the dirichlet problem for nonlinear second order elliptic equations iii functions of the eigenvalues of the hessian on etudie le probleme de dirichlet dans un domaine borne de r n a frontiere lisse f d 2 u dans u sur

model selection in the presence of nonstationarity abstract this paper studies model selection methods in the presence of nonstationarity we focus on the bayesian model selection rule and compare it with other criteria that are frequently used in econometric practice first we derive each of these criteria in the presence of nonstationarity in particular we study the bayesian model selection rule in detail and derive three alternative forms of it in the presence of nonstationarity one important feature of the bayesian model selection criterion bmsc is that bmsc gives different weights to the stationary and nonstationary components of a model while the other criteria do not this feature of bmsc is a desirable property for a model selection rule in the presence of possible nonstationarity second we compare these criteria with regard to parsimony and power we have found that bmsc shows the highest parsimony aic is the second and c p and r 2 having the same level of parsimony are the third with regard to power the order is not clearly established however for the size adjusted power bmsc becomes dominant as the sample size increases without size adjustment the order in the power is exactly the opposite to that in parsimony also we find that bmsc is a consistent selection rule while the other criteria are not third we consider four different cases of practical interest for which bmsc with some of the other criteria is applicable we discuss how our bmsc can be used in these cases of practical interest results of an extensive monte carlo simulation for models in these four cases show that overall the bmsc outperforms other criteria

nonparametric regression with multiple thresholds estimation and inference abstract this paper examines nonparametric regression with an exogenous threshold variable allowing for an unknown number of thresholds given the number of thresholds and corresponding threshold values we first establish the asymptotic properties of the local constant estimator for a nonparametric regression with multiple thresholds however the number of thresholds and corresponding threshold values are typically unknown in practice we then use our testing procedure to determine the unknown number of thresholds and derive the limiting distribution of the proposed test the monte carlo simulation results indicate the adequacy of the modified test and accuracy of the sequential estimation of the threshold values we apply our testing procedure to an empirical study of the 401 k retirement savings plan with income thresholds

regularity of potential functions of the optimal transportation problem the potential function of the optimal transportation problem satisfies a partial differential equation of monge ampere type in this paper we introduce the notion of a generalized solution and prove the existence and uniqueness of generalized solutions of the problem we also prove the solution is smooth under certain structural conditions on the cost function

model selection criteria in multivariate models with multiple structural changes abstract this paper considers the issue of selecting the number of regressors and the number of structural breaks in multivariate regression models in the possible presence of multiple structural changes we develop a modified akaike information criterion aic a modified mallows c p criterion and a modified bayesian information criterion bic the penalty terms in these criteria are shown to be different from the usual terms we prove that the modified bic consistently selects the regressors and the number of breaks whereas the modified aic and the modified c p criterion tend to overfit with positive probability the finite sample performance of these criteria is investigated through monte carlo simulations and it turns out that our modification is successful in comparison to the classical model selection criteria and the sequential testing procedure robust to heteroskedasticity and autocorrelation

partitioning a large simulation as it runs as computer simulations continue to grow in size and complexity they present a particularly challenging class of big data problems many application areas are moving toward exascale computing systems systems that perform 1018 flops floating point operations per second a billion billion calculations per second simulations at this scale can generate output that exceeds both the storage capacity and the bandwidth available for transfer to storage making post processing and analysis challenging one approach is to embed some analyses in the simulation while the simulation is running a strategy often called in situ analysis to reduce the need for transfer to storage another strategy is to save only a reduced set of time steps rather than the full simulation typically the selected time steps are evenly spaced where the spacing can be defined by the budget for storage and transfer this article combines these two ideas to introduce an online in situ method for identifying a reduced set of time steps of

estimating and testing structural changes in multivariate regressions this paper considers issues related to estimation inference and computation with multiple structural changes that occur at unknown dates in a system of equations changes can occur in the regression coefficients and or the covariance matrix of the errors we also allow arbitrary restrictions on these parameters which permits the analysis of partial structural change models common breaks that occur in all equations breaks that occur in a subset of equations and so forth the method of estimation is quasi maximum likelihood based on normal errors the limiting distributions are obtained under more general assumptions than previous studies for testing we propose likelihood ratio type statistics to test the null hypothesis of no structural change and to select the number of changes structural change tests with restrictions on the parameters can be constructed to achieve higher power when prior information is present for computation an algorithm for an efficient procedure is proposed to construct the estimates and test statistics we also introduce a novel locally ordered breaks model which allows the breaks in different equations to be related yet not occurring at the same dates

goodness of fit tests for kernel regression with an application to option implied volatilities this paper proposes a test of a restrictedspeci cation of regression basedon comparing residual sum of squares from kernel regression our main case is where both the restrictedspeci cation andthe general mod el are nonparametric with our test equivalently viewed as a test of dimension reduction we discuss practical features of implementing the test andvariations applicable to testing parametric mod els as the null hypothesis or semiparametric models that depend on a nite parameter vector as well as unknown functions we apply our testing procedure to option prices we reject a parametric version of the black scholes formula but fail to reject a semiparametric version against a general nonparametric regression 2001 elsevier science s a all rights reserved jel classi cation c12 c14

