on error estimates of the penalty method for unsteady navier stokes equations the penalty method has been widely used for numerical computations of the unsteady navier stokes equations however the best error estimates available to the author s knowledge were not optimal an

distribution theory for the studentized mean for long short and negative memory time series abstract we consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory short memory negative intermediate memory or is the first difference of such a process the rate of growth of this variance depends crucially on the type of memory and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically we also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size extending known results to the case of flat top tapers we adopt the fixed proportion bandwidth perspective in our empirical section presenting two methods for estimating the limiting critical values both the subsampling method and a plug in approach simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean both methods perform well although the subsampling method appears to be better sized and provide a viable framework for conducting inference for the mean in summary we supply a unified asymptotic theory that covers all different types of memory under a single umbrella

testing optimal kernel choice in har inference abstract the paper investigates the optimal kernel choice in heteroskedasticity and autocorrelation robust tests based on the fixed b asymptotics in parallel with the optimality of the quadratic spectral kernel under the asymptotic mean squared error criterion of the point estimator of the long run variance as considered in andrews 1991 we show that the optimality of the quadratic spectral kernel continues to hold under the testing oriented criterion of sun philips and jin 2008 which takes a weighted average of the probabilities of type i and type ii errors of the fixed b asymptotic test

the error in rejection probability of simple autocorrelation robust tests a new class of autocorrelation robust test statistics is introduced the class of tests generalizes the kiefer vogelsang and bunzel 2000 test in a manner analogous to anderson and darling s 1952 generalization of the cramer von mises goodness of fit test in a gaussian location model the error in rejection probability of the new tests is found to be o t 1 log t where t denotes the sample size

asymptotic f and t tests in an efficient gmm setting abstract this paper considers two step efficient gmm estimation and inference where the weighting matrix and asymptotic variance matrix are based on the series long run variance estimator we propose a simple and easy to implement modification to the trinity of test statistics in the two step efficient gmm setting and show that the modified test statistics are all asymptotically f distributed under the so called fixed smoothing asymptotics the modification is multiplicative and involves the j statistic for testing over identifying restrictions this leads to convenient asymptotic f tests whose critical values i e the standard f critical values are readily available from standard statistical tables and programming environments for testing a single restriction with a one sided alternative an asymptotic t test theory using the standard t distribution as the reference distribution is also developed

robust adaptive rate optimal testing for the white noise hypothesis abstract a new test is proposed for the weak white noise null hypothesis the test is based on a new automatic selection of the order for a box pierce 1970 test statistic or the test statistic of hong 1996 the heteroskedasticity and autocorrelation consistent hac critical values from lee 2007 are used allowing for estimation of the error term the data driven order selection is tailored to detect a new class of alternatives with autocorrelation coefficients which can be o n 1 2 provided there are sufficiently many of such coefficients a simulation experiment illustrates the good statistical properties of the test both under the weak white noise null and the alternative

nature of singularities for analyticity domains of invariant curves we present theoretical arguments based on infinite dimensional bifurcation theory and numerical evidence based on nonperturbative methods that the boundaries of analyticity of invariant curves can be described as an accumulation of branch points which are typically of order 2 we show how this fact would explain previous numerical results of several authors and how it suggests more efficient numerical algorithms which we implement

simple and powerful gmm over identification tests with accurate size abstract based on the series long run variance estimator we propose a new class of over identification tests that are robust to heteroscedasticity and autocorrelation of unknown forms we show that when the number of terms used in the series long run variance estimator is fixed the conventional j statistic after a simple correction is asymptotically f distributed we apply the idea of the f approximation to the conventional kernel based j tests simulations show that the j tests based on the finite sample corrected j statistic and the f approximation have virtually no size distortion and yet are as powerful as the standard j tests

fixed smoothing asymptotics for time series 1 in this paper we derive higher order edgeworth expansions for the finite sample distributions of the subsampling based t statistic and the wald statistic in the gaussian location model under the so called fixed smoothing paradigm in particular we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions the results are used to justify the second order correctness of a new bootstrap method the gaussian dependent bootstrap in the context of gaussian location model 1 introduction many economic and financial applications involve time series data with autocorrelation and heteroskedasticity properties often the unknown dependence structure is not the chief object of interest but the inference on the parameter of interest involves the estimation of unknown dependence in stationary time series models estimated by generalized method of moments gmm robust inference is typically accomplished by consistently estimating the asymptotic covariance matrix which is proportional to the long run variance lrv matrix of the estimating equations or moment conditions defining the estimator using a kernel smoothing method in the econometrics and statistics literature the bandwidth parameter truncation lag involved in the kernel smoothing method is assumed to grow slowly with sample size in order to achieve consistency the inference is conducted by plugging in a covariance matrix estimator that is consistent under heteroskedasticity and autocorrelation this approach dates back to newey and west 25 and andrews 1 recently kiefer and vogelsang 13 kv hereafter developed an alternative first order asymptotic theory for the hac heteroskedasticity and autocorrelation consistent based robust inference where the proportion of the bandwidth involved in the hac estimator to the sample size t denoted as b is held fixed in the asymptotics under the fixed b asymptotics the hac estimator converges to a nondegenerate yet nonstandard limiting distribution the tests based on the fi xed b asymptotic approximation were shown to enjoy better finite sample properties than the tests based on the small b asymptotic theory

