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Full-Text Articles in Social and Behavioral Sciences
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 …
A General Limit Theory For Nonlinear Functionals Of Nonstationary Time Series, Qiying Wang, Peter C. B. Phillips
A General Limit Theory For Nonlinear Functionals Of Nonstationary Time Series, Qiying Wang, Peter C. B. Phillips
Cowles Foundation Discussion Papers
Limit theory is provided for a wide class of covariance functionals of
a nonstationary process and stationary time series. The results are relevant
to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root or fractional processes and they include both parametric and nonparametric regressions. Self normalized versions of these
statistics are considered that are useful in inference. Numerical evidence reveals a strong bimodality in the finite sample distributions that persists for very large sample sizes although the limit theory is Gaussian. New self normalized versions are introduced that deliver improved approximations.
Discrete Fourier Transforms Of Fractional Processes With Econometric Applications, Peter C. B. Phillips
Discrete Fourier Transforms Of Fractional Processes With Econometric Applications, Peter C. B. Phillips
Cowles Foundation Discussion Papers
The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process. This representation is particularly useful in analyzing the asymptotic behavior of the dft and periodogram in the nonstationary case when the memory parameter d ≥ 1 2: Various asymptotic approximations are established including some new hypergeometric function representations that are of independent interest. It is shown that smoothed periodogram spectral estimates remain consistent for frequencies away from the origin in the nonstationary …
When Bias Contributes To Variance: True Limit Theory In Functional Coefficient Cointegrating Regression, Peter C. B. Phillips, Ying Wang
When Bias Contributes To Variance: True Limit Theory In Functional Coefficient Cointegrating Regression, Peter C. B. Phillips, Ying Wang
Cowles Foundation Discussion Papers
Limit distribution theory in the econometric literature for functional coefficient cointegrating (FCC) regression is shown to be incorrect in important ways, influencing rates of convergence, distributional properties, and practical work. In FCC regression the cointegrating coefficient vector \beta(.) is a function of a covariate z_t. The true limit distribution of the local level kernel estimator of \beta(.) is shown to have multiple forms, each form depending on the bandwidth rate in relation to the sample size n and with an optimal convergence rate of n^{3/4} which is achieved by letting the bandwidth have order 1/n^{1/2}.when z_t is scalar. Unlike stationary …
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 …
Nonlinear Cointegrating Power Function Regression With Endogeneity, Zhishui Hu, Peter C.B. Phillips, Qiying Wang
Nonlinear Cointegrating Power Function Regression With Endogeneity, Zhishui Hu, Peter C.B. Phillips, Qiying Wang
Cowles Foundation Discussion Papers
This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and financial applications, including predictive regression. Accompanying the asymptotic theory of nonlinear regression, the paper establishes some new results on weak convergence to stochastic integrals that go beyond the usual semi-martingale structure and considerably extend existing limit theory, complementing other recent findings on stochastic integral asymptotics. The paper also provides a general framework for extremum estimation limit theory that …
Semiparametric Estimation In Time Series Of Simultaneous Equations, Jiti Gao, Peter C.B. Phillips
Semiparametric Estimation In Time Series Of Simultaneous Equations, Jiti Gao, Peter C.B. Phillips
Cowles Foundation Discussion Papers
A system of vector semiparametric nonlinear time series models is studied with possible dependence structures and nonstationarities in the parametric and nonparametric components. The parametric regressors may be endogenous while the nonparametric regressors are strictly exogenous and represent trends. The parametric regressors may be stationary or nonstationary and the nonparametric regressors are nonstationary time series. This framework allows for the nonparametric treatment of stochastic trends and subsumes many practical cases. Semiparametric least squares (SLS) estimation is considered and its asymptotic properties are derived. Due to endogeneity in the parametric regressors, SLS is generally inconsistent for the parametric component and a …
Nonparametric Structural Estimation Via Continuous Location Shifts In An Endogenous Regressor, Peter C.B. Phillips, Liangjun Su
Nonparametric Structural Estimation Via Continuous Location Shifts In An Endogenous Regressor, Peter C.B. Phillips, Liangjun Su
Cowles Foundation Discussion Papers
Recent work by Wang and Phillips (2009b, c) has shown that ill posed inverse problems do not arise in nonstationary nonparametric regression and there is no need for nonparametric instrumental variable estimation. Instead, simple Nadaraya Watson nonparametric estimation of a (possibly nonlinear) cointegrating regression equation is consistent with a limiting (mixed) normal distribution irrespective of the endogeneity in the regressor, near integration as well as integration in the regressor, and serial dependence in the regression equation. The present paper shows that some closely related results apply in the case of structural nonparametric regression with independent data when there are continuous …
A Paradox Of Inconsistent Parametric And Consistent Nonparametric Regression, Peter C.B. Phillips, Liangjun Su
A Paradox Of Inconsistent Parametric And Consistent Nonparametric Regression, Peter C.B. Phillips, Liangjun Su
Cowles Foundation Discussion Papers
This paper explores a paradox discovered in recent work by Phillips and Su (2009). That paper gave an example in which nonparametric regression is consistent whereas parametric regression is inconsistent even when the true regression functional form is known and used in regression. This appears to be a paradox, as knowing the true functional form should not in general be detrimental in regression. In the present case, local regression methods turn out to have a distinct advantage because of endogeneity in the regressor. The paradox arises because additional correct information is not necessarily advantageous when information is incomplete. In the …
Log Periodogram Regression: The Nonstationary Case, Chang Sik Kim, Peter C.B. Phillips
Log Periodogram Regression: The Nonstationary Case, Chang Sik Kim, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Estimation of the memory parameter ( d ) is considered for models of nonstationary fractionally integrated time series with d > (1/2). It is shown that the log periodogram regression estimator of d is inconsistent when 1 < d < 2 and is consistent when (1/2) < d = 1. For d > 1, the estimator is shown to converge in probability to unity.
