an exact test for multiple inequality and equality constraints in the linear regression model abstract in this article we consider the linear regression model y x e where e is n 0 2i in this context we derive exact tests of the form h r r versus k rk for the case in which 2 is unknown we extend these results to consider hypothesis tests of the form h r1 r1 and r2 r2 versus k rk for each of these hypotheses tests we derive several equivalent forms of the test statistics using the duality theory of the quadratic programming for both tests we derive their exact distribution as a weighted sum of snedecor s f distributions normalized by the numerator degrees of freedom of each f distribution of the sum a methodology for computing critical values as well as probability values for the tests is discussed the relationship between this testing framework and the multivariate one sided hypothesis testing literature is also discussed in this context we show that for any size of the hypothesis test h 0 versus k rk the test statistic and critical value obtained a

likelihood ration test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters likelihood ratio test wald test and kuhn tucker test in linear models with inequality constraints on the regression parameters this paper considers the problem of testing statistical hypotheses in linear regression models with inequality constraints on the regression coefficients the kuhn tucker multiplier test statistic is defined and its relationships with the likelihood ratio test and the wald test are examined it is shown in particular that these relationships are the same as in the equality constrained case it is emphasized however that their common asymptotic distribution is a mixture of chi square distributions under the null hypothesis

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

residuated skew lattices abstract skew lattices are one of the most successful non commutative generalizations of lattices motivated by the study of residuation on ordered structures and that of skew boolean algebras and skew heyting algebras in this paper we introduce the concept of residuated skew lattices as a new non commutative version of residuated lattices the axiomatization and localization for residuated skew lattices are obtained moreover a characterization of residuation on skew lattices via adjointness is presented meanwhile three special subvarieties distributive residuated skew lattices skew mtl algebras and skew bl algebras are investigated in particular we show that every skew heyting algebra is a reduct of a special residuated skew lattice

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

cross sectional averages versus principal components in spite of the increased use of factor augmented regressions in recent years little is known regarding the relative merits of the two main approaches to estimation and inference namely the cross sectional average and principal component estimators by providing a formal comparison of the approaches the current paper fills this gap in the literature

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

seasonal integration and cointegration this paper develops tests for roots in linear time series which have a modulus of one but which correspond to seasonal frequencies critical values for the tests are generated by monte carlo methods or are shown to be available from dickey fuller or dickey hasza fuller critical values representations for multivariate processes with combinations of seasonal and zero frequency unit roots are developed leading to a variety of autoregressive and error correction representations the techniques are used to examine cointegration at different frequencies between consumption and income in the u k

projected principal component analysis in factor models this paper introduces a projected principal component analysis projected pca which employees principal component analysis to the projected smoothed data matrix onto a given linear space spanned by covariates when it applies to high dimensional factor analysis the projection removes noise components we show that the unobserved latent factors can be more accurately estimated than the conventional pca if the projection is genuine or more precisely when the factor loading matrices are related to the projected linear space when the dimensionality is large the factors can be estimated accurately even when the sample size is finite we propose a flexible semi parametric factor model which decomposes the factor loading matrix into the component that can be explained by subject specific covariates and the orthogonal residual component the covariates effects on the factor loadings are further modeled by the additive model via sieve approximations by using the newly proposed projected pca the rates of convergence of the smooth factor loading matrices are obtained which are much faster than those of the conventional factor analysis the convergence is achieved even when the sample size is finite and is particularly appealing in the high dimension low sample size situation this leads us to developing nonparametric tests on whether observed covariates have explaining powers on the loadings and whether they fully explain the loadings the proposed method is illustrated by both simulated data and the returns of the components of the s p 500 index