a simple and trustworthy asymptotic t test in difference in differences regressions abstract we propose an asymptotically valid t test that uses student s t distribution as the reference distribution in a difference in differences regression for the asymptotic variance estimation we adopt the clustering by time approach to accommodate cross sectional dependence this approach often assumes the clusters to be independent across time but we allow them to be temporally dependent the proposed t test is based on a special heteroscedasticity and autocorrelation robust har variance estimator we target the type i and type ii errors and develop a testing oriented method to select the underlying smoothing parameter by capturing the estimation uncertainty of the har variance estimator the t test has more accurate size than the corresponding normal test and is just as powerful as the latter compared to the nonstandard test developed in the literature the standard t test is just as accurate but much more convenient to use model based and empirical data based monte carlo simulations show that the t test works quite well in finite samples

on error estimates of some higher order projection and penalty projection methods for navier stokes equations this paper is a continuation of our previous work 10 on projection methods we study first existing higher order projection schemes in the semidiscretized form for the navier stokes equations one error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent neumann boundary condition satisfied by the pressure approximations we then propose a penalty projection scheme for which we obtain improved error estimates

choosing instrumental variables in conditional moment restriction models properties of gmm estimators are sensitive to the choice of instrument using many instruments leads to high asymptotic asymptotic efficiency but can cause high bias and or variance in small samples in this paper we develop and implement asymptotic mean square error mse based criteria for instrument selection in estimation of conditional moment restriction models the models we consider include various nonlinear simultaneous equations models with unknown heteroskedasticity we develop moment selection criteria for the familiar two step optimal gmm estimator gmm a bias corrected version and generalized empirical likelihood estimators gel that include the continuous updating estimator cue as a special case we also find that the cue has lower higher order variance than the bias corrected gmm estimator and that the higher order efficiency of other gel estimators depends on conditional kurtosis of the moments

sieve semiparametric two step gmm under weak dependence this paper considers semiparametric two step gmm estimation and inference with weakly dependent data where unknown nuisance functions are estimated via sieve extremum estimation in the first step we show that although the asymptotic variance of the second step gmm estimator may not have a closed form expression it can be well approximated by sieve variances that have simple closed form expressions we present consistent or robust variance estimation wald tests and hansen s 1982 over identification tests for the second step gmm that properly reflect the first step estimated functions and the weak dependence of the data our sieve semiparametric two step gmm inference procedures are shown to be numerically equivalent to the ones computed as if the first step were parametric a new consistent random perturbation estimator of the derivative of the expectation of the non smooth moment function is also provided

a nonstandard empirical likelihood for time series standard blockwise empirical likelihood bel for stationary weakly dependent time series requires specifying a fixed block length as a tuning parameter for setting confidence regions this aspect can be difficult and impacts coverage accuracy as an alternative this paper proposes a new version of bel based on a simple though non standard data blocking rule which uses a data block of every possible length consequently the method involves no block selection and is also anticipated to exhibit better coverage performance its non standard blocking scheme however induces non standard asymptotics and requires a significantly different development compared to standard bel we establish the large sample distribution of log ratio statistics from the new bel method for calibrating confidence regions for mean or smooth function parameters of time series this limit law is not the usual chi square one but is distribution free and can be reproduced through straightforward simulations numerical studies indicate that the proposed method generally exhibits better coverage accuracy than standard bel

spatial heteroskedasticity and autocorrelation consistent estimation of covariance matrix this paper considers spatial heteroskedasticity and autocorrelation consistent spatial hac estimation of covariance matrices of parameter estimators we generalize the spatial hac estimator introduced by kelejian and prucha 2007 to apply to linear and nonlinear spatial models with moment conditions we establish its consistency rate of convergence and asymptotic truncated mean squared error mse based on the asymptotic truncated mse criterion we derive the optimal bandwidth parameter and suggest its data dependent estimation procedure using a parametric plug in method the finite sample performances of the spatial hac estimator are evaluated via monte carlo simulation

