameter estimation in this paper we consider a unified framework for parameter estimation problems under this framework the unknown parameters appear in a linear fractional transformation lft a key advantage of the lft problem formulation is that it allows us to efficiently compute gradients hessians and gauss newton directions for general parameter estimation problems without resorting to inefficient finite difference approximations the generality of this approach also allows us to consider issues such as identifiability persistence of excitation and convergence for a large class of model structures under a single unified framework

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

data driven local coordinates for multivariable linear systems and their application to system identification in this paper we introduce a new parametrization for state space systems data driven local coordinates ddlc the parametrization is obtained by restricting the full state space parametrization where all matrix entries are considered to be free to an affine plane containing a given nominal state space realization this affine plane is chosen to be perpendicular to the tangent space to the manifold of observationally equivalent state space systems at the nominal realization the application of the parametrization to prediction error identification is exemplified simulations indicate that the proposed parametrization has numerical advantages as compared to e g the more commonly used observable canonical form

maximum likelihood estimation and inference for high dimensional generalized factor models with application to factor augmented regressions abstract this paper reestablishes the main results in bai 2003 and bai and ng 2006 for generalized factor models with slightly stronger conditions on the relative magnitude of n number of subjects and t number of time periods convergence rates of the estimated factor space and loading space and asymptotic normality of the estimated factors and loadings are established under mild conditions that allow for linear logit probit tobit poisson and some other single index nonlinear models the probability density mass function is allowed to vary across subjects and time thus mixed models are also allowed for for factor augmented regressions this paper establishes the limit distributions of the parameter estimates the conditional mean and the forecast when factors estimated from nonlinear mixed data are used as proxies for the true factors

the rank of demand systems theory and nonparametric estimation w m gorman s 1981 concept of engel curve rank is extended to apply to any demand system rank is shown to have implications for specification separability and aggregation of demands a simple nonparametric test of rank using engel curve data is described and applied to u s and u k consumer survey data the test employs a new general method for testing the rank of estimated matrices the results are used to assess theoretical and empirical aggregation error in representative consumer models and to explain a representative consumer paradox copyright 1991 by the econometric society

quasi maximum likelihood analysis of high dimensional constrained factor models abstract factor models have been widely used in practice however an undesirable feature of a high dimensional factor model is that the model has too many parameters an effective way to address this issue proposed in a seminar work by tsai and tsay 2010 is to decompose the loadings matrix by a high dimensional known matrix multiplying with a low dimensional unknown matrix which tsai and tsay 2010 name the constrained factor models this paper investigates the estimation and inferential theory of constrained factor models under large n and large t setup where n denotes the number of cross sectional units and t the time periods we propose using the quasi maximum likelihood method to estimate the model and investigate the asymptotic properties of the quasi maximum likelihood estimators including consistency rates of convergence and limiting distributions a new statistic is proposed for testing the null hypothesis of constrained factor models against the alternative of standard factor models partially constrained factor models are also investigated monte carlo simulations confirm our theoretical results and show that the quasi maximum likelihood estimators and the proposed new statistic perform well in finite samples we also consider the extension to an approximate constrained factor model where the idiosyncratic errors are allowed to be weakly dependent processes

determining the number of factors in approximate factor models in this paper we develop some econometric theory for factor models of large dimensions the focus is the determination of the number of factors r which is an unresolved issue in the rapidly growing literature on multifactor models we first establish the convergence rate for the factor estimates that will allow for consistent estimation of r we then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria the theory is developed under the framework of large cross sections n and large time dimensions t no restriction is imposed on the relation between n and t simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice

factor space theory in fuzzy information processing composition of states of factors and multifactorial decision making abstract the concept of factor space used in fuzzy information processing is investigated the composition of the states of factors which is a basic tool in multifactorial decision making is first considered then a general model of multifactorial decision making is formulated finally multi factorial decision making with multiple objectives is introduced numerical examples are given to illustrate the approaches