model selection in under specified equations facing breaks although a general unrestricted model may under specify the data generation process especially when breaks occur model selection can still improve over estimating a prior specification impulseindicator saturation iis can correct non constant int ercepts induced by location shifts in omitted variables which surprisingly leave slope parameters unaltered even when correlated with included variables however location shifts in included variables do induce changes in slopes when there are correlated omitted variables iis acts as a robust meth od when models are mis specified and helps mitigate the adverse impacts of induced location shifts on non constant intercepts and equation standard errors

unsupervised self normalized change point testing for time series abstractwe propose a new self normalized method for testing change points in the time series setting self normalization has been celebrated for its ability to avoid direct estimation of the nuisance asymptotic variance and its flexibility of being generalized to handle quantities other than the mean however it was developed and mainly studied for constructing confidence intervals for quantities associated with a stationary time series and its adaptation to change point testing can be nontrivial as direct implementation can lead to tests with nonmonotonic power compared with existing results on using self normalization in this direction the current article proposes a new self normalized change point test that does not require prespecifying the number of total change points and is thus unsupervised in addition we propose a new contrast based approach in generalizing self normalized statistics to handle quantities other than the mean which is specifically tailored for change point testing monte car

time varying instrumental variable estimation abstract we develop non parametric instrumental variable estimation and inferential theory for econometric models with possibly endogenous regressors whose coefficients can vary over time either deterministically or stochastically and the time varying and uniform versions of the standard hausman exogeneity test after deriving the asymptotic properties of the proposed procedures we assess their finite sample performance by means of a set of monte carlo experiments and illustrate their application by means of an empirical example on the phillips curve

breaks or long memory behavior an empirical investigation are structural break models true switching models or long memory processes the answer to this question remains ambiguous in recent years many papers have dealt with this problem some studies have shown that under specific conditions switching models and long memory processes can easily be confused in this paper using several generating models the mean plus noise model the stochastic permanent break model the markov switching model the threshold autoregressive tar model the sign model and the structural change model and several estimation techniques the geweke porter hudak gph technique detrended fluctuation analysis dfa the exact local whittle elw method and wavelet methods we show that even if the answer is quite simple in some cases it can be mitigated in other cases using french and american inflation rates we found that the most appropriate process that takes into account the important features of these series is a model that simultaneously combines changes in regimes and long memory behavior the main result of this study indicates that estimating a long memory parameter without taking into account the presence of breaks in the data sets may lead to misspecification and hence to overestimating the true parameter

confidence sets for the date of a single break in linear time series regressions this paper considers the problem of constructing confidence sets for the date of a single break in a linear time series regression we establish analytically and by small sample simulation that the current standard method in econometrics for constructing such confidence intervals has a coverage rate far below nominal levels when breaks are of moderate magnitude given that breaks of moderate magnitude are a theoretically and empirically relevant phenomenon we proceed to develop an appropriate alternative we suggest constructing confidence sets by inverting a sequence of tests each of the tests maintains a specific break date under the null hypothesis and rejects when a break occurs elsewhere by inverting a certain variant of a locally best invariant test we ensure that the asymptotic critical value does not depend on the maintained break date a valid confidence set can hence be obtained by assessing which of the sequence of test statistics exceeds a single number

the dirichlet problem for nonlinear second order elliptic equations i monge ampegre equation on considere le probleme de dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture d un domaine borne dans r n avec une frontiere c

regularity for an obstacle problem of hessian equations on riemannian manifolds abstract in this paper we study the regularity for solutions to an obstacle problem of hessian type fully nonlinear equations on riemannian manifolds as an application the existence of a c 1 1 solution is proved

small sample properties of forecasts from autoregressive models under structural breaks this paper develops a theoretical framework for the analysis of smallsample properties of forecasts from general autoregressive models under structural breaks finite sample results for the mean squared forecast error of one step ahead forecasts are derived both conditionally and unconditionally and numerical results for different types of break specifications are presented it is established that forecast errors are unconditionally unbiased even in the presence of breaks in the autoregressive coefficients and or error variances so long as the unconditional mean of the process remains unchanged insights from the theoretical analysis are demonstrated in monte carlo simulations and on a range of macroeconomic time series from g7 countries the results are used to draw practical recommendations for the choice of estimation window when forecasting from autoregressive models subject to breaks

on consistency of minimum description length model selection for piecewise autoregressions abstract the auto parm automatic piecewise autoregressive modeling procedure developed by davis et al 2006 uses the minimum description length mdl principle to estimate the number and locations of structural breaks in a non stationary time series consistency of this model selection procedure has been established when using conditional maximum gaussian likelihood variance estimates in contrast the estimate of the number of change points is inconsistent in general if yule walker variance estimates are used instead this surprising result is due to an exact cancellation of first order terms in a taylor series expansion in the conditional maximum likelihood case which does not occur in the yule walker case in order to simplify notation and make the arguments more transparent we only treat in detail the simple case where the time series follows an ar p model with no change points

a flexible approach to parametric inference in nonlinear and time varying time series models many structural break and regime switching models have been used with macroeconomic and financial data in this paper we develop an extremely flexible modeling approach which can accommodate virtually any of these specifications we build on earlier work showing the relationship between flexible functional forms and random variation in parameters our contribution is based around the use of priors on the time variation that is developed from considering a hypothetical reordering of the data and distance between neighboring reordered observations the range of priors produced in this way can accommodate a wide variety of nonlinear time series models including those with regime switching and structural breaks by allowing the amount of random variation in parameters to depend on the distance between reordered observations the parameters can evolve in a wide variety of ways allowing for everything from models exhibiting abrupt change e g threshold autoregressive models or standard structural break models to those which allow for a gradual evolution of parameters e g smooth transition autoregressive models or time varying parameter models bayesian econometric methods for inference are developed for estimating the distance function and types of hypothetical reordering conditional on a hypothetical reordering and distance function a simple reordering of the actual data allows us to estimate our models with standard state space methods by a simple adjustment to the measurement equation we use artificial data to show the advantages of our approach before providing two empirical illustrations involving the modeling of real gdp growth

