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Full-Text Articles in Social and Behavioral Sciences
Estimating Long Run Economic Equilibria, Peter C.B. Phillips, Mico Loretan
Estimating Long Run Economic Equilibria, Peter C.B. Phillips, Mico Loretan
Cowles Foundation Discussion Papers
Our subject is econometric estimation and inference concerning long-run economic equilibria in models with stochastic trends. Our interest is focused on single equation specifications such as those employed in the Error Correction Model (ECM) methodology of David Hendry (1987, 1989 inter alia) and the semiparametric modified least squares method of Phillips and Hansen (1989). We start by reviewing the prescriptions for empirical time series research that are presently available. We argue that the diversity of choices is confusing to practitioners and obscures the fact that statistical theory is clear about optimal inference procedures. Part of the difficulty arises from the …
Asymptotics For Linear Processes, Peter C.B. Phillips, Victor Solo
Asymptotics For Linear Processes, Peter C.B. Phillips, Victor Solo
Cowles Foundation Discussion Papers
A method of deriving asymptotics for linear processes is introduced which uses an explicit algebraic decomposition of the linear filter. The method leads to substantial simplifications in the asymptotics and offers a unified approach to strong laws and central limit theory for linear processes. Sample means and sample covariances are covered. The results also accommodate both homogeneous and heterogeneous innovations as well as innovations with undefined means and variances.
Asymptotics For Semiparametric Econometric Models: Iii. Testing And Examples, Donald W.K. Andrews
Asymptotics For Semiparametric Econometric Models: Iii. Testing And Examples, Donald W.K. Andrews
Cowles Foundation Discussion Papers
This paper considers tests of nonlinear parametric restrictions in semiparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like test statistics are considered and are shown to have asymptotic chi-square distributions under the null and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios. A number of examples are given to illustrate the testing results of this paper and the estimation and stochastic equicontinuity results of the antecedents to this paper, viz. Andrews (1989b, …
Asymptotic Optimality Of Generalized Cl, Cross-Validation, And Generalized Cross-Validation In Regression With Heteroskedastic Errors, Donald W.K. Andrews
Asymptotic Optimality Of Generalized Cl, Cross-Validation, And Generalized Cross-Validation In Regression With Heteroskedastic Errors, Donald W.K. Andrews
Cowles Foundation Discussion Papers
The problem considered here is that of using a data-driven procedure to select a good estimate from a class of linear estimates indexed by a discrete parameter. In contrast to other papers on this subject, we consider models with heteroskedastic errors. The results apply to model selection problems in linear regression and to nonparametric regression estimation via series estimators, nearest neighbor estimators, and local regression estimators, among others. Generalized C L , cross-validation, and generalized cross-validation procedures are analyzed.
Testing For A Unit Root By Generalized Least Squares Methods In The Time And Frequency Domains, In Choi, Peter C.B. Phillips
Testing For A Unit Root By Generalized Least Squares Methods In The Time And Frequency Domains, In Choi, Peter C.B. Phillips
Cowles Foundation Discussion Papers
New time and frequency domain tests for the presence of a unit root are developed. The tests are based on generalized least squares (GLS) methods in both the time and the frequency domains. For the time domain tests, moving average processes are assumed for the error terms on the autoregression. For the frequency domain tests, general assumptions are made which allow for stationary and weakly dependent error processes. The limiting distributions of feasible GLS tests are derived under MA(1) errors in the time domain. This theory is extended to higher order moving average processes under an invertibility condition. The limiting …
The Durbin-Watson Ratio Under Infinite Variance Errors, Peter C.B. Phillips, Mico Loretan
The Durbin-Watson Ratio Under Infinite Variance Errors, Peter C.B. Phillips, Mico Loretan
Cowles Foundation Discussion Papers
This paper studies the properties of the von Neumann ratio for time series with infinite variance. The asymptotic theory is developed using recent results on the weak convergence of partial sums of time series with infinite variance to stable processes and of sample serial correlations to functions of stable variables. Our asymptotics cover the null of iid variates and general moving average (MA) alternatives. Regression residuals are also considered. In the static regression model the Durbin-Watson statistic has the same limit distribution as the von Neumann ratio under general conditions. However, the dynamic models, the results are more complex and …