brief paper constrained state space system identification with application to structural dynamics constrained identification of state space models representing structural dynamic systems is addressed based on physical insight transfer function constraints are formulated in terms of the state space parametrization a simple example shows that a method tailored for this application which utilizes the non uniqueness of a state space model outperforms the classic sequential quadratic programming method in terms of robustness and convergence properties the method is also successfully applied to real experimental data of a plane frame structure

fuzzy clustering method based on perturbation abstract based on the results obtained in the earlier paper 1 the fuzzy clustering method based on perturbation fcmbp is further studied and several important results are obtained first since the fuzzy similarity matrix equation x2 x is one of the most important basic components of the fcmbp approach the structure of the solutions of this matrix equation is investigated to express the solutions the concept of fuzzy equivalent standard form is proposed second the existence of the globally and locally optimal fuzzy equivalent matrices which are nearest to the given fuzzy similarity matrix is proved third an effective fuzzy clustering method based on the above results is proposed finally two examples which show that the result obtained by the fcmbp method is more accurate than that obtained by the transitive closure method are solved

micro versus macro cointegration in heterogeneous panels we consider the issue of cross sectional aggregation in nonstationary and heterogeneous panels where each unit cointegrates we derive asymptotic properties of the aggregate estimate and necessary and sufficient conditions for cointegration to hold in the aggregate relationship we then analyze the case when cointegration does not carry through the aggregation process and we investigate whether the violation of the formal conditions for perfect aggregation can still lead to an aggregate equation that is observationally equivalent to a cointegrated relationship we derive a measure of the degree of noncointegration of the aggregate relationship and we explore its asymptotic properties we propose a valid bootstrap approximation of the test a monte carlo exercise evaluates size and power properties of the bootstrap test

volatility forecast comparison using imperfect volatility proxies the use of a conditionally unbiased but imperfect volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts we motivate our study with analytical results on the distortions caused by some widely used loss functions when used with standard volatility proxies such as squared returns the intra daily range or realised volatility we then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy and derive some useful special cases of this class of robust loss functions the methods are illustrated with an application to the volatility of returns on ibm over the period 1993 to 2003

brief paper new method for identifying finite degree volterra series in this paper the identification of a class of nonlinear systems which admits input output maps described by a finite degree volterra series is considered in actual fact it appears that this class can model many important nonlinear multivariable processes not only in engineering but also in biology socio economics and ecology to solve this identification problem we propose a method based on local gradient search in a local parameterization of the state space realization of finite degree volterra series with infinite horizon using the local parameterization not only reduces the amount of the gradient calculations to the minimal value but also overcomes the nonuniqueness problem of the optimal solution moreover we propose a sequential projection method to provide an initial estimation of the parameters of finite degree volterra series realization this initial estimation is used to initialize the gradient search method

on factor models with random missing em estimation inference and cross validation abstract we consider the estimation and inference in approximate factor models with random missing values we show that with the low rank structure of the common component we can estimate the factors and factor loadings consistently with the missing values replaced by zeros we establish the asymptotic distributions of the resulting estimators and those based on the em algorithm we also propose a cross validation based method to determine the number of factors in factor models with or without missing values and justify its consistency simulations demonstrate that our cross validation method is robust to fat tails in the error distribution and significantly outperforms some existing popular methods in terms of correct percentage in determining the number of factors an application to the factor augmented regression models shows that a proper treatment of the missing values can improve the out of sample forecast of some macroeconomic variables

the structural clustering and analysis of metric based on granular space in this paper the research on granular space theory and structural clusters of metric based on granular space is introduced and a comprehensive of theoretical and analyzing methodologies is developed the granular space theory is established based on normalized equicrural metric and the consistent cluster characteristics of ordered granular spaces are derived details are shared for some related subject such as the granular representation of structural cluster from normalized metric the optimal cluster determination the fusion of structural cluster and the structural clustering analysis of metric space based on granular space etc theories and methodologies are established for structural clustering based on metric space and developed a series of mathematical models and formal description tools for the research on its potential applications direct and geometric interpretations for structural clustering analysis are provided to assist deeper understanding the essence of clustering or classifying procedure