panel data models with interactive fixed effects and multiple structural breaks abstractin this article we consider estimation of common structural breaks in panel data models with unobservable interactive fixed effects we introduce a penalized principal component ppc estimation procedure with an adaptive group fused lasso to detect the multiple structural breaks in the models under some mild conditions we show that with probability approaching one the proposed method can correctly determine the unknown number of breaks and consistently estimate the common break dates furthermore we estimate the regression coefficients through the post lasso method and establish the asymptotic distribution theory for the resulting estimators the developed methodology and theory are applicable to the case of dynamic panel data models simulation results demonstrate that the proposed method works well in finite samples with low false detection probability when there is no structural break and high probability of correctly estimating the break numbers when the structural breaks exist we finall

free boundaries in optimal transport and monge ampere obstacle problems given compactly supported 0 f g 2 l 1 r n the problem of trans porting a fraction m min kfkl1 kgkl1 of the mass of f onto g as cheaply as possible is considered where cost per unit mass transported is given by a cost function c typically quadratic c x y x y 2 2 this question is shown to be equivalent to a double obstacle problem for the monge ampere equation for which sucient conditions are given to guarantee uniqueness of the solution such as f vanishing on sptg in the quadratic case the part of f to be transported increases monotonically with m and if sptf and sptg are separated by a hyperplane h then this part will separated from the balance of f by a semiconcave lipschitz graph over the hyperplane if f f and g g are bounded away from zero and infinity on separated strictly convex domains r n for the quadratic cost this graph is shown to be a c 1 loc hypersurface in whose normal coincides with the direction transported the optimal map between f and g is shown to be holder continuous up to this free bound ary and to those parts of the fixed boundary which map to locally convex parts of the path connected target region

modeling and testing smooth structural changes with endogenous regressors abstract modeling and detecting parameter stability of econometric models is a long standing problem most existing estimation and testing methods are designed for models without endogeneity little attention has been paid to models with endogeneous regressors which may arise in many scenarios in economics in this paper we first consider a time varying coefficient time series model with potential time varying endogeneity a local linear two stage least squared estimation is developed to estimate coefficient functions the consistency and asymptotic normality of the estimator are derived furthermore a nonparametric test is proposed to check smooth structural changes as well as abrupt structural breaks with possibly unknown change points in regression models with potential endogeneity the idea is to compare the fitted values of the unrestricted nonparametric time varying coefficient model and the restricted constant parameter model the test has an asymptotic n 0 1 distribution and does not require any prior information about the alternatives a simulation study highlights the merits of the proposed estimator and test in an application we estimate the new keynesian phillips curve for the us nonparametrically and find strong evidence against its stability

structural break models under mis specification implications for forecasting abstract this paper revisits the least squares estimator of the linear regression with a structural break we view the model as an approximation to the true data generating process whose exact nature is unknown but perhaps changing over time either continuously or with some jumps this view is widely held in the forecasting literature and under this view the time series dependence property of all the observed variables is unstable as well we establish that the rate of convergence of the estimator to a properly defined limit is at most the cube root of t where t is the sample size which is much slower than the standard super consistent rate we also provide an asymptotic distribution of the estimator and that of the gaussian quasi likelihood ratio statistic for a certain class of true data generating processes we relate our finding to current forecast combination methods and propose a new averaging scheme our method compares favourably with various contemporary forecasting methods in forecasting a number of macroeconomic series

threshold effects in non dynamic panels estimation testing and inference abstract threshold regression methods are developed for non dynamic panels with individual specific fixed effects least squares estimation of the threshold and regression slopes is proposed using fixed effects transformations a non standard asymptotic theory of inference is developed which allows construction of confidence intervals and testing of hypotheses the methods are applied to a 15 year sample of 565 us firms to test whether financial constraints affect investment decisions

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

the dirichlet problem for the convex envelope the convex envelope of a given function was recently characterized as the solution of a fully nonlinear partial differential equation pde in this article we study a modified problem the dirichlet problem for the underlying pde the main result is an optimal regularity result differentiability c1 regularity of the boundary data implies the corresponding result for the solution in the interior despite the fact that the solution need not be continuous up to the boundary secondary results are the characterization of the convex envelope as i the value function of a stochastic control problem and ii the optimal underestimator for a class of nonlinear elliptic pdes

inference for non stationary time series regression with or without inequality constraints summary we consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non stationary behaviours over time meanwhile the regression parameters may be subject to linear inequality constraints a simple and unified procedure for structural stability checks and parameter inference is proposed in the case where the regression parameters are constrained the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones

the obstacle problem for hessian equations on riemannian manifolds abstract in this paper we consider the obstacle problem for a class of fully nonlinear equations on riemannian manifolds the c 1 1 regularity of the greatest viscosity solutions is established

an obstacle problem for a class of monge ampere type functionals abstract in this paper we study an obstacle problem for monge ampere type functionals whose euler lagrange equations are a class of fourth order equations including the affine maximal surface equation and abreu s equation