singularities of periodic orbits near invariant curves abstract we show numerically for standard like maps how the singularities in the complex parameter of the function which conjugates the map to a rotation of rational period behave when the period goes to an irrational number furthermore we propose a numerical method to extrapolate the radius of convergence of the series parametrizing the solution of periodic orbits the results are compared with analyses performed by pade approximants greene s method root criterion and the prediction by renormalization theory

fixed smoothing asymptotics in a two step generalized method of moments framework fixed smoothing asymptotics this paper develops the fixed smoothing asymptotics in a two step generalized method of moments gmm framework under this type of asymptotics the weighting matrix in the second step gmm criterion function converges weakly to a random matrix and the two step gmm estimator is asymptotically mixed normal nevertheless the wald statistic the gmm criterion function statistic and the lagrange multiplier statistic remain asymptotically pivotal it is shown that critical values from the fixed smoothing asymptotic distribution are high order correct under the conventional increasing smoothing asymptotics when an orthonormal series covariance estimator is used the critical values can be approximated very well by the quantiles of a noncentral f distribution a simulation study shows that statistical tests based on the new fixed smoothing approximation are much more accurate in size than existing tests

fixed b subsampling and the block bootstrap improved confidence sets based on p value calibration summary subsampling and block based bootstrap methods have been used in a wide range of inference problems for time series to accommodate the dependence these resampling methods involve a bandwidth parameter such as the subsampling window width and block size in the block based bootstrap in empirical work using different bandwidth parameters could lead to different inference results but traditional first order asymptotic theory does not capture the choice of the bandwidth we propose to adopt the fixed b approach as advocated by kiefer and vogelsang in the heteroscedasticity auto correlation robust testing context to account for the influence of the bandwidth on inference under the fixed b asymptotic framework we derive the asymptotic null distribution of the p values for subsampling and the moving block bootstrap and further propose a calibration of the traditional small b based confidence intervals regions or bands and tests our treatment is fairly general as it includes both finite dimensional parameters and infinite dimensional parameters such as the marginal distribution function simulation results show that the fixed b approach is more accurate than the traditional small b approach in terms of approximating the finite sample distribution and that the calibrated confidence sets tend to have smaller coverage errors than the uncalibrated counterparts

fixed smoothing asymptotics in the generalized empirical likelihood estimation framework this paper concerns the fixed smoothing asymptotics for two commonly used estimators in the generalized empirical likelihood estimation framework for time series data namely the continuous updating estimator and the maximum blockwise empirical likelihood estimator for continuously updating generalized method of moments gmm estimator we show that the results for the two step gmm estimator in sun 2014a continue to hold under suitable assumptions for continuous updating estimator obtained through solving a saddle point problem newey and smith 2004 and the maximum blockwise empirical likelihood estimator kitamura 1997 we show that their fixed smoothing asymptotic distributions up to an unknown linear transformation are mixed normal based on these results we derive the asymptotic distributions of the specification tests including the over identification testing and testing on parameters under the fixed smoothing asymptotics where the corresponding limiting distributions are nonstandard yet pivotal simulation studies show that i the fixed smoothing asymptotics provides better approximation to the sampling distributions of the continuous updating estimator and the maximum blockwise empirical likelihood estimator as compared to the standard normal approximation the testing procedures based on the fixed smoothing critical values are more accurate in size than the conventional chi square based tests ii the continuously updating gmm estimator is asymptotically more efficient and the corresponding specification tests are generally more powerful than the other two competitors finite sample results from an empirical data analysis are also reported

improved quantile inference via fixed smoothing asymptotics and edgeworth expansion to estimate a sample quantile s variance the quantile spacing method involves smoothing parameter m when m n the corresponding studentized test statistic is asymptotically n 0 1 holding m fixed instead the asymptotic distribution contains the edgeworth expansion term capturing the variance of the quantile spacing consequently the fixed m distribution is more accurate than the standard normal under both asymptotic frameworks a testing optimal m is proposed to maximize power subject to size control in simulations the new method controls size better than similar methods while maintaining good power throughout are results for two sample quantile treatment effect inference code is available online

spectral density and spectral distribution inference for long memory time series via fixed b asymptotics this paper studies taper based estimates of the spectral density utilizing a fixed bandwidth ratio asymptotic framework and makes several theoretical contributions i we treat multiple frequencies jointly ii we allow for long range dependence or anti persistence at differing frequencies iii we allow for tapers that are only piecewise smooth or discontinuous including flat top and truncation tapers iv we study higher order accuracy through the limit distribution s laplace transform v we develop a taper based estimation theory for the spectral distribution and show how confidence bands can be constructed simulation results produce quantiles and document the finite sample size properties of the estimators and a few empirical applications demonstrate the utility of the new methods