factor garch ito models for high frequency data with application to large volatility matrix prediction abstract several novel large volatility matrix estimation methods have been developed based on the high frequency financial data they often employ the approximate factor model that leads to a low rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices however for predicting future volatility matrices these nonparametric estimators do not have a dynamic structure to implement in this paper we introduce a novel ito diffusion process based on the approximate factor models and call it a factor garch ito model we then investigate its properties and propose a quasi maximum likelihood estimation method for the parameter of the factor garch ito model we also apply it to estimating conditional expected large volatility matrices and establish their asymptotic properties simulation studies are conducted to validate the finite sample performance of the proposed estimation methods the proposed method is also illustrated by using data from the constituents of the s p 500 index and an application to constructing the minimum variance portfolio with gross exposure constraints

estimation and inference in large heterogeneous panels with a multifactor error structure this paper presents a new approach to estimation and inference in panel data models with a general multifactor error structure the unobserved factors and the individual specific errors are allowed to follow arbitrary stationary processes and the number of unobserved factors need not be estimated the basic idea is to filter the individual specific regressors by means of cross section averages such that asymptotically as the cross section dimension n tends to infinity the differential effects of unobserved common factors are eliminated the estimation procedure has the advantage that it can be computed by least squares applied to auxiliary regressions where the observed regressors are augmented with cross sectional averages of the dependent variable and the individual specific regressors a number of estimators referred to as common correlated effects cce estimators are proposed and their asymptotic distributions are derived the small sample properties of mean group and pooled cce estimators are investigated by monte carlo experiments showing that the cce estimators have satisfactory small sample properties even under a substantial degree of heterogeneity and dynamics and for relatively small values of n and t

iv estimation of panels with factor residuals this paper considers panel data regression models with weakly exogenous or endogenous regressors and residuals generated by a multi factor error structure in this case the standard dynamic panel estimators fail to provide consistent estimates of the parameters we propose a new estimation approach based on instrumental variables which retains the traditional attractive features of method of moments estimators one novelty of our approach is that we introduce new parameters to represent the unobserved covariances between the instruments and the factor component of the residual these parameters are typically estimable when n is large some important estimation and identification issues are studied in detail the finite sample performance of the proposed estimators is investigated using simulated data the results show that the method produces reliable estimates of the parameters over various parametrizations and is robust to large values of the autoregressive parameter and or the variance of the factor loadings

a relaxation approach to the fuzzy clustering problem abstract in this paper a new algorithm for fuzzy clustering is presented the proposed algorithm utilizes the idea of relaxation convergence of the proposed algorithm is proved and limits on the relaxation parameter are derived stopping criteria and resulting convergence behaviour of the algorithms are discussed the performance of the new algorithm is compared to the fuzzy c means algorithm by testing both on three published data sets theoretical and empirical results reported in this paper show that the new algorithm is more efficient and leads to significant computational savings

computing a t transitive lower approximation or opening of a proximity relation since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation assuming that such a violation is mainly due to decision maker estimation errors in some way the more number of elicitations the more probable inconsistency is this is mostly the case within a fuzzy framework even when the number of alternatives or object to be classified is relatively small in this paper we propose a fast method to compute a t indistinguishability from a reflexive and symmetric fuzzy relation being t any left continuous t norm the computed approximation we propose will take o n 3 time complexity where n is the number of elements under consideration and is expected to produce a t transitive opening to the authors knowledge there are no other proposed algorithm that computes t transitive lower approximations or openings while preserving the reflexivity and symmetry properties

on transitive solutions of fuzzy equations inequalities and lower approximations of fuzzy relations abstract in the present paper we determine the greatest resp maximal transitive solution of a fuzzy equation resp inequality such problem arises among others when we approximate arbitrary fuzzy relations by transitive ones from below a sketch of extension of these results to interval valued fuzzy sets is given as well

