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Full-Text Articles in Economics
New Asymptotics Applied To Functional Coefficient Regression And Climate Sensitivity Analysis, Qiying Wang, Peter C. B. Phillips, Ying Wang
New Asymptotics Applied To Functional Coefficient Regression And Climate Sensitivity Analysis, Qiying Wang, Peter C. B. Phillips, Ying Wang
Cowles Foundation Discussion Papers
A general asymptotic theory is established for sample cross moments of nonstationary time series, allowing for long range dependence and local unit roots. The theory provides a substantial extension of earlier results on nonparametric regression that include near-cointegrated nonparametric regression as well as spurious nonparametric regression. Many new models are covered by the limit theory, among which are functional coefficient regressions in which both regressors and the functional covariate are nonstationary. Simulations show finite sample performance matching well with the asymptotic theory and having broad relevance to applications, while revealing how dual nonstationarity in regressors and covariates raises sensitivity to …
On Multicointegration, Peter C. B. Phillips, Igor Kheifets
On Multicointegration, Peter C. B. Phillips, Igor Kheifets
Cowles Foundation Discussion Papers
A semiparametric triangular systems approach shows how multicointegration can occur naturally in an I(1) cointegrated regression model. The framework reveals the source of multicointegration as singularity of the long run error covariance matrix in an I(1) system, a feature noted but little explored in earlier work. Under such singularity, cointegrated I(1) systems embody a multicointegrated structure and may be analyzed and estimated without appealing to the associated I(2) system but with consequential asymptotic properties that can introduce asymptotic bias into conventional methods of cointegrating regression. The present paper shows how estimation of such systems may be accomplished under multicointegration without …
Copula-Based Time Series With Filtered Nonstationarity, Xiaohong Chen, Zhijie Xiao, Bo Wang
Copula-Based Time Series With Filtered Nonstationarity, Xiaohong Chen, Zhijie Xiao, Bo Wang
Cowles Foundation Discussion Papers
Economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously. This paper studies copula-based time series models that capture both patterns. We introduce a procedure where nonstationarity is removed via a filtration, and then the nonlinear temporal dependence in the filtered data is captured via a flexible Markov copula. We propose two estimators of the copula dependence parameters: the parametric (two-step) copula estimator where the marginal distribution of the filtered series is estimated parametrically; and the semiparametric (two-step) copula estimator where the marginal distribution is estimated via a rescaled empirical distribution of the filtered series. We show …
Fully Modified Least Squares For Multicointegrated Systems, Igor Kheifets, Peter C.B. Phillips
Fully Modified Least Squares For Multicointegrated Systems, Igor Kheifets, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model that introduces links between these variables and partial sums of the equilibrium errors. This paper departs from the parametric model, using a semiparametric formulation that reveals the explicit role that singularity of the long run conditional covariance matrix plays in determining multicointegration. The semiparametric framework has the advantage that short run dynamics do not need to be modeled and estimation by standard techniques such as fully modified least squares (FM-OLS) on the original I(1) system is straightforward. The paper derives FM-OLS limit …
Dynamic Panel Modeling Of Climate Change, Peter C.B. Phillips
Dynamic Panel Modeling Of Climate Change, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We discuss some conceptual and practical issues that arise from the presence of global energy balance effects on station level adjustment mechanisms in dynamic panel regressions with climate data. The paper provides asymptotic analyses, observational data computations, and Monte Carlo simulations to assess the use of various estimation methodologies, including standard dynamic panel regression and cointegration techniques that have been used in earlier research. The findings reveal massive bias in system GMM estimation of the dynamic panel regression parameters, which arise from fixed effect heterogeneity across individual station level observations. Difference GMM and Within Group (WG) estimation have little bias …
Kernel-Based Inference In Time-Varying Coefficient Cointegrating Regression, Degui Li, Peter C.B. Phillips, Jiti Gao
Kernel-Based Inference In Time-Varying Coefficient Cointegrating Regression, Degui Li, Peter C.B. Phillips, Jiti Gao
Cowles Foundation Discussion Papers
This paper studies nonlinear cointegrating models with time-varying coefficients and multiple nonstationary regressors using classic kernel smoothing methods to estimate the coefficient functions. Extending earlier work on nonstationary kernel regression to take account of practical features of the data, we allow the regressors to be cointegrated and to embody a mixture of stochastic and deterministic trends, complications which result in asymptotic degeneracy of the kernel-weighted signal matrix. To address these complications new \textsl{local} and \textsl{global rotation} techniques are introduced to transform the covariate space to accommodate multiple scenarios of induced degeneracy. Under certain regularity conditions we derive asymptotic results that …