gaussian tests for seasonal unit roots based on cauchy estimation and recursive mean adjustments abstract we propose tests for seasonal unit roots whose limiting null distributions are always standard normal regardless of the period of seasonality and types of mean adjustments the seasonal models of dickey hasza and fuller 1984 journal of american statistical association 79 355 367 dhf and hylleberg engle granger and yoo 1990 journal of econometrics 44 215 238 hegy are considered for estimating parameters related to the seasonal unit roots regressor signs are used as instrumental variables while recursive sample means are used for adjusting the seasonal means in addition to normality of the limiting null distributions in seasonal mean models the recursive mean adjustment provides the new tests with locally higher powers than those of the existing tests of dhf and hegy based on the ordinary least squares estimators if data have a strong linear time trend the recursive mean adjustment is a source of both power gains of some tests for local alternatives and power losses of all tests for other alternatives limiting normality allow evaluation of p values and testing joint significance of subsets of seasonal unit roots

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

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

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

tests for parameter instability and structural change with unknown change point this paper considers tests for parameter instability and structural change with unknown change point the results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures the asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null the tests considered here are shown to have nontrivial asymptotic local power against all alternatives for which the parameters are nonconstant the tests are found to perform quite well in a monte carlo experiment reported elsewhere copyright 1993 by the econometric society

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

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

asymmetry and nonstationarity for a seasonal time series model abstract tests for symmetry and seasonal unit roots are developed for an extended model of hylleberg et al 1990 seasonal integration and cointegration journal econometrics 44 215 238 which can represent both partial seasonal unit roots and threshold effects methods based on ordinary least squares ols estimation and instrumental variable iv estimation are proposed and compared for adjusting mean functions ordinary mean adjustment and recursive mean adjustment are both considered several tests are constructed from various combination of estimation schemes and mean adjustment schemes among the tests the tests based on iv estimation are recommended because they have very simple limiting null distributions and have finite sample power properties comparable to those based on the olse the recommended tests are applied to a us unemployment rate data set and find evidences for both nonstationarities associated with zero frequency and threshold effects

multivariable aumann integrals and controlled wave equations abstract the paper is concerned with the closure convexity and other properties of joint marginal integrals of multifunctions in several independent variables the results are then applied to a controlled wave equation obtaining a bang bang theorem and an existence theorem for optimal distributed controls without the usual convexity assumptions

martingale difference divergence matrix and its application to dimension reduction for stationary multivariate time series in this article we introduce a new methodology to perform dimension reduction for a stationary multivariate time series our method is motivated by the consideration of optimal prediction and focu

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

skew residuated lattices we replace the so called adjointness in the definition of residuated lattice by its strict version where inequalities are replaced by equalities we prove that such structures called skew residuated lattices can be characterized as lattices with certain involutions in principal filters since skew residuated lattices have the cancellation property they are close to divisibility loops introduced by b bosbach in 1988 we show under what condition can skew residuated lattices be represented by such loops

dynamic orthogonal components for multivariate time series we introduce dynamic orthogonal components doc for multivariate time series and propose a procedure for estimating and testing the existence of docs for a given time series we estimate the dynamic orthogonal components via a generalized decorrelation method that minimizes the linear and quadratic dependence across components and across time we then use ljung box type statistics to test the existence of dynamic orthogonal components when docs exist univariate analysis can be applied to build a model for each component those univariate models are then combined to obtain a multivariate model for the original time series we demonstrate the usefulness of dynamic orthogonal components with two real examples and compare the proposed modeling method with other dimension reduction methods available in the literature including principal component and independent component analyses we also prove consistency and asymptotic normality of the proposed estimator under some regularity conditions we provide some

testing against constant factor loading matrix with large panel high frequency data abstract in this paper we introduce a nonparametric test against the constancy of the factor loading matrix of a high dimensional continuous time factor model using high frequency data the central limit theorems on the test statistics with and without perturbation are established under the null hypothesis that the factor loading matrix is constant as time evolves the tests perform well in size and power interestingly the test statistic without perturbation converges at a rate that depends not only on the sample size but also on the dimension through the cross sectional dependence of the residual process which is a distinctive feature that contrasts with the low dimensional setting extensive numerical studies including monte carlo simulations and real data analysis validate the performance of our test