hierarchical statistical models and a generalized likelihood ratio test this paper deals with statistical inference for statistical models which have a nested structure the emphasis here is on the use of a classical test of significance and on a confidence set construction approach for model identification and the paper proposes a generalized likelihood ratio test with equal marginal error rate as a basic tool the power performance of this test is characterized and some applications are illustrated

optimal tests when a nuisance parameter is present only under the alternative this paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null for example the results apply to tests of structural change with unknown changepoint the testing problem considered is nonstandard and the classical asymptotic optimality results for the lagrange multiplier wald and likelihood ratio do not apply a weighted average power criterion is used here to generate optimal tests this criterion is similar to that used by a wald 1943 to obtain the classical asymptotic optimality properties of wald tests in regular testing problems copyright 1994 by the econometric society

does modeling a structural break improve forecast accuracy mean square forecast error loss implies a bias variance trade off that suggests that structural breaks of small magnitude should be ignored in this paper we provide a test to determine whether modeling a structural break improves forecast accuracy the test is near optimal even when the date of a local to zero break is not consistently estimable the results extend to forecast combinations that weight the post break sample and the full sample forecasts by our test statistic in a large number of macroeconomic time series we find that structural breaks that are relevant for forecasting occur much less frequently than existing tests indicate

model selection when there are multiple breaks abstract we consider model selection facing uncertainty over the choice of variables and the occurrence and timing of multiple location shifts general to simple selection is extended by adding an impulse indicator for every observation to the set of candidate regressors see johansen and nielsen 2009 we apply that approach to a fat tailed distribution and to processes with breaks monte carlo experiments show its capability of detecting up to 20 shifts in 100 observations while jointly selecting variables an illustration to us real interest rates compares impulse indicator saturation with the procedure in bai and perron 1998

change point analysis of imprecise time series abstract in this paper we describe how to conduct a change point analysis when dealing with time series imprecisely or vaguely observed i e time ordered observations whose values are not known exactly such as interval or ordinal time series imprecise time series in order to treat such time series we propose to employ a fuzzy approach i e data are parameterized in the form of fuzzy variables then to detect the number and location of change points we employ a deviation measure for fuzzy variables in the framework of atheoretical regression trees art we present simulation results pertaining to the behavior of the proposed approach as well as two empirical applications to real imprecise time series

consistency and limiting distribution of the least squares estimator of a threshold autoregressive model it is shown that under some regularity conditions the least squares estimator of a stationary ergodic threshold autoregressive model is strongly consistent the limiting distribution of the least squares estimator is derived it is shown that the estimator of the threshold parameter is n consistent and its limiting distribution is related to a compound poisson process

nonparametric inference on structural breaks this paper proposes estimators of location and size of structural breaks in a possibly dynamic nonparametric regression model the structural breaks can be located at given periods of time and or they can be explained by the values taken by some regressor as in threshold models no previous knowledge of the underlying regression function is required the paper also studies the case in which several regressors explain the breaks we derive the rate of convergence and provide central limit theorems for the estimators of the location s and size s a monte carlo experiment illustrates the performance of our estimators in small samples

some existence results for fully nonlinear elliptic equations of monge ampere type we study the existence and uniqueness of solutions of monge ampere type equations this type of equations has been studied extensively by caffarelli nirenberg spruck and many others see 5 through 8 and the references therein we present some existence and uniqueness results for this type of equations on compact riemannian manifolds with non negative sectional curvature we have also generalized some results in 7

optimal forecasts in the presence of structural breaks this paper considers the problem of forecasting under continuous and discrete structural breaks and proposes weighting observations to obtain optimal forecasts in the msfe sense we derive optimal weights for continuous and discrete break processes under continuous breaks our approach recovers exponential smoothing weights under discrete breaks we provide analytical expressions for the weights in models with a single regressor and asympotically for larger models it is shown that in these cases the value of the optimal weight is the same across observations within a given regime and differs only across regimes in practice where information on structural breaks is uncertain a forecasting procedure based on robust weights is proposed monte carlo experiments and an empirical application to the predictive power of the yield curve analyze the performance of our approach relative to other forecasting methods

estimating structural changes in regression quantiles this paper considers the estimation of multiple structural changes occurring at unknown dates in one or multiple conditional quantile functions the analysis covers time series models as well as models with repeated cross sections we estimate the break dates and other parameters jointly by minimizing the check function over all permissible break dates the limiting distribution of the estimator is derived and the coverage property of the resulting confidence interval is assessed via simulations a procedure to determine the number of breaks is also discussed empirical applications to the quarterly us real gdp growth rate and the underage drunk driving data suggest that the method can deliver more informative results than the analysis of the conditional mean function alone

heterogeneous change point inference summary we propose a heterogeneous simultaneous multiscale change point estimator called h smuce for the detection of multiple change points of the signal in a heterogeneous gaussian regression model a piecewise constant function is estimated by minimizing the number of change points over the acceptance region of a multiscale test which locally adapts to changes in the variance the multiscale test is a combination of local likelihood ratio tests which are properly calibrated by scale dependent critical values to keep a global nominal level even for finite samples we show that h smuce controls the error of overestimation and underestimation of the number of change points for this new deviation bounds for f type statistics are derived moreover we obtain confidence sets for the whole signal all results are non asymptotic and uniform over a large class of heterogeneous change point models h smuce is fast to compute achieves the optimal detection rate and estimates the number of change points at almost optimal accuracy for vanishing signals while still being robust we compare h smuce with several state of the art methods in simulations and analyse current recordings of a transmembrane protein in the bacterial outer membrane with pronounced heterogeneity for its states an r package is available on line