natural boundaries for area preserving twist maps we consider kam invariant curves for generalizations of the standard map of the form x y x y y f x wheref x is an odd trigonometric polynomial we study numerically their analytic properties by a pade approximant method applied to the function which conjugates the dynamics to a rotation in the complex plane natural boundaries of different shapes are found in the complex plane the analyticity region appears to be a strip bounded by a natural boundary whose width tends linearly to 0 as tends to the critical value

computation of domains of analyticity for some perturbative expansions of mechanics abstract we compute the domain of analyticity of some perturbative expansions for invariant circles appearing in mechanics we use pade approximants for the perturbative expansions and introduce methods to ascertain their domain of convergence we also use non perturbative methods based on direct computation of the invariant circles and in analogy with greene s criterion approximation by circles with rational rotation we find that the domains computed by all the methods agree within the limits of accuracy we also study rigorously the nature of the singularities when the frequency is rational

finite element approximation of the nonstationary navier stokes problem i regularity of solutions and second order error estimates for spatial discretization this is the first part of a work dealing with the rigorous error analysis of finite element solutions of the nonstationary navier stokes equations second order error estimates are proven for spatial discretization using conforming or nonconforming elements the results indicate a fluid like behavior of the approximations even in the case of large data so long as the solution remains regular the analysis is based on sharp a priori estimates for the solution particularly reflecting its behavior as t to 0 and as t to infty it is shown that the regularity customarily assumed in the error analysis for corresponding parabolic problems cannot be realistically assumed in the case of the navier stokes equations as it depends on nonlocal compatibility conditions for the data the results which are presented here are independent of such compatibility conditions which cannot be verified in practice

penalty finite element method for stokes problem with nonlinear slip boundary conditions abstract the penalty finite element method for stokes problem with nonlinear slip boundary conditions based on the finite element subspace v h m h which satisfies the discrete inf sup condition is investigated in this paper since this class of nonlinear slip boundary conditions include the subdifferential property the weak variational formulation associated with stokes problem is variational inequality under some regularity assumptions we obtain the optimal h 1 and l 2 error estimates between u and u h and between u and u h e where the error orders are e h for h 1 error and e h 2 for l 2 error

inference with dependent data using cluster covariance estimators this paper presents a novel way to conduct inference using dependent data in time series spatial and panel data applications our method involves constructing t and wald statistics utilizing a cluster covariance matrix estimator cce we then use an approximation that takes the number of clusters groups as xed and the number of observations per group to be large and calcu late limiting distributions of the t and wald statistics this approximation is analogous to xed b asymptotics of kiefer and vogelsang 2002 2005 kv for heteroskedasticity and autocorrelation consistent inference but in our case yields standard t and f distributions where the number of groups essentially plays the role of sample size we provide simulation evidence that demonstrates our procedure outperforms conventional inference procedures and performs comparably to kv

heteroskedasticity autocorrelation and spatial correlation robust inference in linear panel models with fixed effects abstract this paper develops an asymptotic theory for test statistics in linear panel models that are robust to heteroskedasticity autocorrelation and or spatial correlation two classes of standard errors are analyzed both are based on nonparametric heteroskedasticity autocorrelation hac covariance matrix estimators the first class is based on averages of hac estimators across individuals in the cross section i e averages of hacs this class includes the well known cluster standard errors analyzed by arellano 1987 as a special case the second class is based on the hac of cross section averages and was proposed by driscoll and kraay 1998 the hac of averages standard errors are robust to heteroskedasticity serial correlation and spatial correlation but weak dependence in the time dimension is required the averages of hacs standard errors are robust to heteroskedasticity and serial correlation including the nonstationary case but they are not valid in the presence of spatial correlation the main contribution of the paper is to develop a fixed b asymptotic theory for statistics based on both classes of standard errors in models with individual and possibly time fixed effects dummy variables the asymptotics is carried out for large time sample sizes for both fixed and large cross section sample sizes extensive simulations show that the fixed b approximation is usually much better than the traditional normal or chi square approximation especially for the driscoll kraay standard errors the use of fixed b critical values will lead to more reliable inference in practice especially for tests of joint hypotheses

inference in time series models using smoothed clustered standard errors abstract this paper proposes a long run variance estimator for conducting inference in time series regression models that combines the nonparametric approach with a cluster approach the basic idea is to divide the time periods into non overlapping clusters the long run variance estimator is constructed by first aggregating within clusters and then kernel smoothing across clusters or applying the nonparametric series method to the clusters with type ii discrete cosine transform we develop an asymptotic theory for test statistics based on these smoothed clustered long run variance estimators we derive asymptotic results holding the number of clusters fixed and also treating the number of clusters as increasing with the sample size for the kernel smoothing approach these two asymptotic limits are different whereas for the cosine series approach the two limits are the same when clustering before kernel smoothing we find that the fixed number of clusters asymptotic approximation works well whether the number of clusters is small or large finite sample simulations suggest that the naive i i d bootstrap mimics the fixed number of clusters critical values the simulations also suggest that clustering before kernel smoothing can reduce over rejections caused by strong serial correlation at a cost of power when there is a natural way of clustering clustering can reduce over rejection problems and achieve small gains in power for the kernel approach in contrast the cosine series approach does not benefit from clustering

