optimization of structures in frictional contact this paper describes a new approach to optimization of linear elastic structures in frictional contact it uses a novel method to determine an in a specified sense likely equilibrium state of the structure using only the static equilibrium conditions that is no complex dynamic quasi static analyses have to be performed the approach has the advantage that it is not necessary to know the complete load history which is most often unknown for practical problems to illustrate the theory numerical results are given for the optimal design problem of sizing a truss to attain a more uniform normal contact force distribution

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

tests of equal forecast accuracy and encompassing for nested models we examine the asymptotic and finite sample properties of tests for equal forecast accuracy and encompassing applied to 1 step ahead forecasts from nested linear models we first derive the asymptotic distributions of two standard tests and one new test of encompassing and provide tables of asymptotically valid critical values monte carlo methods are then used to evaluate the size and power of tests of equal forecast accuracy and encompassing the simulations indicate that post sample tests can be reasonably well sized of the post sample tests considered the encompassing test proposed in this paper is the most powerful we conclude with an empirical application regarding the predictive content of unemployment for inflation

the three pass regression filter a new approach to forecasting using many predictors we forecast a single time series using many predictor variables with a new estimator called the three pass regression lter 3prf it is calculated in closed form and conveniently represented as a set of ordinary least squares regressions 3prf forecasts converge to the infeasible best forecast when both the time dimension and cross section dimension become large this requires only specifying the number of relevant factors driving the forecast target regardless of the total number of common including potentially irrelevant factors driving the cross section of predictors we derive inferential theory including limiting distributions for estimated relevant factors predictive coefcients and forecasts and provide consistent standard error estimators we explore two empirical applications forecasting macroeconomic aggregates with a large panel of economic indices and forecasting stock market aggregates with many individual assets price dividend ratios these combined with a range of monte carlo experiments demonstrate the 3prf s forecasting power

on the convergence of stationary sequences in topology optimization summary we consider structural topology optimization problems including unilateral constraints arising from non penetration conditions in contact mechanics the resulting non convex non smooth problems are instances of mathematical programs with equilibrium constraints mpec or bi level programs applying nested implicit programming algorithms to this class of problems is problematic owing to the singularity of the feasible set we propose a perturbation strategy combining the relaxation of the equilibrium constraint with the restriction of the design domain to its regular part only this strategy allows us to attack the problem numerically using standard non linear programming algorithms we rigorously study the optimality conditions for the original singular problem as well as the convergence of stationary points and globally optimal solutions to approximating problems towards respective stationary points and globally optimal solutions to the original problem a limited numerical benchmarking of the algorithm is performed copyright 2005 john wiley sons ltd

minimization of maximum unilateral force abstract the paper treats the structural optimization problem of minimizing forces arising from unilateral contact and or non compressive constraints we formulate this design problem as a mathematical program with complementarity constraints and establish some analytical results that pertain to the existence of an optimal design and the first order necessary conditions for such a design we apply three numerical algorithms and compare their performance on several examples the computational result suggest that together these algorithms are well suited for solving this class of structural optimization problems

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

bootstrapping factor augmented regression models abstract this paper proposes and theoretically justifies bootstrap methods for regressions where some of the regressors are factors estimated from a large panel of data we derive our results under the assumption that t n c where 0 c n and t are the cross sectional and the time series dimensions respectively thus allowing for the possibility that the factor estimation error enters the limiting distribution of the ols estimator as an asymptotic bias term as was recently discussed by ludvigson and ng 2011 we consider general residual based bootstrap methods and provide a set of high level conditions on the bootstrap residuals and on the idiosyncratic errors such that the bootstrap distribution of a rotated ols estimator is consistent we subsequently verify these conditions for a simple wild bootstrap residual based procedure

asymptotics for out of sample tests of granger causality abstract this paper presents analytical monte carlo and empirical evidence concerning out of sample tests of granger causality the environment is one in which the relative predictive ability of two nested parametric regression models is of interest results are provided for three statistics a regression based statistic suggested by granger and newbold 1977 forecasting economic time series academic press inc london a t type statistic comparable to those suggested by diebold and mariano 1995 comparing predictive accuracy journal of business and economic statistics 13 253 263 and west 1996 asymptotic inference about predictive ability econometrica 64 1067 1084 and an f type statistic akin to theil s u since the asymptotic distributions under the null are nonstandard tables of asymptotically valid critical values are provided monte carlo evidence supports the theoretical results an empirical example evaluates the predictive content of the chicago fed national activity index for growth in industrial production and core pce based inflation

