a new conservation law constructed without using either lagrangians or hamiltonians a new conservation theorem is derived the conserved quantity is constructed in terms of a symmetry transformation vector of the equations of motion only without using either lagrangian or hamiltonian structures which may even fail to exist for the equations at hand one example and implications of the theorem on the structure of point symmetry transformations are presented

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

an infinite dimensional morse theory with applications in this paper we construct an infinite dimensional extraordinary cohomology theory and a morse theory corresponding to it these theories have some special properties which make them useful in the study of critical points of strongly indefinite functionals by strongly indefinite we mean a functional unbounded from below and from above on any subspace of finite codimension several applications are given to hamiltonian systems the onedimensional wave equation of vibrating string type and systems of elliptic partial differential equations 0 introduction let e be a real hilbert space with an inner product and let be a twice continuously differentiable functional denote the frechet derivative and the gradient of at x by x and x respectively where as usual x y x y y e recall that a point x0 e is said to be critical if x0 0 or equivalently if x0 0 the level c r will be called regular if 1 c contains no critical points and critical if x0 0 for some x0 1 c let a b a b be two regular levels of denote m 1 a b and consider the restriction of to m in morse theory one is interested in the local topological structure of the level sets of m near a critical point and in the relation between this local structure and the topological structure of the set m to be more specific suppose that x0 m is an isolated critical point of then one defines a sequence of critical groups of at x0 by setting cq x0 hq c u u x0 q 0 1 2 0 1 where c x0 c x e x c hq is the q th singular homology group with coefficients in some field f and u is a neighbourhood of x0 define the morse index of x0 to be the maximal dimension of a subspace of e on which the quadratic form x0 y y is negative definite one shows that if x0 is a nondegenerate critical point i e if x0 e e is invertible then cq x0 f received by the editors march 20 1995 1991 mathematics subject classification primary 58e05 secondary 34c25 35j65 35l05 55n20 58f05

morse theory and asymptotic linear hamiltonian system on considere l existence de solutions 2 periodiques des systemes hamiltoniens asymptotiquement quadratiques jz h z t ou j 0 i i 0 i in la matrice identite de n n

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

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

estimation in change point hazard rate models summary this paper discusses the estimation of parameters in hazard rate models with a changepoint due to the irregularity of the models the classical maximum likelihood method and the method of moments cannot be used a consistent estimator of the change point is obtained by examining the properties of the density represented as a mixture the performance of the estimator is checked via simulation

a remark on symmetry of stochastic dynamical systems and their conserved quantities the symmetry properties of stochastic dynamical systems described by a stochastic differential equation of stratonovich type and related conserved quantities are discussed extending previous results by misawa new conserved quantities are given by applying symmetry operators to known conserved quantities some detailed examples are presented

remarks on a recent theorem about conserved quantities a recently proved theorem is used to derive a conserved quantity associated with a velocity dependent symmetry for lagrangian systems in addition a generalization of the theorem is given

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

a monte carlo approach for change point detection in the cox proportional hazards model detecting a time lag of treatment effect or identifying change points in a hazard function is of great interest and importance in survival analysis the testing procedures hereto are primarily based on analytical approximations for the asymptotic null distribution of either the likelihood ratio test or the score test in the presence of random censoring and or covariates however the justification for the limiting distribution often requires some technical assumptions and conditions that are difficult to verify in practice moreover a satisfactory asymptotic theory for testing the existence of multiple change points in hazard function has not emerged in this paper we consider maximal score tests for detecting change point s in the cox proportional hazards model with censored data we propose to use a simple monte carlo approach for assessing the statistical significance of tests the proposed approach is applicable for testing a single change point in the cox model with covariates and sample stratifications over various types of candidate regions including discrete time point sets or disjoint intervals we also show that the proposed test statistics and the monte carlo procedure are well applicable under situations with multiple change points simulation studies and an analysis of a real data from a randomized cancer trial are conducted to demonstrate the finite sample performance of the proposed approach

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

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

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

likelihood ratio tests for a changepoint with survival data summary we consider the likelihood ratio test for a changepoint or lag of the effect of some covariates e g treatment in regression modelling of survival data subject to right censoring asymptotic distributions under null hypotheses are derived numerical examples are used to illustrate the implementation of the procedure finally we apply the theory to data from a large randomised cancer prevention trial

lagrangian structures integrability and chaos for 3d dynamical equations in this paper we consider the general setting for constructing action principles for three dimensional first order autonomous equations we present the results for some integrable and non integrable cases of the lotka volterra equation and show lagrangian descriptions which are valid for systems satisfying shil nikov criteria on the existence of strange attractors though chaotic behaviour has not been verified up to now the euler lagrange equations we get for these systems usually present time reparametrization invariance though other kinds of invariance may be found according to the kernel of the associated symplectic 2 form the formulation of a hamiltonian structure poisson brackets and hamiltonians for these systems from the lagrangian viewpoint leads to a method of finding new constants of the motion starting from known ones which is applied to some systems found in the literature known to possess a constant of the motion to find the other and thus showing their integrability in particular we show that the so called abc system is completely integrable if it possesses one constant of the motion

comment on a theorem of hojman and its generalizations an invariant derived using hojman s conservation law is shown to be trivial for all noether symmetries