should we go one step further an accurate comparison of one step and two step procedures in a generalized method of moments framework abstract according to conventional asymptotic theory the two step generalized method of moments gmm estimator and test perform at least as well as the one step estimator and test in large samples the conventional asymptotic theory completely ignores the estimation uncertainty in the weighting matrix and as a result it may not reflect finite sample situations well in this paper we employ the more accurate fixed smoothing asymptotic framework to compare the performances of the one step and two step procedures we show that the two step procedures outperform the one step procedures only when the squared long run canonical correlation coefficients between two blocks of transformed moment conditions are larger than the thresholds established in this paper the thresholds depend on the criteria of interest a monte carlo study lends support to our asymptotic results

construction of analytic kam surfaces and effective stability bounds a class of analytic possibly time dependent hamiltonian systems withd degrees of freedom and the corresponding class of area preserving twist diffeomorphisms of the plane are considered implementing a recent scheme due to moser salamon and zehnder we provide a method that allows us to construct explicitly kam surfaces and hence to give lower bounds on their breakdown thresholds we then apply this method to the hamiltonianh y2 2 e cosx cos x t and to the map y x y e sinx x y e sinx obtaining with the aid of computer assisted estimations explicit approximations within an error of 10 5 of the golden mean kam surfaces for complex values of e with e less or equal than respectively 0 015 and 0 65 the experimental numerical values at which such surfaces are expected to disappear are about respectively 0 027 and 0 97 a possible connection between break down thresholds and singularities in the complex e plane is pointed out

simple robust testing of regression hypotheses in this paper we consider the problem of hypothesis testing in models with errors that have serial correlation or heteroskedasticity of unknown form this situation is often encountered in regression models applied to economic time series data it is a classic textbook result that while ordinary least squares ols estimates of regression parameters remain consistent and asymptotically normal when errors are heteroskedastic or autocorrelated provided usual regularity conditions hold and no lagged dependent variables are in the model standard tests are no longer valid if the true form of serial correlation heteroskedasticity were known then generalized least squares gls provides efficient estimates and standard inference can be conducted on the gls transformed model but in practice the form of serial correlation heteroskedasticity is often unknown and this has led to the development of techniques that permit valid asymptotic inference without having to specify a model of the serial correlation or heteroskedasticity the most common approach is to estimate the variance covariance matrix of the ols estimates nonparametrically using spectral methods heteroskedasticity and autocorrelation consistent hac estimators and construct standard tests using the asymptotic normality of the ols estimates hac estimators have been extensively analyzed in the econometrics literature and important contributions are given by andrews 1991 andrews and monahan 1992 gallant 1987 hansen 1992 newey and west 1987 robinson 1991 1998 and white 1984 among others the benefit of hac estimator tests is asymptotically valid inference that is robust to general forms of serial correlation heteroskedasticity in the errors we propose an alternative method of constructing robust test statistics we apply a nonsingular data dependent stochastic transformation to the ols estimates the asymptotic distribution of the transformed estimates does not depend on nuisance parameters then test statistics that are asymptotically invariant to nuisance parameters asymptotic pivotal statistics are constructed the resulting test statistics have nonstandard asymptotic distributions that only depend on the number of restrictions being tested and critical values are easy to simulate using standard techniques the main advantage of our approach compared to standard approaches is that estimates of the variance covariance matrix are not explicitly required to construct the tests this is potentially important for two reasons first with the exception of the estimator proposed by robinson 1998 2 consistent nonparametric estimates of variance covariance matrices in models with serial

asymptotic f tests under possibly weak identification abstract this paper develops asymptotic f tests robust to weak identification and temporal dependence the test statistics we focus on are modified versions of the s statistic of stock and wright 2000 and the k statistic of kleibergen 2005 in the former case the modification involves only a multiplicative degree of freedom adjustment and the modified s statistic is asymptotically f distributed under fixed smoothing asymptotics regardless of the strength of the model identification in the latter case the modification involves an additional multiplicative adjustment that uses a j statistic for testing overidentification we show that the modified k statistic is asymptotically f distributed when the model parameters are completely unidentified or nearly weakly identified when the model parameters are weakly identified the f approximation for the k statistic can be justified under the conventional asymptotics the f approximations account for the estimation errors in the underlying heteroskedasticity and autocorrelation robust variance estimators which the chi squared approximations ignore monte carlo simulations show that the f approximations are much more accurate than the corresponding chi squared approximations in finite samples