unobserved component time series models with arch disturbances abstract this paper considers how arch effects may be handled in time series models formulated in terms of unobserved components a general model is formulated but this includes as special cases a random walk plus noise model with both disturbances subject to arch effects an arch m model with a time varying parameter and a latent factor model with arch effects in the factors although the model is not conditionally gaussian an approximate filter can be obtained and used as the basis for estimation the performance of this method is examined on real data sets and monte carlo experiments are carried out the method is extended to handle garch and a latent factor model based on the t distribution

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

partial factor modeling predictor dependent shrinkage for linear regression we develop a modified gaussian factor model for the purpose of inducing predictor dependent shrinkage for linear regression the new model predicts well across a wide range of covariance structures on real and simulated data furthermore the new model facilitates variable selection in the case of correlated predictor variables which often stymies other methods

estimation of latent factors for high dimensional time series this paper deals with the dimension reduction of high dimensional time series based on common factors in particular we allow the dimension of time series p to be as large as or even larger than the sample size n the estimation of the factor loading matrix and the factor process itself is carried out via an eigenanalysis of a p p non negative de nite matrix we show that when all the factors are strong in the sense that the norm of each column in the factor loading matrix is of the order p1 2 the estimator of the factor loading matrix is weakly consistent in l2 norm with the convergence rate independent of p this result exhibits clearly that the curse is canceled out by the blessing of dimensionality we also establish the asymptotic properties of the estimation when factors are not strong the proposed method together with their asymptotic properties are further illustrated in a simulation study an application to an implied volatility data set together with a trading strategy derived from the tted factor model is also reported

multifactorial fuzzy sets and multifactorial degree of nearness abstract two new concepts multifactorial fuzzy sets and multifactorial degree of nearness are advanced first an axiomatic definition for multifactorial functions is given and multifactorial fuzzy sets and multifactorial degree of nearness are defined by using the multifactorial function second three direct methods of multifactorial pattern recognition and two methods for fuzzy clustering with fuzzy characteristics are given last we advance an interesting open problem

estimation of the global minimum variance portfolio in high dimensions abstract we estimate the global minimum variance gmv portfolio in the high dimensional case using results from random matrix theory this approach leads to a shrinkage type estimator which is distribution free and optimal in the sense of minimizing the out of sample variance its asymptotic properties are investigated assuming that the number of assets p depends on the sample size n such that p n c 0 as n tends to infinity the results are obtained under weak assumptions imposed on the distribution of the asset returns only the existence of the fourth moments is required furthermore we make no assumption on the upper bound of the spectrum of the covariance matrix as a result the theoretical findings are also valid if the dependencies between the asset returns are described by a factor model which appears to be very popular in the financial literature nowadays this is also documented in a numerical study where the small and large sample behavior of the derived estimator is compared with existing estimators of the gmv portfolio the resulting estimator shows significant improvements and it turns out to be robust if the assumption of normality is violated

principal components estimation and identification of static factors a b s t r a c t it is known that the principal component estimates of the factors and the loadings are rotations of the un derlying latent factors and loadings we study conditions under which the latent factors can be estimated asymptotically without rotation we derive the limiting distributions for the estimated factors and factor loadings when n and t are large and make precise how identification of the factors affects inference based on factor augmented regressions we also consider factor models with additive individual and time effects the asymptotic analysis can be modified to analyze identification schemes not considered in this analysis

balanced canonical forms for system identification parameterizations of linear state space systems by balanced canonical forms are considered the structure in particular the topological properties of these parameterizations are investigated based on these results an algorithm for identification obtained by optimizing a likelihood type criterion function is proposed and analyzed in the algorithm both the estimation of real valued parameters and of integer parameters defining dynamic specification is incorporated the analysis of the algorithm emphasizes consistency results