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

a pointwise constrained version of the liapunov convexity theorem for vectorial linear first order control systems we generalize the liapunov convexity theorem s version for vectorial control systems driven by linear odes of first order p 1p 1 in any dimension d nd n by including a pointwise state constraint more precisely given a x wp 1 a b rd solving the convexified p th order differential inclusion lpx t co u0 t u1 t um t a e consider the general problem consisting in finding bang bang solutions i e lpx t u0 t u1 t um t a e under the same boundary data x k a x k a x k b x k b k 0 1 p 1k 0 1 p 1 but restricted moreover by a pointwise state constraint of the type x t x t t a b e g 1 0 0 1 0 0 yielding x 1 t x 1 t previous results in the scalar d 1d 1 case were the pioneering amar cellina paper dealing with lpx x followed by cerf mariconda results who solved the general case of linear differential operators lplp of order p 2p 2 with c0 a b coefficients this paper is dedicated to focus on the missing case p 1p 1 i e using lpx x a x generalize the dimension of x x from the scalar case d 1d 1 to the vectorial d nd n case weaken the coefficients from continuous to integrable so that a a now becomes a d dd d integrable matrix and allow the directional vector to become a moving ac function previous vectorial results had constant no matrix i e a 0a 0 and considered constant control vertices amar mariconda and more recently integrable control vertices ourselves

on non associative generalizations of mv algebras and lattice ordered commutative loops the aim of the paper is to describe the connections between lattice ordered commutative loops and certain basic algebras which are a non associative generalization of mv algebras and are related to commutative semicopulas this extends the well known equivalence between lattice ordered abelian groups with strong order unit and mv algebras

a time series illustration of approximate conditional likelihood summary we consider the calculation of confidence intervals for the correlation parameter based on observations of a large number of short gaussian first order autoregressive processes with different means but common correlation and variance ordinary profile likelihood gives very misleading answers the approximate conditional likelihood of cox reid 1987 is calculated and shown to lead to consistent estimation of the correlation simulations verify that the usual asymptotic properties of the statistics derived from the conditional likelihood are quite satisfactory in this example the approximate conditional likelihood is the same as the marginal likelihood for the standardized residuals although this is not true in general

nonconvex variational problems related to a hyperbolic equation we first prove a new lyapunov type theorem which will yield existence of solutions to nonconvex minimum problems involving some hyperbolic equations on rectangular domains with darboux boundary conditions some problems with obstacle and bang bang results are also considered

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

an instrumental variable approach for panel unit root tests under cross sectional dependence for dynamic panel models with cross sectional dependence several unit root tests are constructed using a huber type instrument whose null asymptotics are standard gaussian and do not depend on nuisance parameters a monte carlo simulation shows that the proposed tests have better sizes and comparable powers relative to other two existing tests developed for cross sectionally dependent dynamic panel models

an instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models the unit root tests of caner and hansen econometrica 69 2001 1555 for asymmetric time series models based on the ordinary least squares estimator olse have asymptotic null distributions that depend on parameters of asymmetry we resolve this parameter dependency by adopting the instrumental variable estimation of shin and lee j business economic statist 19 2001 233 and the recursive mean adjustment of shin and so j time series anal 22 2001b 595 if the threshold parameter is known the limiting null distribution of the proposed wald test does not depend on any nuisance parameter and is chi squared if the threshold parameter is unknown and is estimated from data then under threshold effect the limiting null distributions of the proposed wald tests are chi squared as those for model with known threshold parameter whereas under no threshold effect they are chi squared only conditionally on the weak limit of the estimated threshold parameter our wald tests extend to seasonal models retaining the chi square asymptotics regardless of the parameter of seasonality which is not the case of the olse based tests moreover the proposed tests can be modified into one sided wald tests which are significantly more powerful than the tests of caner and hansen 2001 we apply our method to the monthly us unemployment rate and find some evidences of seasonal unit roots suggesting nonstationarity rather than the strong stationarity of caner and hansen 2001

testing for unit roots in seasonal time series abstract regression estimators of coefficients in seasonal autoregressive models are described the percentiles of the distributions for time series that have unit roots at the seasonal lag are computed by monte carlo integration for finite samples and by analytic techniques and monte carlo integration for the limit case the tabled distributions may be used to test the hypothesis that a time series has a seasonal unit root

