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Full-Text Articles in Social and Behavioral Sciences
Latent Variable Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips, Ioannis Kasparis
Latent Variable Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips, Ioannis Kasparis
Cowles Foundation Discussion Papers
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 …
Sequentially Testing Polynomial Model Hypotheses Using Power Transforms Of Regressors, Jin Seo Cho, Peter C.B. Phillips
Sequentially Testing Polynomial Model Hypotheses Using Power Transforms Of Regressors, Jin Seo Cho, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We provide a methodology for testing a polynomial model hypothesis by extending the approach and results of Baek, Cho, and Phillips (2015; Journal of Econometrics; BCP) that tests for neglected nonlinearity using power transforms of regressors against arbitrary nonlinearity. We examine and generalize the BCP quasi-likelihood ratio test dealing with the multifold identification problem that arises under the null of the polynomial model. The approach leads to convenient asymptotic theory for inference, has omnibus power against general nonlinear alternatives, and allows estimation of an unknown polynomial degree in a model by way of sequential testing, a technique that is useful …
Sieve Inference On Semi-Nonparametric Time Series Models, Xiaohong Chen, Zhipeng Liao, Yixiao Sun
Sieve Inference On Semi-Nonparametric Time Series Models, Xiaohong Chen, Zhipeng Liao, Yixiao Sun
Cowles Foundation Discussion Papers
The method of sieves has been widely used in estimating semiparametric and nonparametric models. In this paper, we first provide a general theory on the asymptotic normality of plug-in sieve M estimators of possibly irregular functionals of semi/nonparametric time series models. Next, we establish a surprising result that the asymptotic variances of plug-in sieve M estimators of irregular (i.e., slower than root-T estimable) functionals do not depend on temporal dependence. Nevertheless, ignoring the temporal dependence in small samples may not lead to accurate inference. We then propose an easy-to-compute and more accurate inference procedure based on a “pre-asymptotic” sieve variance …
Optimal Comparison Of Misspecified Moment Restriction Models Under A Chosen Measure Of Fit, Vadim Marmer, Taisuke Otsu
Optimal Comparison Of Misspecified Moment Restriction Models Under A Chosen Measure Of Fit, Vadim Marmer, Taisuke Otsu
Cowles Foundation Discussion Papers
Suppose that the econometrician is interested in comparing two misspecified moment restriction models, where the comparison is performed in terms of some chosen measure of fit. This paper is concerned with describing an optimal test of the Vuong (1989) and Rivers and Vuong (2002) type null hypothesis that the two models are equivalent under the given measure of fit (the ranking may vary for different measures). We adopt the generalized Neyman-Pearson optimality criterion, which focuses on the decay rates of the type I and II error probabilities under fixed non-local alternatives, and derive an optimal but practically infeasible test. Then, …
Dynamic Misspecification In Nonparametric Cointegrating Regression, Ioannis Kasparis, Peter C.B. Phillips
Dynamic Misspecification In Nonparametric Cointegrating Regression, Ioannis Kasparis, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Linear cointegration is known to have the important property of invariance under temporal translation. The same property is shown not to apply for nonlinear cointegration. The requisite limit theory involves sample covariances of integrable transformations of non-stationary sequences and time translated sequences, allowing for the presence of a bandwidth parameter so as to accommodate kernel regression. The theory is an extension of Wang and Phillips (2008) and is useful for the analysis of nonparametric regression models with a misspecified lag structure and in situations where temporal aggregation issues arise. The limit properties of the Nadaraya-Watson (NW) estimator for cointegrating regression …
Trends Versus Random Walks In Time Series Analysis, Steven N. Durlauf, Peter C.B. Phillips
Trends Versus Random Walks In Time Series Analysis, Steven N. Durlauf, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies the effects of spurious detrending in regression. The asymptotic behavior of traditional least squares estimators and tests are examined in the context of models where the generating mechanism is systematically misspecified by the presence of deterministic time trends. Most previous work on the subject has relied upon Monte Carlo studies to understand the issues involved in detrending data that is generated by integrated processes and our analytical results help to shed light on many of the simulation findings. Standard F tests and Hausman tests are shown to inadequately discriminate between the competing hypotheses. Durbin-Watson statistics, on the …