forecasting with factor augmented regression a frequentist model averaging approach abstract this paper considers forecast combination with factor augmented regression in this framework a large number of forecasting models are available varying by the choice of factors and the number of lags we investigate forecast combination across models using weights that minimize the mallows and the leave h out cross validation criteria the unobserved factor regressors are estimated by principle components of a large panel with n predictors over t periods with these generated regressors we show that the mallows and leave h out cross validation criteria are asymptotically unbiased estimators of the one step ahead and multi step ahead mean squared forecast errors respectively provided that n t however the paper does not establish any optimality properties for the methods in contrast to well known results in the literature this result suggests that the generated regressor issue can be ignored for forecast combination without restrictions on the relation between n and t simulations show that the mallows model averaging and leave h out cross validation averaging methods yield lower mean squared forecast errors than alternative model selection and averaging methods such as aic bic cross validation and bayesian model averaging we apply the proposed methods to the us macroeconomic data set in stock and watson 2012 and find that they compare favorably to many popular shrinkage type forecasting methods

formulation and comparison of algorithms for frictional contact problems this paper presents two algorithms for solving the discrete quasi static small displacement linear elastic contact problem with coulomb friction the algorithms are adoptions of a newton method for solving b differentiable equations and an interior point method for solving smooth constrained equations for the application of the former method the contact problem is formulated as a system of b differentiable equations involving the projection operator onto sets with simple structure for the application of the latter method the contact problem is formulated as a system of smooth equations involving complementarity conditions and with the non negativity of variables treated as constraints the two algorithms are numerically tested for two dimensional problems containing up to 100 contact nodes and up to 100 time increments results show that at the present stage of development the newton method is superior both in robustness and speed additional comparison is made with a commercial finite element code

equivalence between out of sample forecast comparisons and wald statistics we demonstrate the equivalence between a commonly used out of sample test of equal predictive accuracy and the dierence between two wald statistics this equivalence greatly simplies the computational burden of calculating recursive out of sample tests and evaluating their critical values next we show that the limit distribution which has previously been expressed through stochastic integrals has a simple representation in terms of 2 distributed random variables and we derive the density of the limit distribution we also generalize the limit theory to cover local alternatives and characterize the power properties of the test our results shed new light on the test and establish certain weaknesses associated with using out of sample forecast comparison tests to conduct inference about nested regression models

the method of moving asymptotes a new method for structural optimization a new method for non linear programming in general and structural optimization in particular is presented in each step of the iterative process a strictly convex approximating subproblem is generated and solved the generation of these subproblems is controlled by so called moving asymptotes which may both stabilize and speed up the convergence of the general process

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

tests of equal accuracy for nested models with estimated factors abstract in this paper we develop asymptotics for tests of equal predictive ability between nested models when factor augmented regressions are used to forecast we provide conditions under which the estimation of the factors does not affect the asymptotic distributions developed in clark and mccracken 2001 and mccracken 2007 this enables researchers to use the existing tabulated critical values when conducting inference despite the presence of estimated predictors as an intermediate result we derive the asymptotic properties of the principal components estimator over recursive windows we provide simulation evidence on the finite sample effects of factor estimation and apply the tests to the case of forecasting excess returns to the s p 500 composite index

confidence intervals for diffusion index forecasts and inference for factor augmented regressions we consider the situation when there is a large number of series n e ach witht observations and each series has some predictive ability for some variable of interest a methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors in this paper we show that the least squares estimates obtained from these factor augmented regressions are t consistent and asymptotically normal if t n 0 the conditional mean predicted by the estimated factors is min t n consistent and asymptotically normal except when t n goes to zero inference should take into account the effect of estimated regressors on the estimated conditional mean we present analytical formulas for prediction intervals that are valid regardless of the magnitude of n t and that can also be used when the factors are nonstationary

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