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

efficient estimation of heterogeneous coefficients in panel data models with common shocks this paper investigates efficient estimation of heterogeneous coefficients in panel data models with common shocks which have been a particular focus of recent theoretical and empirical literature we propose a new two step method to estimate the heterogeneous coefficients in the first step the maximum likelihood ml method is first conducted to estimate the loadings and idiosyncratic variances the second step estimates the heterogeneous coefficients by using the structural relations implied by the model and replacing the unknown parameters with their ml estimates we establish the asymptotic theory of our estimator including consistency asymptotic representation and limiting distribution the two step estimator is asymptotically efficient in the sense that it has the same limiting distribution as the infeasible generalized least squares gls estimator intensive monte carlo simulations show that the proposed estimator performs robustly in a variety of data setups

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

testing for unit roots in heterogeneous panels abstract this paper proposes unit root tests for dynamic heterogeneous panels based on the mean of individual unit root statistics in particular it proposes a standardized t bar test statistic based on the augmented dickey fuller statistics averaged across the groups under a general setting this statistic is shown to converge in probability to a standard normal variate sequentially with t the time series dimension followed by n the cross sectional dimension a diagonal convergence result with t and n while n t k k being a finite non negative constant is also conjectured in the special case where errors in individual dickey fuller df regressions are serially uncorrelated a modified version of the standardized t bar statistic is shown to be distributed as standard normal as n for a fixed t so long as t 5 in the case of df regressions with intercepts and t 6 in the case of df regressions with intercepts and linear time trends an exact fixed n and t test is also developed using the simple average of the df statistics monte carlo results show that if a large enough lag order is selected for the underlying adf regressions then the small sample performances of the t bar test is reasonably satisfactory and generally better than the test proposed by levin and lin unpublished manuscript university of california san diego 1993

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

bootstrapping factor models with cross sectional dependence abstract we consider bootstrap methods for factor augmented regressions with cross sectional dependence among idiosyncratic errors this is important to capture the bias of the ols estimator derived recently by goncalves and perron 2014 we first show that a common approach of resampling cross sectional vectors over time is invalid in this context because it induces a zero bias we then propose the cross sectional dependent csd bootstrap where bootstrap samples are obtained by taking a random vector and multiplying it by the square root of a consistent estimator of the covariance matrix of the idiosyncratic errors we show that if the covariance matrix estimator is consistent in the spectral norm then the csd bootstrap is consistent and we verify this condition for the thresholding estimator of bickel and levina 2008 finally we apply our new bootstrap procedure to forecasting inflation using convenience yields as recently explored by gospodinov and ng 2013

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

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

the effect of recursive detrending on panel unit root tests this paper analyzes the properties of panel unit root tests based on recursively detrended data the analysis is conducted while allowing for a potentially non linear trend function which represents a more general consideration than the current state of affairs with at most a linear trend a new test statistic is proposed whose asymptotic behavior under the unit root null hypothesis and the simplifying assumptions of a polynomial trend and iid errors are shown to be surprisingly simple indeed the test statistic is not only asymptotically independent of the true trend polynomial but also is in fact unique in that it is independent also of the degree of the fitted polynomial however this invariance property does not carry over to the local alternative under which it is shown that local power is a decreasing function of the trend degree but while power does decrease the rate of shrinking of the local alternative is generally constant in the trend degree which goes against the common belief that the rate of shrinking should be decreasing in the trend degree the above results are based on simplifying assumptions to compensate for this lack of generality a second robust test statistic is proposed whose validity does not require that the trend function is a polynomial or that the errors are iid

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

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

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

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