detecting gradual changes in locally stationary processes in a wide range of applications the stochastic properties of the observed time series change over time the changes often occur gradually rather than abruptly the properties are approximately constant for some time and then slowly start to change in such situations it is frequently of interest to locate the time point where the properties start to vary in contrast to the analysis of abrupt changes methods for detecting smooth or gradual change points are less developed and often require strong parametric assumptions in this paper we develop a fully nonparametric method to estimate a smooth change point in a locally stationary framework we set up a general procedure which allows to deal with a wide variety of stochastic properties including the mean auto covariances and higher order moments the theoretical part of the paper establishes the convergence rate of the new estimator in addition we examine its finite sample performance by means of a simulation study and illustrate the methodology by applications to temperature and financial return data

a semiparametric change point regression model for longitudinal observations many longitudinal studies involve relating an outcome process to a set of possibly time varying covariates giving rise to the usual regression models for longitudinal data when the purpose of the study is to investigate the covariate effects when experimental environment undergoes abrupt changes or to locate the periods with different levels of covariate effects a simple and easy to interpret approach is to introduce change points in regression coefficients in this connection we propose a semiparametric change point regression model in which the error process stochastic component is nonparametric and the baseline mean function functional part is completely unspecified the observation times are allowed to be subject specific and the number locations and magnitudes of change points are unknown and need to be estimated we further develop an estimation procedure that combines the recent advance in semiparametric analysis based on counting process argument and multiple change points inference an

asymptotic theory for time series with changing mean and variance abstract the paper develops point estimation and asymptotic theory with respect to a semiparametric model for time series with moving mean and unconditional heteroscedasticity these two features are modelled nonparametrically whereas autocorrelations are described by a short memory stationary parametric time series model we first study the usual least squares estimate of the coefficient of the first order autoregressive model based on constant but unknown mean and variance allowing for both the latter to vary over time in a general way we establish its probability limit and a central limit theorem for a suitably normed and centred statistic giving explicit bias and variance formulae as expected mean variation is the main source of inconsistency and heteroscedasticity the main source of inefficiency though we discuss circumstances in which the estimate is consistent for and asymptotically normal about the autoregressive coefficient albeit inefficient we then consider standard implicitly defined whittle estimates of a more general class of short memory parametric time series model under otherwise more restrictive conditions when the mean is correctly assumed to be constant estimates that ignore the heteroscedasticity are again found to be asymptotically normal but inefficient allowing a slowly time varying mean we resort to trimming out of low frequencies to achieve the same outcome returning to finite order autoregression nonparametric estimates of the varying mean and variance are given asymptotic justification and forecasting formulae developed finite sample properties are studied by a small monte carlo simulation and an empirical example is also included

a nonparametric test for changing trends many tests of parameter change in dynamic models exhibit nonmonotonic power an important source of the nonmonotonic power comes from the bias in estimating parameters when there is a change in the deterministic component to avoid this bias we propose a nonparametric test for changing trends based on nonparametrically detrended data the tests are similar in spirit to nonparametric conditional moment tests such as fan and li j nonparametr stat 10 1999a 245 11 1999b 251 and zheng j econometrics 75 1996 263 the resulting statistics have a standard normal distribution a monte carlo experiment suggests that the tests have good power against changes in the deterministic component

estimating and testing linear models with multiple structural changes this paper develops the statistical theory for testing and estimating multiple change points in regression models the rate of convergence and limiting distribution for the estimated parameters are obtained several test statistics are proposed to determine the existence as well as the number of change points a partial structural change model is considered the authors study both fixed and shrinking magnitudes of shifts in addition the models allow for serially correlated disturbances mixingales an estimation strategy for which the location of the breaks need not be simultaneously determined is discussed instead the authors method successively estimates each break point

new distribution theory for the estimation of structural break point in mean abstract based on the girsanov theorem this paper obtains the exact distribution of the maximum likelihood estimator of structural break point in a continuous time model the exact distribution is asymmetric and tri modal indicating that the estimator is biased these two properties are also found in the finite sample distribution of the least squares ls estimator of structural break point in the discrete time model suggesting the classical long span asymptotic theory is inadequate the paper then builds a continuous time approximation to the discrete time model and develops an in fill asymptotic theory for the ls estimator the in fill asymptotic distribution is asymmetric and tri modal and delivers good approximations to the finite sample distribution to reduce the bias in the estimation of both the continuous time and the discrete time models a simulation based method based on the indirect estimation ie approach is proposed monte carlo studies show that ie achieves substantial bias reductions