on error estimates of projection methods for navier stokes equations first order schemes in this paper projection methods or fractional step methods are studied in the semi discretized form for the navier stokes equations in a two or three dimensional bounded domain error estimates for the velocity and the pressure of the classical projection scheme are established via the energy method a modified projection scheme which leads to improved error estimates is also proposed

finite element approximations of the nonstationary navier stokes problem part iv error estimates for second order time discretization this paper provides an error analysis for the crank nicolson method of time discretization applied to spatially discrete galerkin approximations of the nonstationary navier stokes equations second order error estimates are proven locally in time under realistic assumptions about the regularity of the solution for approximations of an exponentially stable solution these local error estimates are extended uniformly in time as text t to infty

testing for stationarity at high frequency abstract the high frequency behavior of the kpss test which is most commonly used to test for stationarity is analyzed in a continuous time framework our asymptotics show that the test has no discriminatory power at high frequency it either always rejects stationarity or has no nontrivial power at high frequency the test becomes valid at high frequency only when the bandwidth of its long run variance estimate is chosen suitably in our framework we also analyze the residual based kpss test for cointegration

testing for smooth structural changes in time series models via nonparametric regression checking parameter stability of econometric models is a long standing problem almost all existing structural change tests in econometrics are designed to detect abrupt breaks little attention has been paid to smooth structural changes which may be more realistic in economics we propose a consistent test for smooth structural changes as well as abrupt structural breaks with known or unknown change points the idea is to estimate smooth time varying parameters by local smoothing and compare the fitted values of the restricted constant parameter model and the unrestricted time varying parameter model the test is asymptotically pivotal and does not require prior information about the alternative a simulation study highlights the merits of the proposed test relative to a variety of popular tests for structural changes in an application we strongly reject the stability of univariate and multivariate stock return prediction models in the postwar and post oil shocks periods

the cross quantilogram measuring quantile dependence and testing directional predictability between time series this paper proposes the cross quantilogram to measure the quantile dependence between two time series we apply it to test the hypothesis that one time series has no directional predictability to another time series we establish the asymptotic distribution of the cross quantilogram and the corresponding test statistic the limiting distributions depend on nuisance parameters to construct consistent confidence intervals we employ the stationary bootstrap procedure we show the consistency of this bootstrap also we consider the self normalized approach which is shown to be asymptotically pivotal under the null hypothesis of no predictability we provide simulation studies and two empirical applications first we use the cross quantilogram to detect predictability from stock variance to excess stock return compared to existing tools used in the literature of stock return predictability our method provides a more complete relationship between a predictor and stock return second we investigate the systemic risk of individual financial institutions such as jp morgan chase goldman sachs and aig this article has supplementary materials online

optimal bandwidth selection in heteroskedasticity autocorrelation robust testing the paper considers studentized tests in time series regressions with nonparametrically autocorrelated errors the studentization is based on robust standard errors with truncation lag m bt for some constant b 2 0 1 and sample size t it is shown that the nonstandard xed b limit distributions of such nonparametrically studentized tests provide more accurate approximations to the nite sample distributions than the standard small b limit distribution we further show that for typical economic time series the optimal bandwidth that minimizes a weighted average of type i and type ii errors is larger by an order of magnitude than the bandwidth that minimizes the asymptotic mean squared error of the corresponding long run variance estimator a plug in procedure for implementing this optimal bandwidth is suggested and simulations not reported here con rm that the new plug in procedure works well in nite samples

analysis of locally stabilized mixed finite element methods for the stokes problem in this paper a locally stabilized finite element formulation of the stokes problem is analyzed a macroelement condition which is sufficient for the stability of locally stabilized mixed methods based on a piecewise constant pressure approximation is introduced by satisfying this condition the stability of the qi po quadrilateral and the pi po triangular element can be established

heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects abstract this paper studies robust inference for linear panel models with fixed effects in the presence of heteroskedasticity and spatiotemporal dependence of unknown forms we propose a bivariate kernel covariance estimator that nests existing estimators as special cases our estimator improves upon existing estimators in terms of robustness efficiency and adaptiveness for distributional approximations we considered two types of asymptotics the increasing smoothing asymptotics and the fixed smoothing asymptotics under the former asymptotics the wald statistic based on our covariance estimator converges to a chi square distribution under the latter asymptotics the wald statistic is asymptotically equivalent to a distribution that can be well approximated by an f distribution simulation results show that our proposed testing procedure works well in finite samples

