mode identification of volatility in time varying autoregression in many applications time series exhibit nonstationary behavior that might reasonably be modeled as a time varying autoregressive ar process in the context of such a model we discuss the problem of testing for modality of the variance function we propose a test of modality that is local and when used iteratively can be used to identify the total number of modes in a given series this problem is closely related to peak detection and identification which has applications in many fields we propose a test that under appropriate assumptions is asymptotically distribution free under the null hypothesis even though nonparametric estimation of the ar parameter functions is involved simulation studies and applications to real datasets illustrate the behavior of the test

asymptotic optimality of cl and generalized cross validation in ridge regression with application to spline smoothing the asymptotic optimality of mallows c l and generalized cross validation is demonstrated in the setting of ridge regression an application is made to spline smoothing in nonparametric regression a counterexample is given to help understand why sometimes gcv may not be asymptotically optimal the coefficient of variation for the eigenvalues of the information matrix must be large in order to guarantee the optimality of gcv the proff is based on the connection between gcv and stein s unbiased risk estimate

fitting time series models to nonstationary processes a general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation the asymptotic properties of the estimate are derived under the assumption of possible model misspecification for autoregressive processes with time varying coefficients the estimate is compared to the least squares estimate furthermore the behavior of estimates is explained when a stationary model is fitted to a nonstationary process

evaluation of the constant strain triangle with drilling rotations the performance of the constant strain triangle with added drilling rotations is evaluated by solving a variety of plane test problems numerical results confirm that the new element is always superior to the standard constant strain triangle and that it is of similar accuracy to the best available alternative triangular elements of other authors it is however less accurate than some rectangular elements which include drilling rotations

specification of varying coefficient time series models via generalized flexible least squares abstract flexible least squares fls is a method for recursively estimating the time paths of the coefficients of a regression model with time varying coefficients in its standard form the fls solution is capable of capturing smooth changes of the coefficients over the sample period for time series models erratic coefficient changes for instance due to seasonal variation are possible a generalization of fls is proposed which can account for such phenomena the method is applied to artificially generated as well as real economic data specifically west german income and consumption time series are analyzed in some detail

semiparametric model building for regression models with time varying parameters abstract this paper considers the problem of semiparametric model building for linear regression models with potentially time varying coefficients by allowing the response variable and explanatory variables be jointly a nonstationary process the proposed methods are widely applicable to nonstationary and dependent observations we propose a local linear shrinkage method that can simultaneously achieve parameter estimation and variable selection its selection consistency and the favorable oracle property are established due to the fear of losing efficiency an information criterion is further proposed for distinguishing between time varying and time constant components numerical examples are presented to illustrate the proposed methods

a likelihood approximation for locally stationary processes a new approximation to the gaussian likelihood of a multivariate locally stationary process is introduced it is based on an approximation of the inverse of the covariance matrix of such processes the new quasi likelihood is a generalisation of the classical whittle likelihood for stationary processes for parametric models asymptotic normality and efficiency of the resulting estimator are proved since the likelihood has a special local structure it can be used for nonparametric inference as well this is briefly sketched for different estimates

trigonometric collocation methods with product integration for boundary integral equations on closed curves considering boundary integral equations on smooth closed curves the product integration methods have turned out to be very efficient to define fully discrete schemes with a high convergence rate here we give a general approach to product integration methods in connection with the trigonometric collocation the discretization scheme has arbitrarily high convergence rate even exponential if the solution and the curve are analytic applications and numerical experiments confirming our theoretical results are discussed

an efficient estimator for locally stationary gaussian long memory processes this paper addresses the estimation of locally stationary long range dependent processes a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency a time varying parametric formulation of these models is introduced and a whittle likelihood technique is proposed for estimating the parameters involved large sample properties of these whittle estimates such as consistency normality and efficiency are established in this work furthermore the finite sample behavior of the estimators is investigated through monte carlo experiments as a result from these simulations we show that the estimates behave well even for relatively small sample sizes

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

boosting high dimensional predictive regressions with time varying parameters abstract high dimensional predictive regressions are useful in wide range of applications however the theory is mainly developed assuming that the model is stationary with time invariant parameters this is at odds with the prevalent evidence for parameter instability in economic time series but theories for parameter instability are mainly developed for models with a small number of covariates in this paper we present two l 2 boosting algorithms for estimating high dimensional models in which the coefficients are modeled as functions evolving smoothly over time and the predictors are locally stationary the first method uses componentwise local constant estimators as base learner while the second relies on componentwise local linear estimators we establish consistency of both methods and address the practical issues of choosing the bandwidth for the base learners and the number of boosting iterations in an extensive application to macroeconomic forecasting with many potential predictors we find that the benefits to modeling time variation are substantial and they increase with the forecast horizon furthermore the timing of the benefits suggests that the great moderation is associated with substantial instability in the conditional mean of various economic series

nonparametric estimation of time varying parameters under shape restrictions in recent years a lot of econometric literature has been devoted to estimating time varying coefficients in regression models here a new method based on smoothers is proposed which is able to introduce shape restrictions over the coefficients the statistical properties of the estimator are obtained for very general situations including locally stationary regressors in particular the procedure provides consistent results for time varying autoregressive models the practical problem of implementation is also addressed a data driven method for selecting the control parameters is provided together with an algorithm that reduces the computational cost a simulation study and an application to real data supports the theoretical results

adaptive forecasting in the presence of recent and ongoing structural change we consider time series forecasting in the presence of ongoing structural change where both the time series dependence and the nature of the structural change are unknown methods that downweight older data such as rolling regressions forecast averaging over different windows and exponentially weighted moving averages known to be robust to historical structural change are found to be also useful in the presence of ongoing structural change in the forecast period a crucial issue is how to select the degree of downweighting usually defined by an arbitrary tuning parameter we make this choice data dependent by minimizing forecast mean square error and provide a detailed theoretical analysis of our proposal monte carlo results illustrate the methods we examine their performance on 191 uk and us macro series forecasts using data based tuning of the data discount rate are shown to perform well

testing for parallelism among trends in multiple time series this paper considers the inference of trends in multiple nonstationary time series to test whether trends are parallel to each other we use a parallelism index based on the l2 distances between nonparametric trend estimators and their average a central limit theorem is obtained for the test statistic and the test s consistency is established we propose a simulation based approximation to the distribution of the test statistic which significantly improves upon the normal approximation the test is also applied to devise a clustering algorithm finally the finite sample properties of the test are assessed through simulations and the test methodology is illustrated by a cell phone download data collected in the united states

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail

smooth coefficient estimation of a seemingly unrelated regression abstract this paper proposes estimation and inference for the semiparametric smooth coefficient seemingly unrelated regression model we discuss the imposition of cross equation restrictions which are required by economic theory as well as methods for data driven bandwidth selection a test of correct functional form for the entire system of equations is also constructed asymptotic and finite sample results are given we illustrate our estimator by applying it to a cost system for us commercial banks our results show that most of the banks are operating under increasing returns to scale but that returns to scale decrease with bank size

simultaneous inference of linear models with time varying coefficients summary the paper considers construction of simultaneous confidence tubes for time varying regression coefficients in functional linear models using a gaussian approximation result for non stationary multiple time series we show that the constructed simultaneous confidence tubes have asymptotically correct nominal coverage probabilities our results are applied to the problem of testing whether the regression coefficients are of certain parametric forms which is a fundamental problem in the inference of functional linear models as an application we analyse an environmental data set and study the association between levels of pollutants and hospital admissions