Structural Nonparametric Cointegrating Regression

Nonparametric estimation of a structural cointegrating regression model is studied. As in the standard linear cointegrating regression model, the regressor and the dependent variable are jointly dependent and contemporaneously correlated. In nonparametric estimation problems, joint dependence is known to be a major complication that affects identification, induces bias in conventional kernel estimates, and frequently leads to ill-posed inverse problems. In functional cointegrating regressions where the regressor is an integrated time series, it is shown here that inverse and ill-posed inverse problems do not arise. Remarkably, nonparametric kernel estimation of a structural nonparametric cointegrating regression is consistent and the limit distribution theory is mixed normal, giving simple useable asymptotics in practical work. The results provide a convenient basis for inference in structural nonparametric regression with nonstationary time series. The methods may be applied to a wide range of empirical models where functional estimation of cointegrating relations is required.Brownian Local time, Cointegration, Functional regression, Gaussian process, Integrated process, Kernel estimate, Nonlinear functional, Nonparametric regression, Structural estimation, Unit root

Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression

We provide a new asymptotic theory for local time density estimation for a general class of functionals of integrated time series. This result provides a convenient basis for developing an asymptotic theory for nonparametric cointegrating regression and autoregression. Our treatment directly involves the density function of the processes under consideration and avoids Fourier integral representations and Markov process theory which have been used in earlier research on this type of problem. The approach provides results of wide applicability to important practical cases and involves rather simple derivations that should make the limit theory more accessible and useable in econometric applications. Our main result is applied to offer an alternative development of the asymptotic theory for non-parametric estimation of a non-linear cointegrating regression involving non-stationary time series. In place of the framework of null recurrent Markov chains as developed in recent work of Karlsen, Myklebust and Tjostheim (2007), the direct local time density argument used here more closely resembles conventional nonparametric arguments, making the conditions simpler and more easily verified.Brownian Local time, Cointegration, Integrated process, Local time density estimation, Nonlinear functionals, Nonparametric regression, Unit root

Functional Coefficient Panel Modeling with Communal Smoothing Covariates

Behavior at the individual level in panels or at the station level in spatial models is often influenced by aspects of the system in aggregate. In particular, the nature of the interaction between individual-specific explanatory variables and an individual dependent variable may be affected by `global’ variables that are relevant in decision making and shared communally by all individuals in the sample. To capture such behavioral features, we employ a functional coefficient panel model in which certain communal covariates may jointly influence panel interactions by means of their impact on the model coefficients. Two classes of estimation procedures are proposed, one based on station averaged data the other on the full panel, and their asymptotic properties are derived. Inference regarding the functional coefficient is also considered. The finite sample performance of the proposed estimators and tests are examined by simulation. An empirical spatial model illustration is provided in which the climate sensitivity of temperature to atmospheric CO_2 concentration is studied at both station and global levels

Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression

We provide a new asymptotic theory for local time density estimation for a general class of functionals of integrated time series. This result provides a convenient basis for developing an asymptotic theory for nonparametric cointegrating regression and autoregression. Our treatment directly involves the density function of the processes under consideration and avoids Fourier integral representations and Markov process theory which have been used in earlier research on this type of problem. The approach provides results of wide applicability to important practical cases and involves rather simple derivations that should make the limit theory more accessible and useable in econometric applications. Our main result is applied to offer an alternative development of the asymptotic theory for non-parametric estimation of a non-linear cointegrating regression involving non-stationary time series. In place of the framework of null recurrent Markov chains as developed in recent work of Karlsen, Myklebust and Tjostheim (2007), the direct local time density argument used here more closely resembles conventional nonparametric arguments, making the conditions simpler and more easily verified

Asymptotic Theory for Zero Energy Density Estimation with Nonparametric Regression Applications

A local limit theorem is given for the sample mean of a zero energy function of a nonstationary time series involving twin numerical sequences that pass to infinity. The result is applicable in certain nonparametric kernel density estimation and regression problems where the relevant quantities are functions of both sample size and bandwidth. An interesting outcome of the theory in nonparametric regression is that the linear term is eliminated from the asymptotic bias. In consequence and in contrast to the stationary case, the Nadaraya-Watson estimator has the same limit distribution (to the second order including bias) as the local linear nonparametric estimator