a two level method with backtracking for the navier stokes equations we consider a two level method for resolving the nonlinearity in finite element approximations of the equilibrium navier stokes equations the method yields l2 and h1 optimal velocity approximations and an l2 optimal pressure approximation the two level method involves solving one small nonlinear coarse mesh system one oseen problem hence linear with positive definite symmetric part on the fine mesh and one linear correction problem on the coarse mesh the algorithm we study produces an approximate solution with the optimal asymptotic in h accuracy for any fixed reynolds number we do not consider the behavior of the error for fixed h as re rightarrow infty i e for flows in transition to turbulence

inference for linear models with dependent errors summary the paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors theoretically we obtain asymptotic normality for the m estimator of the regression parameter under mild conditions and establish a uniform bahadur representation for recursive m estimators methodologically we extend the recently proposed self normalized approach of shao from stationary time series to the regression set up where the sequence of response variables is typically non stationary in mean since the limiting distribution of the self normalized statistic depends on the design matrix and its corresponding critical values are case dependent we develop a simulation based approach to approximate the critical values consistently through a simulation study we demonstrate favourable finite sample performance of our method in comparison with a block bootstrap based approach empirical illustrations using two real data sets are also provided

optimal error estimate of the penalty finite element method for the time dependent navier stokes equations a fully discrete penalty finite element method is presented for the two dimensional time dependent navier stokes equations the time discretization of the penalty navier stokes equations is based on the backward euler scheme the spatial discretization of the time discretized penalty navier stokes equations is based on a finite element space pair x h m h which satisfies some approximate assumption an optimal error estimate of the numerical velocity and pressure is provided for the fully discrete penalty finite element method when the parameters e at and h are sufficiently small

estimation of longrun variance of continuous time stochastic process using discrete sample abstract this paper develops the methodology and asymptotic theory for the estimation of longrun variance of continuous time process we analyze the asymptotic bias and variance of the longrun variance estimator in continuous time and provide the optimal bandwidth balancing them off and minimizing the asymptotic mean squared error in the paper we present not only how to consistently estimate the longrun variance of continuous time process but also how to choose bandwidth optimally with data dependent procedures using discrete samples our framework is also useful to analyze the high frequency behaviors of usual longrun variance estimators for discrete time series in particular we show that they all diverge to infinity as the sampling frequency increases the relevance and usefulness of our continuous time framework and asymptotic theory are demonstrated by illustration and simulation

iterative methods in penalty finite element discretization for the steady mhd equations this paper characterizes one penalty finite element method for the incompressible mhd equations the method is an interesting combination of the classic iterative schemes stokes newton and oseen iterations with two different finite element pairs p1b p1 p1b and p1 p0 p1 moreover the rigorous analysis of stability and error estimate for the proposed methods are given finally the applicability and effectiveness of the presented schemes are illustrated in several numerical experiments

controlling the size of autocorrelation robust tests autocorrelation robust tests are notorious for suffering from size distortions and power problems we investigate under which conditions the size of autocorrelation robust tests can be controlled by an appropriate choice of critical value

two level penalty finite element methods for the stationary incompressible magnetohydrodynamics problem in the paper we consider the penalty finite element method for the stationary incompressible magnetohydrodynamics mhd problem with a factor of penalty parameter stability and convergence of numerical solutions are established furthermore two level penalty methods are also developed for the mhd problem our methods consist of solving a nonlinear mhd problem by the usual penalty method on a coarse mesh with mesh size h and then a linearized mhd problem based on the stokes newton and oseen iterations on a fine mesh is solved by the penalty method with mesh size h h h respectively stability and error estimates of numerical solutions in two level penalty methods are presented finally some numerical tests are provided to demonstrate the effectiveness of the developed algorithms

a fixed bandwidth view of the pre asymptotic inference for kernel smoothing with time series data this paper develops robust testing procedures for nonparametric kernel methods in the presence of temporal dependence of unknown forms based on the xed bandwidth asymptotic variance and the pre asymptotic variance we propose a heteroskedasticity and autocorrelation robust har variance estimator that achieves double robustness it is asymptotically valid regardless of whether the temporal dependence is present or not and whether the kernel smoothing bandwidth is held constant or allowed to decay with the sample size using the har variance estimator we construct the studentized test statistic and examine its asymptotic properties under both the xed smoothing and increasing smoothing asymptotics the xed smoothing approximation and the associated convenient t approximation achieve extra robustness it is asymptotically valid regardless of whether the truncation lag parameter governing the covariance weighting grows at the same rate as or a slower rate than the sample size finally we suggest a simulation based calibration approach to choose smoothing parameters that optimize testing oriented criteria simulation shows that the proposed procedures work very well in nite samples