Econometric Measurement Of Earth's Transient Climate Sensitivity, Peter C.B. Phillips, Thomas Leirvik, Trude Storelvmo
Econometric Measurement Of Earth's Transient Climate Sensitivity, Peter C.B. Phillips, Thomas Leirvik, Trude Storelvmo
Cowles Foundation Discussion Papers
How sensitive is Earth’s climate to a given increase in atmospheric greenhouse gas (GHG) concentrations? This long-standing and fundamental question in climate science was recently analyzed by dynamic panel data methods using extensive spatiotemporal data of global surface temperatures, solar radiation, and GHG concentrations over the last half century to 2010 (Storelvmo et al, 2016). These methods revealed that atmospheric aerosol effects masked approximately one-third of the continental warming due to increasing GHG concentrations over this period, thereby implying greater climate sensitivity to GHGs than previously thought. The present study provides asymptotic theory justifying the use of these methods when …
Uniform Consistency Of Nonstationary Kernel-Weighted Sample Covariances For Nonparametric Regression, Degui Li, Peter C.B. Phillips, Jiti Gao
Uniform Consistency Of Nonstationary Kernel-Weighted Sample Covariances For Nonparametric Regression, Degui Li, Peter C.B. Phillips, Jiti Gao
Cowles Foundation Discussion Papers
We obtain uniform consistency results for kernel-weighted sample covariances in a nonstationary multiple regression framework that allows for both fixed design and random design coefficient variation. In the fixed design case these nonparametric sample covariances have different uniform convergence rates depending on direction, a result that differs fundamentally from the random design and stationary cases. The uniform convergence rates derived are faster than the corresponding rates in the stationary case and confirm the existence of uniform super-consistency. The modelling framework and convergence rates allow for endogeneity and thus broaden the practical econometric import of these results. As a specific application, …
Functional Coefficient Nonstationary Regression, Jiti Gao, Peter C.B. Phillips
Functional Coefficient Nonstationary Regression, Jiti Gao, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper studies a general class of nonlinear varying coefficient time series models with possible nonstationarity in both the regressors and the varying coffiecient components. The model accommodates a cointegrating structure and allows for endogeneity with contemporaneous correlation among the regressors, the varying coefficient drivers, and the residuals. This framework allows for a mixture of stationary and non-stationary data and is well suited to a variety of models that are commonly used in applied econometric work. Nonparametric and semiparametric estimation methods are proposed to estimate the varying coefficient functions. The analytical findings reveal some important differences, including convergence rates, that …
Asymptotic Theory For Zero Energy Density Estimation With Nonparametric Regression Applications, Qiying Wang, Peter C.B. Phillips
Asymptotic Theory For Zero Energy Density Estimation With Nonparametric Regression Applications, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
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 …
Unit Root And Cointegrating Limit Theory When Initialization Is In The Infinite Past, Peter C.B. Phillips, Tassos Magdalinos
Unit Root And Cointegrating Limit Theory When Initialization Is In The Infinite Past, Peter C.B. Phillips, Tassos Magdalinos
Cowles Foundation Discussion Papers
It is well known that unit root limit distributions are sensitive to initial conditions in the distant past. If the distant past initialization is extended to the infinite past, the initial condition dominates the limit theory producing a faster rate of convergence, a limiting Cauchy distribution for the least squares coefficient and a limit normal distribution for the t ratio. This amounts to the tail of the unit root process wagging the dog of the unit root limit theory. These simple results apply in the case of a univariate autoregression with no intercept. The limit theory for vector unit root …
Structural Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Structural Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
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 …
Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression, Qiying Wang, Peter C.B. Phillips
Cowles Foundation Discussion Papers
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. …
A New Approach To Robust Inference In Cointegration, Sainan Jin, Peter C.B. Phillips, Yixiao Sun
A New Approach To Robust Inference In Cointegration, Sainan Jin, Peter C.B. Phillips, Yixiao Sun
Cowles Foundation Discussion Papers
A new approach to robust testing in cointegrated systems is proposed using nonparametric HAC estimators without truncation. While such HAC estimates are inconsistent, they still produce asymptotically pivotal tests and, as in conventional regression settings, can improve testing and inference. The present contribution makes use of steep origin kernels which are obtained by exponentiating traditional quadratic kernels. Simulations indicate that tests based on these methods have improved size properties relative to conventional tests and better power properties than other tests that use Bartlett or other traditional kernels with no truncation.