estimation and inference of dynamic structural factor models with over identifying restrictions abstract this paper develops a new estimator for the impulse response functions in structural factor models with a fixed number of over identifying restrictions the proposed identification scheme nests the conventional just identified recursive scheme as a special case we establish the asymptotic distributions of the new estimator and develop test statistics for the over identifying restrictions simulation results show that adding a few more over identifying restrictions can lead to a substantial improvement in estimation accuracy for impulse response functions at both zero and nonzero horizons we estimate the effects of a monetary policy shock using a u s data set the results show that our over identified scheme can help to detect incorrect specifications that lead to spurious impulse responses

inferential theory for factor models of large dimensions this paper develops an inferential theory for factor models of large dimensions the principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator if normality is assumed we derive the rate of convergence and the limiting distributions of the estimated factors factor loadings and common components the theory is developed within the framework of large cross sections n and a large time dimension t to which classical factor analysis does not apply we show that the estimated common components are asymptotically normal with a convergence rate equal to the minimum of the square roots of n and t the estimated factors and their loadings are generally normal although not always so the convergence rate of the estimated factors and factor loadings can be faster than that of the estimated common components these results are obtained under general conditions that allow for correlations and heteroskedasticities in both dimensions stronger results are obtained when the idiosyncratic errors are serially uncorrelated and homoskedastic a necessary and sufficient condition for consistency is derived for large n but fixed t

estimation of large dimensional factor models with an unknown number of breaks abstract in this paper we study the estimation of a large dimensional factor model when the factor loadings exhibit an unknown number of changes over time we propose a novel three step procedure to detect the breaks if any and then identify their locations in the first step we divide the whole time span into subintervals and fit a conventional factor model on each interval in the second step we apply the adaptive fused group lasso to identify intervals containing a break in the third step we devise a grid search method to estimate the location of the break on each identified interval we show that with probability approaching one our method can identify the correct number of changes and estimate the break locations simulation studies indicate superb finite sample performance of our method we apply our method to investigate stock and watson s 2009 u s monthly macroeconomic dataset and identify five breaks in the factor loadings spanning 1959 2006

the general dynamic factor model one sided representation results recent dynamic factor models have been almost exclusively developed under the assumption that the common components span a finite dimensional vector space however this finite dimension assumption rules out very simple factor loading patterns and is therefore severely restrictive the general case has been studied using a frequency domain approach in forni et al 2000 that paper produces an estimator of the common components that is consistent but is based on filters that are two sided and therefore unsuitable for prediction the present paper assuming a rational spectral density for the common components obtains a one sided estimator without the finite dimension assumption

fuzzy clustering in cell formation with multiple attributes an approach based on fuzzy clustering and aggregation operators is proposed to design cell formation involving multiple criteria or multiple attributes the three most basic attributes in cell formation namely number of machines required processing time and common tools required on machines are considered the results are compared with the single attribute results of chu and hayya 1991 27

fuzzy clustering methods based on perturbation the fuzzy clustering method as it is known to us transforms a fuzzy similarity matrix r into a fuzzy equivalent matrix r t r which is the transmission closure of r in this paper we put forward a new fuzzy clustering method using the idea to find a fuzzy equivalent matrix r which is closest to r by a certain distance in general the distance between r and r is much less than the distance between r and r which means that the lack of fidelity that is brought about by clustering according to r is much less than the lack of fidelity by r