robust trend inference with series variance estimator and testing optimal smoothing parameter abstract the paper develops a novel testing procedure for hypotheses on deterministic trends in a multivariate trend stationary model the trends are estimated by the ols estimator and the long run variance lrv matrix is estimated by a series type estimator with carefully selected basis functions regardless of whether the number of basis functions k is fixed or grows with the sample size the wald statistic converges to a standard distribution it is shown that critical values from the fixed k asymptotics are second order correct under the large k asymptotics a new practical approach is proposed to select k that addresses the central concern of hypothesis testing the selected smoothing parameter is testing optimal in that it minimizes the type ii error while controlling for the type i error simulations indicate that the new test is as accurate in size as the nonstandard test of vogelsang and franses 2005 and as powerful as the corresponding wald test based on the large k asymptotics the new test therefore combines the advantages of the nonstandard test and the standard wald test while avoiding their main disadvantages power loss and size distortion respectively

simple and trustworthy cluster robust gmm inference abstract this paper develops a new asymptotic theory for gmm estimation and inference in the presence of clustered dependence the key feature of our alternative asymptotics is that the number of clusters g is regarded as fixed as the sample size increases under the fixed g asymptotics we show that the wald and t tests in two step gmm are asymptotically pivotal only if we recenter the estimated moment process in the clustered covariance estimator cce also the j statistic the trinity of two step gmm statistics qlr lm and wald and the t statistic can be modified to have an asymptotic standard f distribution or t distribution we suggest a finite sample variance correction to further improve the accuracy of the f and t approximations the proposed tests are very appealing to practitioners because the test statistics are simple modifications of conventional gmm test statistics and critical values are readily available from f and t tables no further simulations or resampling methods are needed a monte carlo study shows that our proposed tests are more accurate than the conventional large g asymptotic inferences

heteroskedasticity autocorrelation robust standard errors using the bartlett kernel without truncation in this paper we analyze heteroskedasticity autocorrelation hac robust tests constructed using the bartlett kernel without truncation we show that while such an hac estimator is not consistent asymptotically valid testing is still possible we show that tests using the bartlett kernel without truncation are exactly equivalent to recent hac robust tests proposed by kiefer vogelsang and bunzel 2000 econometrica 68 pp 695 714

jackknife estimation of stationary autoregressive models abstract this paper explores the properties of jackknife methods of estimation in stationary autoregressive models some general results concerning the correct weights for bias reduction under various sampling schemes are provided and the asymptotic properties of a jackknife estimator based on non overlapping sub samples are derived for the case of a stationary autoregression of order p when the number of sub samples is either fixed or increases with the sample size at an appropriate rate the results of a detailed investigation into the finite sample properties of various jackknife and alternative estimators are reported and it is found that the jackknife can deliver substantial reductions in bias in autoregressive models this finding is robust to departures from normality arch effects and misspecification the median unbiasedness and mean squared error properties are also investigated and compared with alternative methods as are the coverage rates of jackknife based confidence intervals

robustifying multivariate trend tests to nonstationary volatility abstract this article studies inference of multivariate trend model when the volatility process is nonstationary within a quite general framework we analyze four classes of tests based on least squares estimation one of which is robust to both weak serial correlation and nonstationary volatility the existing multivariate trend tests which either use non robust standard errors or rely on non standard distribution theory are generally non pivotal involving the unknown time varying volatility function in the limit two step residual based i i d bootstrap and wild bootstrap procedures are proposed for the robust tests and are shown to be asymptotically valid simulations demonstrate the effects of nonstationary volatility on the trend tests and the good behavior of the robust tests in finite samples

numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors we study numerically the complex domains of validity for kam theory in generalized standard mappings we compare methods based on pade approximants and methods based on the study of periodic orbits

let s fix it fixed b asymptotics versus small b asymptotics in heteroskedasticity and autocorrelation robust inference in the presence of heteroscedasticity and autocorrelation of unknown forms the covariance matrix of the parameter estimator is often estimated using a nonparametric kernel method that involves a lag truncation parameter depending on whether this lag truncation parameter is speci ed to grow at a slower rate than or the same rate as the sample size we obtain two types of asymptotic approximations the small b asymptotics and the xed b asymptotics using techniques for probability distribution approximation and high order expansions this paper shows that the xed b asymptotic approximation provides a higher order re nement to the rst order small b asymptotics this result provides a theoretical justi cation on the use of the xed b asymptotics in empirical applications on the basis of the xed b asymptotics and higher order small b asymptotics the paper introduces a new and easy to use asymptotic f test that employs a nite sample corrected wald statistic and uses an f distribution as the reference distribution finally the paper develops a bandwidth selection rule that is testing optimal in that the bandwidth minimizes the type ii error of the asymptotic f test while controlling for its type i error monte carlo simulations show that the asymptoticf test with the testing optimal bandwidth works very well in nite samples