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

likelihood ratio tests for multiple structural changes abstract this paper proposes a likelihood ratio type test for multiple structural changes in regression models the model allows for lagged dependent variables and trending regressors the limiting distribution of the test is derived we show that asymptotic critical values can be obtained analytically in addition the number and the locations of change points can be consistently determined via the test procedure the method is straightforward to implement

the cohomological span of ls conley index abstract in this paper we introduce a new homotopy invariant the cohomological span of ls conley index we prove the theorems on the existence of critical points for a class of strongly indefinite functionals with the gradient of the form l x k x where l is bounded linear and k is completely continuous we give examples of hamiltonian systems for which our methods give better results than the morse inequalities we also give a formula for the ls index of an isolated critical point which is an extension of the classical dancer theorem for the case of ls index

a cohomological conley index in hilbert spaces and applications to strongly indefinite problems abstract a cohomological conley index is defined for flows on infinite dimensional real hilbert spaces generated by vector fields of the form f h h f x lx k x where l h h is a bounded linear operator satisfying certain technical assumptions and k is a completely continuous perturbation generalized morse inequalities for morse decompositions of isolated invariant sets are proved simple examples are presented to show how the theory can be applied to strongly indefinite problems

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

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

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

new conserved quantities derived from symmetry for stochastic dynamical systems recently the author has proposed an elementary theory of conserved quantities and symmetry for stochastic dynamical systems described by stochastic differential equations of stratonovich type within the framework a new method for deriving conserved quantities from symmetry is developed in a similar manner to that of hojman s work 1992 which gives a new conservation law constructed without using either lagrangians or hamiltonians for deterministic dynamical systems some examples of the conserved quantities obtained through the new method are given

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

homotopy invariance of the conley index and local morse homology in hilbert spaces in this paper we introduce a new compactness condition property c for flows in not necessary locally compact metric spaces for such flows a conley type theory can be developed for example regular index pairs always exist for property c flows and a conley index can be defined an important class of flows satisfying the this compactness condition are ls flows we apply e cohomology to index pairs of ls flows and obtain the e cohomological conley index we formulate a continuation principle for the e cohomological conley index and show that all ls flows can be continued to ls gradient flows we show that the morse homology of ls gradient flows computes the e cohomological conley index we use lyapunov functions to define the morse conley floer cohomology in this context and show that it is also isomorphic to the e cohomological conley index

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

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

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

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

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

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

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

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

conservation laws for divergenceless differential equations a paper by hojman 1992 shows how to use a symmetry to construct a constant of the motion for a system of second order differential equations directly from the equations without using either a lagrangian or hamiltonian it is however necessary to impose some constraint on the nature of these equations this constraint is recognized as saying that the differential equation field is divergenceless with respect to some connection on the extended tangent bundle however for the simplest example of a lagrangian consisting of a kinetic energy and velocity independent potential all the conserved quantities constructed in this way from noether symmetries are identically zero the relation of this work to earlier work is pointed out

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

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

symmetries of lagrangians and of their equations of motion a new kind of lagrangian symmetry is defined in such a way that the resulting set of lagrangian symmetries coincides with the set of symmetries of its equations of motion several constants of motion may be associated to each of the new symmetry transformations one example is presented

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

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

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

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

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

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

geometric foundations of a new conservation law discovered by hojman the geometric foundations of a recent new conservation law obtained by hojman 1992 for second order differential equations are given

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

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

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

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

first integrals of holonomic systems without noether symmetries a theorem is proved that determines the first integrals of the form i kab t q qaqb ka t q qa k t q of autonomous holonomic systems using only the collineations of the kinetic metric that is defined by the kinetic energy or the lagrangian of the system it is shown how these first integrals can be associated via the inverse noether theorem with a gauged weak noether symmetry which admits the given first integral as a noether integral it is shown also that the associated noether symmetry is possible to satisfy the conditions for a hojman or a form invariance symmetry therefore the so called non noetherian first integrals are gauged weak noether integrals the application of the theorem requires a certain algorithm due to the complexity of the special conditions involved we demonstrate this algorithm by a number of solved examples we choose examples from published works in order to show that our approach produces new first integrals not found before with the standard methods

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

the likelihood ratio test for a change point in simple linear regression summary we consider likelihood ratio tests to detect a change point in simple linear regression a when the alternative specifies that only the intercept changes and b when the alternative permits the intercept and the slope to change approximations for the significance level are obtained under reasonably general assumptions about the empirical distribution of the independent variable the approximations are compared with simulations in order to assess their accuracy for the model in which only the intercept is allowed to change a confidence region for the change point and an approximate joint confidence region for the change point the difference in intercepts and the slope are obtained by inversion of the appropriate likelihood ratio tests

new derivation of a conserved quantity for lagrangian systems a new derivation of a recently discussed conserved quantity is given using a general procedure which determines n constants of the motion for any n dimensional system possessing a non noether symmetry

morse type index theory for flows and periodic solutions for hamiltonian equations an index theory for flows is presented which extends the classical morse theory for gradient flows on compact manifolds the theory is used to prove a morse type existence statement for periodic solutions of a time dependent periodic in time and asymptotically linear hamiltonian equation

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