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

closed weingarten hypersurfaces in semi riemannian manifolds the existence of closed hypersurfaces of prescribed curvature in semi riemannian manifolds is proved provided there are barriers

finite sample multivariate structural change tests with application to energy demand models abstract this paper considers finite sample motivated structural change tests in the multivariate linear regression model with application to energy demand models in which case commonly used structural change tests remain asymptotic as in dufour and kiviet 1996 exact tests for structural change in first order dynamic models journal of econometrics 70 39 68 we account for intervening nuisance parameters through a two stage maximized monte carlo test procedure our contributions can be classified into five categories i we extend tests for which a finite sample theory has been supplied for gaussian distributions to the non gaussian context ii we show that bai et al 1998 testing and dating common breaks in multi variate time series the review of economic studies 65 3 395 432 test severely over rejects and propose exact variants of this test iii we consider predictive break test approaches which generalize tests in dufour 1980 dummy variables and predictive tests for structural change economics letters 6 241 247 and dufour and kiviet 1996 exact tests for structural change in first order dynamic models journal of econometrics 70 39 68 iv we propose exact non bonferonni based extensions of the multivariate outliers test from wilks 1963 multivariate statistical outliers sankhya series a 25 407 426 to models with covariates v we apply these tests to the energy demand system analyzed by arsenault et al 1995 a total energy demand model of quebec forecasting properties energy economics 17 2 163 171 for two out of the six industrial sectors analyzed over the 1962 2000 period break and further goodness of fit and diagnostic tests allow to identify and correct specification problems arising from historical regulatory changes or possibly random industry specific effects the procedures we propose have potential useful applications in statistics econometrics and finance e g event studies

sample splitting and threshold estimation threshold models have a wide variety of applications in economics direct applications include models of separating and multiple equilibria other applications include empirical sample splitting when the sample split is based on a continuously distributed variable such as firm size in addition threshold models may be used as a parsimonious strategy for nonparametric function estimation for example the threshold autoregressive model tar is popular in the nonlinear time series literature threshold models also emerge as special cases of more complex statistical frameworks such as mixture models switching models markov switching models and smooth transition threshold models it may be important to understand the statistical properties of threshold models as a preliminary step in the development of statistical tools to handle these more complicated structures despite the large number of potential applications the statistical theory of threshold estimation is undeveloped it is known that threshold estimates are super consistent but a distribution theory useful for testing and inference has yet to be provided this paper develops a statistical theory for threshold estimation in the regression context we allow for either cross section or time series observations least squares estimation of the regression parameters is considered an asymptotic distribution theory for the regression estimates the threshold and the regression slopes is developed it is found that the distribution of the threshold estimate is nonstandard a method to construct asymptotic confidence intervals is developed by inverting the likelihood ratio statistic it is shown that this yields asymptotically conservative confidence regions monte carlo simulations are presented to assess the accuracy of the asymptotic approximations the empirical relevance of the theory is illustrated through an application to the multiple equilibria growth model of durlauf and johnson 1995

structural breaks with deterministic and stochastic trends abstract this paper analyzes the consistency rate of convergence and limiting distributions of parameter estimates in models where the trend function exhibits a slope change at some unknown date and the errors can be either stationary or have a unit root these estimates are obtained by minimizing the sum of squared residuals in simple regressions involving a constant a trend a slope shift regressor and possibly a level shift regressor special attention is given to the effects induced by alternative specifications of the slope shift regressor and the inclusion or exclusion of a level shift regressor some surprising results are found for which we provide more detailed explanations we also show via simulations that our asymptotic results provide good approximations in finite samples we illustrate the issues analyzed applying our results to investigate dates and magnitudes of changes in the growth rates of log real per capita gdp series for 10 countries using a historical data set that covers the period 1870 1986

assessing the relative power of structural break tests using a framework based on the approximate bahadur slope abstract we compare the asymptotic relative efficiency of the exp mean and sup functionals of the wald lm and lr tests for structural change analyzed by andrews andrews d w k 1993 tests for parameter instability and structural change with unknown change point econometrica 61 821 856 and andrews and ploberger andrews d w k ploberger w 1994 optimal tests when a nuisance parameter is present only under the alternative econometrica 62 1383 1414 we derive the approximate bahadur slopes of these tests using large deviations techniques these show that tests based on the mean functional are inferior to those based on the sup and exp when using the same base statistic also for a given functional the wald based test dominates the lr based test which dominates the lm based one we show that the sup and mean type tests satisfy wieand s wieand h s 1976 a condition under which the pitman and bahadur approaches to efficiency coincide annals of statistics 4 1003 1011 condition so that their slopes yield the limiting as the size tends to zero asymptotic relative pitman efficiency whether this holds for the exp type tests still remains a conjecture using this measure of efficiency the mean type tests are also inferior to the sup we also compare tests based on the wald and lm statistics modified with a hac estimator in this case the inferiority of the lm based tests is especially pronounced the relevance of our theoretical results in finite samples is assessed via simulations our results are in contrast to those obtained by the authors in the second reference cited above based on a local asymptotic framework and our analysis thereby reveals its potential weaknesses in the context of structural change problems

multiscale change point inference summary we introduce a new estimator the simultaneous multiscale change point estimator smuce for the change point problem in exponential family regression an unknown step function is estimated by minimizing the number of change points over the acceptance region of a multiscale test at a level the probability of overestimating the true number of change points k is controlled by the asymptotic null distribution of the multiscale test statistic further we derive exponential bounds for the probability of underestimating k by balancing these quantities will be chosen such that the probability of correctly estimating k is maximized all results are even non asymptotic for the normal case on the basis of these bounds we construct asymptotically honest confidence sets for the unknown step function and its change points at the same time we obtain exponential bounds for estimating the change point locations which for example yield the minimax rate up to a log term finally the simultaneous multiscale change point estimator achieves the optimal detection rate of vanishing signals as n even for an unbounded number of change points we illustrate how dynamic programming techniques can be employed for efficient computation of estimators and confidence regions the performance of the multiscale approach proposed is illustrated by simulations and in two cutting edge applications from genetic engineering and photoemission spectroscopy