panel data models with interactive fixed effects this paper considers large n and large t panel data models with unobservable multiple interactive eects these models are useful for both micro and macro econometric modelings in earnings studies for example workers motivation persistence and diligence combined to influence the earnings in addition to the usual argument of innate ability in macroeconomics the interactive eects represent unobservable common shocks and their heterogeneous responses over cross sections since the interactive eects are allowed to be correlated with the regressors they are treated as fixed eects parameters to be estimated along with the common slope coecients the model is estimated by the least squares method which provides the interactive eect s counterpart of the within estimator we first consider model identification and then derive the rate of convergence and the limiting distribution of the interactive eect s estimator of the common slope coecients the estimator is shown to be p nt consistent this rate is valid even in the presence of correlations and heteroskedasticities in both dimensions a striking contrast with fixed t framework in which serial correlation and heteroskedasticity imply unidentification the asymptotic distribution is not necessarily centered at zero biased corrected estimators are derived we also derive the constrained estimator and its limiting distribution imposing additivity coupled with interactive eects the problem of testing additive versus interactive eects is also studied we also derive identification conditions for models with grand mean time invariant regressors and common regressors it is shown that there exists a set of necessary and sucient identification conditions for those models given identification the rate of convergence and limiting results continue to hold

modified fuzzy c means algorithm for cellular manufacturing several studies have used the fuzzy c means fcm algorithm for part machine grouping in cellular manufacturing however the application of the standard fcm algorithm to this problem has a number of drawbacks this paper proposes a modified fcm mfcm algorithm that groups components and machines in parallel and through an annealing process with the weighting exponent arrives at a crisp solution and an objective function value which can be interpreted in terms of the number of voids and intercellular movements of the part machine grouping obtained computational experiences show that although mfcm may sometimes require slightly more computing time than other methods not only is it able to find better solutions but also it has higher discriminating power for determining the number of cells

an improved fcmbp fuzzy clustering method based on evolutionary programming in current pc computing environment the fuzzy clustering method based on perturbation fcmbp is failed when dealing with similar matrices whose orders are higher than tens the reason is that the traversal process adopted in fcmbp is exponential complexity this paper treated the process of finding fuzzy equivalent matrices with smallest error from an optimization point of view and proposed an improved fcmbp fuzzy clustering method based on evolutionary programming the method seeks the optimal fuzzy equivalent matrix which is nearest to the given fuzzy similar matrix by evolving a population of candidate solutions over a number of generations a new population is formed from an existing population through the use of a mutation operator better solutions survive into next generation and finally the globally optimal fuzzy equivalent matrix could be obtained or approximately obtained compared with fcmbp the improved method has the following advantages 1 traversal searching is avoided by introducing an evolutionary programming based optimization technique 2 for low order matrices the method has much better efficiency in finding the globally optimal fuzzy equivalent matrix 3 matrices with hundreds of orders could be managed the method could quickly get a more accurate solution than that obtained by the transitive closure method and higher precision requirement could be achieved by further iterations and the method is adaptable for matrices of higher order 4 the method is robust and not sensitive to parameters

estimation and inference of change points in high dimensional factor models abstract in this paper we consider the estimation of break points in high dimensional factor models where the unobserved factors are estimated by principal component analysis pca the factor loading matrix is assumed to have a structural break at an unknown time we establish the conditions under which the least squares ls estimator is consistent for the break date our consistency result holds for both large and small breaks we also find the ls estimator s asymptotic distribution simulation results confirm that the break date can be accurately estimated by the ls even if the magnitudes of breaks are small in two empirical applications we implement the method to estimate break points in the u s stock market and u s macroeconomy respectively

consistent noisy independent component analysis we study linear factor models under the assumptions that factors are mutually independent and independent of errors and errors can be correlated to some extent under the factor non gaussianity second to fourth order moments are shown to yield full identification of the matrix of factor loadings we develop a simple algorithm to estimate the matrix of factor loadings from these moments we run monte carlo simulations and apply our methodology to data on cognitive test scores and financial data on stock returns