Challenges Of Trending Time Series Econometrics, Peter C.B. Phillips
Challenges Of Trending Time Series Econometrics, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We discuss some challenges presented by trending data in time series econometrics. To the empirical economist there is little guidance from theory about the source of trend behavior and even less guidance about practical formulations. Moreover, recent proximity theorems reveal that trends are more elusive to model empirically than stationary processes, with the upshot that optimal forecasts are also harder to estimate when the data involve trends. These limitations are implicitly acknowledged in much practical modeling and forecasting work, where adaptive methods are often used to help keep models on track as trends evolve. The paper discusses these broader issues …
Laws And Limits Of Econometrics, Peter C.B. Phillips
Laws And Limits Of Econometrics, Peter C.B. Phillips
Cowles Foundation Discussion Papers
We start by discussing some general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterize mainstream activities of econometrics and the scientific limits of those activities., we discuss some proximity theorems that quantify by means of explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and the trajectory of the observed data. The results show that trends are more …
Local Whittle Estimation Of Fractional Integration, Katsumi Shimotsu, Peter C.B. Phillips
Local Whittle Estimation Of Fractional Integration, Katsumi Shimotsu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
An exact form of the local Whittle likelihood is studied with the intent of developing a general purpose estimation procedure for the memory parameter ( d ) that does not rely on tapering or differencing prefilters. The resulting exact local Whittle estimator is shown to be consistent and to have the same N (0,1/4) limit distribution for all values of d if the optimization covers an interval of width less than 9/2 and the initial value of the process is known.
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 …
Modified Local Whittle Estimation Of The Memory Parameter In The Nonstationary Case, Katsumi Shimotsu, Peter C.B. Phillips
Modified Local Whittle Estimation Of The Memory Parameter In The Nonstationary Case, Katsumi Shimotsu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an estimator of the memory parameter that covers a range of values of d commonly encountered in applied work with economic data. The new estimator is called the modified local Whittle estimator and employs a version of the Whittle likelihood based on frequencies adjacent to the origin and modified to take into account the form of …
Local Whittle Estimation In Nonstationary And Unit Root Cases, Katsumi Shimotsu, Peter C.B. Phillips
Local Whittle Estimation In Nonstationary And Unit Root Cases, Katsumi Shimotsu, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d < 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d . For d = 1, the limit distribution is mixed normal. For d > 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.
Unit Root Log Periodogram Regression, Peter C.B. Phillips
Unit Root Log Periodogram Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Log periodogram (LP) regression is shown to be consistent and to have a mixed normal limit distribution when the memory parameter d = 1. Gaussian errors are not required. Tests of d = 1 based on LP regression are consistent against d < 1 alternatives but inconsistent against d > 1 alternatives. A test based on a modified LP regression that is consistent in both directions is provided.
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 …
Robust Nonstationary Regression, Peter C.B. Phillips
Robust Nonstationary Regression, Peter C.B. Phillips
Cowles Foundation Discussion Papers
This paper provides a robust statistical approach to nonstationary time series regression and inference. Fully modified extensions of traditional robust statistical procedures are developed which allow for endogeneities in the nonstationary regressors and serial dependence in the shocks that drive the regressors and the errors that appear in the equation being estimated. The suggested estimators involve semiparametric corrections to accommodate these possibilities and they belong to the same family as the fully modified least squares (FM-OLS) estimator of Phillips and Hansen (1990). Specific attention is given to fully modified least absolute deviation (FM-LAD) estimation and fully modified M (FM-M)-estimation. The …
Unit Roots, Peter C.B. Phillips
Unit Roots, Peter C.B. Phillips
Cowles Foundation Discussion Papers
Nonstationarity is certainly one of the most dominant and enduring characteristics of macroeconomic and financial time series. It therefore seems appropriate that this feature of the data be seriously addressed both in econometric methodology and in empirical practice. However, until recently this has not been the case. Before 1980, it was standard empirical practice in econometrics to treat observed trends as simple deterministic functions of time. Nelson-Plosser (1982) challenged this practice and showed that observed trends are better modeled if one allows for stochastic trends. Since their work there has been a continuing reappraisal of trend behavior in economic methods …