End-Of-Sample Cointegration Breakdown Tests, Donald W.K. Andrews, Jae-Young Kim
End-Of-Sample Cointegration Breakdown Tests, Donald W.K. Andrews, Jae-Young Kim
Cowles Foundation Discussion Papers
This paper introduces tests for cointegration breakdown that may occur over a relatively short time period, such as at the end of the sample. The breakdown may be due to a shift in the cointegrating vector or due to a shift in the errors from being I (0) to being I (1). Tests are introduced based on the post-breakdown sum of squared residuals and the post-breakdown sum of squared reverse partial sums of residuals. Critical values are provided using a parametric subsampling method. The regressors in the model are taken to be arbitrary linear combinations of deterministic, stationary, and integrated …
Bootstrapping Spurious Regression, Peter C.B. Phillips
Bootstrapping Spurious Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap effectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coefficient of the residuals in the bootstrap regression does not converge to unity, so the bootstrap is not even first order consistent. The block bootstrap serial correlation coefficient does converge to unity and is therefore first order consistent, but has a slower rate of convergence and a different limit distribution from that of the sample data serial correlation coefficient. The analysis covers spurious regressions involving …
Automated Forecasts Of Asia-Pacific Economic Activity, Peter C.B. Phillips
Automated Forecasts Of Asia-Pacific Economic Activity, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper reports quarterly ex ante forecasts of macroeconomic activity for the U.S.A., Japan and Australia for the period 1995-1997. The forecasts are based on automated time series models of vector autoregressions (VAR’s), reduced rank regressions (RRR’s), error correction models (ECM’s) and Bayesian vector autoregressions (BVAR’s). The models are automated by using an asymptotic predictive form of the model selection criterion PIC to determine autoregressive lag order, cointegrating rank and trend degree in the VAR’s, RRR’s, and ECM’s. The same criterion is used to find optimal values of the hyperparameters in the BVAR’s. The forecasts are graphed and tabulated. In …
Fully Modified Iv, Give And Gmm Estimation With Possibly Non-Stationary Regressions And Instruments, Yuichi Kitamura, Peter C.B. Phillips
Fully Modified Iv, Give And Gmm Estimation With Possibly Non-Stationary Regressions And Instruments, Yuichi Kitamura, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops a general theory of instrumental variables (IV) estimation that allows for both I(1) and I(0) regressors and instruments. The estimation techniques involve an extension of the fully modified (FM) regression procedure that was introduced in earlier work by Phillips-Hansen (1990). FM versions of the generalized instrumental variable estimation (GIVE) method and the generalized method of moments (GMM) estimator are developed. In models with both stationary and nonstationary components, the FM-GIVE and FM-GMM techniques provide efficiency gains over FM-IV in the estimation of the stationary components of a model that has both stationary and nonstationary regressors. The paper …
The Tail Behavior Of Maximum Likelihood Estimates Of Cointegrating Coefficients In Error Correction Models, Peter C.B. Phillips
The Tail Behavior Of Maximum Likelihood Estimates Of Cointegrating Coefficients In Error Correction Models, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper derives exact finite sample distributions of maximum likelihood estimators of the cointegrating coefficients in error correction models. The distributions are derived for the leading case where the variables in the system are independent random walks. But important aspects of the theory, in particular the tail behavior of the distributions, continue to apply when the system is cointegrated. The reduced rank regression estimator is shown to have a distribution with Cauchy-like tails and no finite moments of integer order. The maximum likelihood estimator of the coefficients in the triangular system representation has matrix t -distribution tails with finite integer …
Unidentified Components In Reduced Rank Regression Estimation Of Ecm's, Peter C.B. Phillips
Unidentified Components In Reduced Rank Regression Estimation Of Ecm's, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Reduced rank regression procedures in error correction models (ECM’s) permit consistent estimation of the cointegration space but do not provide consistent estimates of individual structural relations when the dimension of the cointegration space is greater than one. Indeed, individual structural cointegrating equations are unidentified without additional a priori restrictions, just as in the conventional simultaneous equations framework. The effect of this lack of identification is explored by considering the distributions and limit distributions of reduced rank regression estimates of unidentified components of the cointegrating matrix in a typical VAR formulation of the ECM. Some recommendations are made for empirical practice.
Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips
Statistical Inference In Regressions With Integrated Processes: Part 1, Joon Y. Park, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F -tests is explored and new transformations are introduced to deal with these dependencies. Some specializations of our theory are considered in detail. In models with strictly exogenous regressors we demonstrate the validity of conventional asymptotic theory for appropriately constructed Wald tests. These tests provide a simple …
Regression Theory For Near-Integrated Time Series, Peter C.B. Phillips
Regression Theory For Near-Integrated Time Series, Peter C.B. Phillips
Cowles Foundation Discussion Papers
The concept of a near-integrated vector random process is introduced. Such processes help us to work towards a general asymptotic theory of regression for multiple time series in which some series may be integrated processes of the ARIMA type, others may be stable ARMA processes with near unit roots, and yet others may be mildly explosive. A limit theory for the sample moments of such time series is developed using weak convergence and is shown to involve a simple functionals of a vector diffusion. The results suggest finite sample approximations which in the stationary case correspond to conventional central limit …