Pileup Behavior in Sharp Nanoindentation of AISI 1045 Steel

AbstractExperimental measurements have been used to investigate the pileup behavior during nanoindentation with a sharp indenter. The AISI 1045 steels treated by quenching and annealing were examined. The results show that during sharp nanoindentation process, the amount of pileup is related to the residual stress state, the indentation depth and the work hardening. The quenched steel with compressive residual stress will tend to pile up, and the stress-free annealed steel can decrease the pileup height. It is found that the pileup height gradually increases for the two steels as the indentation depth becomes larger. It is also shown that the low work hardening of the two steels can also result in the pileup deformation

A Study of the Cyclone Fractional Efficiency Curves

Rosana G. Moreira, Editor-in-Chief; Texas A&M UniversityThis is a Technical Article from International Commission of Agricultural Engineering (CIGR, Commission Internationale du Genie Rural) E-Journal Volume 4 (2002): L. Wang, C.B. Parnell and B.W. Shaw. A Study of the Cyclone Fractional Efficiency Curves. Vol. IV. June 2002

Weak Convergence to Stochastic Integrals for Econometric Applications

Limit theory involving stochastic integrals is now widespread in time series econometrics and relies on a few key results on function space weak convergence. In establishing weak convergence of sample covariances to stochastic integrals, the literature commonly uses martingale and semimartingale structures. While these structures have wide relevance, many applications in econometrics involve a cointegration framework where endogeneity and nonlinearity play a major role and lead to complications in the limit theory. This paper explores weak convergence limit theory to stochastic integral functionals in such settings. We use a novel decomposition of sample covariances of functions of I(1) and I(0) time series that simplifies the asymptotic development and we provide limit results for such covariances when linear process, long memory, and mixing variates are involved in the innovations. The limit results extend earlier findings in the literature, are relevant in many econometric applications, and involve simple conditions that facilitate implementation in practice. A nonlinear extension of FM regression is used to illustrate practical application of the methods

Latent Variable Nonparametric Cointegrating Regression

This paper studies the asymptotic properties of empirical nonparametric regressions that partially misspecify the relationships between nonstationary variables. In particular, we analyze nonparametric kernel regressions in which a potential nonlinear cointegrating regression is misspecified through the use of a proxy regressor in place of the true regressor. Such regressions arise naturally in linear and nonlinear regressions where the regressor suffers from measurement error or where the true regressor is a latent variable. The model considered allows for endogenous regressors as the latent variable and proxy variables that cointegrate asymptotically with the true latent variable. Such a framework includes correctly specified systems as well as misspecified models in which the actual regressor serves as a proxy variable for the true regressor. The system is therefore intermediate between nonlinear nonparametric cointegrating regression (Wang and Phillips, 2009a, 2009b) and completely misspecified nonparametric regressions in which the relationship is entirely spurious (Phillips, 2009). The asymptotic results relate to recent work on dynamic misspecification in nonparametric nonstationary systems by Kasparis and Phillips (2012) and Duffy (2014). The limit theory accommodates regressor variables with autoregressive roots that are local to unity and whose errors are driven by long memory and short memory innovations, thereby encompassing applications with a wide range of economic and financial time series

Homogeneity Pursuit in Panel Data Models: Theory and Applications

This paper studies estimation of a panel data model with latent structures where individuals can be classified into different groups where slope parameters are homogeneous within the same group but heterogeneous across groups. To identify the unknown group structure of vector parameters, we design an algorithm called Panel-CARDS which is a systematic extension of the CARDS procedure proposed by Ke, Fan, and Wu (2015) in a cross section framework. The extension addresses the problem of comparing vector coefficients in a panel model for homogeneity and introduces a new concept of controlled classification of multidimensional quantities called the segmentation net. We show that the Panel-CARDS method identifies group structure asymptotically and consistently estimates model parameters at the same time. External information on the minimum number of elements within each group is not required but can be used to improve the accuracy of classification and estimation in finite samples. Simulations evaluate performance and corroborate the asymptotic theory in several practical design settings. Two empirical economic applications are considered: one explores the effect of income on democracy by using cross-country data over the period 1961-2000; the other examines the effect of minimum wage legislation on unemployment in 50 states of the United States over the period 1988-2014. Both applications reveal the presence of latent groupings in these panel data