change point detection in multinomial data with a large number of categories we consider a sequence of multinomial data for which the probabilities associated with the categories are subject to abrupt changes of unknown magnitudes at unknown locations when the number of categories is comparable to or even larger than the number of subjects allocated to these categories conventional methods such as the classical pearson s chi squared test and the deviance test may not work well motivated by high dimensional homogeneity tests we propose a novel change point detection procedure that allows the number of categories to tend to infinity the null distribution of our test statistic is asymptotically normal and the test performs well with finite samples the number of change points is determined by minimizing a penalized objective function based on segmentation and the locations of the change points are estimated by minimizing the objective function with the dynamic programming algorithm under some mild conditions the consistency of the estimators of multiple change points is established simulation studies show that the proposed method performs satisfactorily for identifying change points in terms of power and estimation accuracy and it is illustrated with an analysis of a real data set

common breaks in means and variances for panel data this paper establishes the consistency of the estimated common break point in panel data consistency is obtainable even when a regime contains a single observation making it possible to quickly identify the onset of a new regime we also propose a new framework for developing the limiting distribution for the estimated break point and show how to construct confidence intervals the least squares method is used for estimating breaks in means and the quasi maximum likelihood qml method is used to estimate breaks in means and in variances qml is shown to be more efficient than the least squares even if there is no change in the variances

asymptotics for change point models under varying degrees of mis specification change point models are widely used by statisticians to model drastic changes in the pattern of observed data least squares maximum likelihood based estimation of change points leads to curious asymptotic phenomena when the change point model is correctly specified such estimates generally converge at a fast rate n and are asymptotically described by minimizers of a jump process under complete mis specification by a smooth curve i e when a change point model is fitted to data described by a smooth curve the rate of convergence slows down to n1 3 and the limit distribution changes to that of the minimizer of a continuous gaussian process in this paper we provide a bridge between these two extreme scenarios by studying the limit behavior of change point estimates under varying degrees of model mis specification by smooth curves which can be viewed as local alternatives we find that the limiting regime depends on how quickly the alternatives approach a change point model we unravel a family of intermediate limits that can transition at least qualitatively to the limits in the two extreme scenarios the theoretical results are illustrated via a set of carefully designed simulations we also demonstrate how inference for the change point parameter can be performed in absence of knowledge of the underlying scenario by resorting to subsampling techniques that involve estimation of the convergence rate

identifying optimal risk windows for self controlled case series studies of vaccine safety in vaccine safety studies subjects are considered at increased risk for adverse events for a period of time after vaccination known as risk window to our knowledge risk windows for vaccine safety studies have tended to be pre defined and not to use information from the current study inaccurate specification of the risk window can result in either including the true control period in the risk window or including some of the risk window in the control period which can introduce bias we propose a data based approach for identifying the optimal risk windows for self controlled case series studies of vaccine safety the approach involves fitting conditional poisson regression models to obtain incidence rate ratio estimates for different risk window lengths for a specified risk window length l the average time at risk t l is calculated when the specified risk window is shorter than the true the incidence rate ratio decreases with 1 t l increasing but there is no explicit relationship when the specified risk window is longer than the true the incidence rate ratio increases linearly with 1 t l increasing theoretically the risk window with the maximum incidence ratio is the optimal risk window because of sparse data problem we recommend using both the maximum incidence rate ratio and the linear relationship when the specified risk window is longer than the true to identify the optimal risk windows both simulation studies and vaccine safety data applications show that our proposed approach is effective in identifying medium and long risk windows

testing for change points in time series models and limiting theorems for ned sequences this paper first establishes a strong law of large numbers and a strong invariance principle for forward and backward sums of near epoch dependent sequences using these limiting theorems we develop a general asymptotic theory on the wald test for change points in a general class of time series models under the no change point hypothesis as an application we verify our assumptions for the long memory fractional arima model

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

estimating restricted structural change models abstract this paper considers issues related to multiple structural changes occurring at unknown dates in the linear regression model when restrictions are imposed on the parameters this includes for example the important special case where different nonadjacent regimes are the same the estimates are constructed as global minimizers of the restricted sum of squared residuals and we provide an extension of the algorithm discussed in bai and perron 2003b computation and analysis of multiple structural change models journal of applied econometrics 18 1 22 to efficiently compute them we show that the estimates of the break dates have the same asymptotic properties with or without the restrictions imposed that is in large samples there is no efficiency gain from imposing valid restrictions as far as the estimates of the break dates are concerned of course efficiency gains occur for the other parameters of the model simulations show that in small samples all parameters are more efficiently estimated using the restrictions we also consider tests of the null hypothesis of no structural change these are also more powerful when the restrictions are imposed a gauss code for all the procedures discussed in this paper is available from the authors

causality tests and conditional heteroskedasticity monte carlo evidence abstract this paper investigates the reliability of causality tests based on least squares when conditional heteroskedasticity exists monte carlo evidence documents considerable size distortion if the conditional variances are correlated inference based on a heteroskedasticity and autocorrelation consistent covariance matrix offers little improvement this size distortion traces to an inability to discriminate between causality in mean and causality in variance as a result this paper endorses conducting causality tests based on an empirical specification that explicitly models the conditional means and conditional variances the relationship between money and prices serves as an illustrative example