sufficient forecasting using factor models we consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect the dimensionality was first reduced via a high dimensional approximate factor model implemented by the principal component analysis using the extracted factors we develop a novel forecasting method called the sufficient forecasting which provides a set of sufficient predictive indices inferred from high dimensional predictors to deliver additional predictive power the projected principal component analysis will be employed to enhance the accuracy of inferred factors when a semi parametric approximate factor model is assumed our method is also applicable to cross sectional sufficient regression using extracted factors the connection between the sufficient forecasting and the deep learning architecture is explicitly stated the sufficient forecasting correctly estimates projection indices of the underlying factors even in the presence of a nonparametric forecasting function the proposed method extends the sufficient dimension reduction to high dimensional regimes by condensing the cross sectional information through factor models we derive asymptotic properties for the estimate of the central subspace spanned by these projection directions as well as the estimates of the sufficient predictive indices we further show that the natural method of running multiple regression of target on estimated factors yields a linear estimate that actually falls into this central subspace our method and theory allow the number of predictors to be larger than the number of observations we finally demonstrate that the sufficient forecasting improves upon the linear forecasting in both simulation studies and an empirical study of forecasting macroeconomic variables

factor and idiosyncratic empirical processes the distributions of the common and idiosyncratic components for an individual variable are important in forecasting and applications however they are not identified with low dimensional observat

l 1 norm based fuzzy clustering abstract the paper presents the l1 version of the well known fuzzy clustering method namely fuzzy isodata proposed by bezdek and dunn due to their robustness l1 norm based methods gained much attention in statistics the presented fuzzy clustering problem uses the distance between observations and location parameter vectors which is based on the l1 norm instead of the inner product induced norm used in classical fuzzy isodata two alternative methods to solve the l1 fuzzy clustering problem are derived in practice both membership grades and location parameter vectors are unknown the paper presents two iterative algorithms each the implementation of the derived method finally numerical examples are presented one of them refers to famous iris data

dynamic factor models with infinite dimensional factor spaces one sided representations abstract factor model methods recently have become extremely popular in the theory and practice of large panels of time series data those methods rely on various factor models which all are particular cases of the generalized dynamic factor model gdfm introduced in forniet al 2000 that paper however rests on brillinger s dynamic principal components the corresponding estimators are two sided filters whose performance at the end of the observation period or for forecasting purposes is rather poor no such problem arises with estimators based on standard principal components which have been dominant in this literature on the other hand those estimators require the assumption that the space spanned by the factors has finite dimension in the present paper we argue that such an assumption is extremely restrictive and potentially quite harmful elaborating upon recent results by anderson and deistler 2008a b on singular stationary processes with rational spectrum we obtain one sided representations for the gdfm without assuming finite dimension of the factor space construction of the corresponding estimators is also briefly outlined in a companion paper we establish consistency and rates for such estimators and provide monte carlo results further motivating our approach

a long run pure variance common features model for the common volatilities of the dow jones abstract in this paper a new model to analyze the comovements in the volatilities of a portfolio is proposed the pure variance common features model is a factor model for the conditional variances of a portfolio of assets designed to isolate a small number of variance features that drive all assets volatilities it decomposes the conditional variance into a short run idiosyncratic component a low order arch process and a long run component the variance factors an empirical example provides evidence that models with very few variance features perform well in capturing the long run common volatilities of the equity components of the dow jones

indirect estimation of large conditionally heteroskedastic factor models with an application to the dow 30 stocks we derive indirect estimators of conditionally heteroskedastic factor models in which the volatilities of common and idiosyncratic factors depend on their past unobserved values by calibrating the score of a kalman filter approximation with inequality constraints on the auxiliary model parameters we also propose alternative indirect estimators for large scale models and explain how to apply our procedures to many other dynamic latent variable models we analyse the small sample behaviour of our indirect estimators and several likelihood based procedures through an extensive monte carlo experiment with empirically realistic designs finally we apply our procedures to weekly returns on the dow 30 stocks

an analysis of the parametrization by data driven local coordinates for multivariable linear systems in this paper we study a novel parametrization for state space systems namely data driven local coordinates ddlc which have recently been introduced and applied even though ddlc has meanwhile become the default parametrization used in the system identification toolbox of the software package matlab an analysis of properties of ddlc which are relevant to identification has not been performed up to now in this paper we provide insights into the geometry and topology of the ddlc construction and show a number of results which are important for actual identification such as maximum likelihood type estimation