estimating a common deterministic time trend break in large panels with cross sectional dependence abstract this paper develops an estimation procedure for a common deterministic time trend break in large panels the dependent variable in each equation consists of a deterministic trend and an error term the deterministic trend is subject to a change in the intercept slope or both and the break date is common for all equations the estimation method is simply minimizing the sum of squared residuals for all possible break dates both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate the rate of convergence is faster when the errors are stationary than when they have a unit root when there is no cross sectional dependence among the errors the rate of convergence depends on the number of equations and thus is faster than the univariate case when the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters the rate of convergence does not depend on the number of equations and thus reduces to the univariate case the limiting distribution of the break date estimate is also provided some monte carlo experiments are performed to assess the adequacy of the asymptotic results a brief empirical example using the us gdp price index is offered

bootstrapping structural change tests this paper demonstrates the asymptotic validity of methods based on the wild recursive and wild fixed bootstraps for testing hypotheses about discrete parameter change in linear models estimated via two stage least squares the framework allows for the errors to exhibit conditional and or unconditional heteroscedasticity and for the reduced form to be unstable simulation evidence indicates the bootstrap tests yield reliable inferences in the sample sizes often encountered in macroeconomics if the errors exhibit unconditional heteroscedasticity and or the reduced form is unstable then the bootstrap methods are particularly attractive because the limiting distributions of the test statistics are not pivotal

τ estimators of regression models with structural change of unknown location abstract this paper concerns with robust estimation of linear regression models with structural change of unknown location under possibly contaminated distributions both for the regressors and for the perturbance term existing estimators will be inefficient in this context furthermore they may protect against outlying yt but cannot cope with leverage points namely outliers in the factor space which could have large influence on the fit as a result these estimators could not discriminate between outlier observations and structural break points misplacing the shift location this fact can be of special importance in practice therefore it may be advisable to consider robust estimators under possible leverage points in a structural change context thus we propose the estimator introduced by yohai and zamar j am stat assoc 83 1988 406 in the standard context of no change this type of estimator is qualitatively robust with the best possible breakdown point and highly efficient under normal errors the asymptotic distribution of the break location estimator is obtained both for fixed magnitude of shift and for shift with magnitude converging to zero as the sample size increases the analysis is carried out in the framework of general ned dependence conditions for the data monte carlo experiments illustrates the performance of our estimators in finite samples

differentiating between coefficient break and volatility break a new method for differentiating between a coefficient break and a volatility break is proposed in the proposed method time series observations are divided into several segments and an autoregressive model is fitted to each segment the goodness of fit of the global model composed of these local models is evaluated using the bayesian information criterion and the division which minimizes this criterion defines the best model the proposed method makes a mixture model such as that with a volatility break in the first break and a coefficient break in the second break applicable simulation results show the efficacy and limitations of the proposed method empirical applications to quarterly time series of industrial production for 19 countries provide interesting results

testing for structural change in regression quantiles abstract most studies in the structural change literature focus solely on the conditional mean while under various circumstances structural change in the conditional distribution or in conditional quantiles is of key importance this paper proposes several tests for structural change in regression quantiles two types of statistics are considered namely a fluctuation type statistic based on the subgradient and a wald type statistic based on comparing parameter estimates obtained from different subsamples the former requires estimating the model under the null hypothesis and the latter involves estimation under the alternative hypothesis the tests proposed can be used to test for structural change occurring in a pre specified quantile or across quantiles which can be viewed as testing for change in the conditional distribution with a linear specification of the conditional quantile function both single and multiple structural changes are considered we derive the limiting distributions under the null hypothesis and show they are nuisance parameter free and can be easily simulated a simulation study is conducted to assess the size and power in finite samples

the power of tests of predictive ability in the presence of structural breaks this paper presents analytical monte carlo and empirical evidence on the effects of structural breaks on tests for equal forecast accuracy and encompassing we show that out of sample predictive content can be hard to find because out of sample tests are highly dependent on the timing of the predictive ability moreover predictive content is harder to find with some tests than others in power f type tests of equal forecast accuracy and encompassing often dominate t type alternatives based on these results and evidence from an empirical application we conclude that structural breaks under the alternative may explain why researchers often find evidence of in sample but not out of sample predictive content

fuzzy change point algorithms for regression models change point cp regression models have been widely applied in various fields where detecting cps is an important problem detecting the location of cps in regression models could be equivalent to partitioning data points into clusters of similar individuals in the literature fuzzy clustering has been widely applied in various fields but it is less used in locating cps in cp regression models in this paper a new method called fuzzy cp fcp algorithm is proposed to detect the cps and simultaneously estimate the parameters of regression models the fuzzy c partitions concept is first embedded into the cp regression models any possible collection of all cps is considered as a partitioning of data with a fuzzy membership we then transfer these memberships into the pseudomemberships of data points belonging to each individual cluster and therefore we can obtain the estimates for model parameters by the fuzzy c regressions method subsequently we use the fuzzy c means clustering to obtain the new iterates of the cp collection memberships by minimizing an objective function concerning the deviations between the predicted response values and data values we illustrate the new approach with several numerical examples and real datasets experimental results actually show that the proposed fcp is an effective and useful cp detection algorithm for cp regression models and can be applied to various fields such as econometrics medicine quality control and signal processing