Econometric Theory - Current Issue

Volume 24 Issue 03

Sat, 31 May 2008 23:00:00 GMT

Econometric Theory, Volume 24 Issue 03

Econometric Theory provides an authoritative outlet for original contributions in all of the major areas of econometrics. As well as articles that embody original theoretical research, the journal publishes periodic book reviews, historical studies on the evolution of econometric thought and on its major scholars. Econometric Theory also has an on-going ‘Notes and Problems’ series and a distinguished ‘ET Interviews’ series with pre-eminent scholars in the field.

ASYMPTOTICS FOR COINTEGRATED PROCESSES WITH INFREQUENT STOCHASTIC LEVEL SHIFTS AND OUTLIERS

Research Articles
Iliyan Georgiev,
Econometric Theory, Volume 24 Issue 03 , pp 587-615

Abstract
This is an analytical study of the effect of level-shift and temporary-change components, when present but neglected, on the trace test for cointegration. The contribution is threefold. First, we discuss in a multivariate framework, and jointly, effects that in the previous literature have been discussed in a univariate setting and in isolation. Second, we consider a rather general specification of shifts and outliers with random size, number, and timing and with flexible dynamics. It nests the classical cases of additive shifts, innovational outliers, and additive outliers. Third, as an instrument for this analysis we develop an asymptotic theory for product moment matrices of linear processes with stochastic level-shift components, generalizing results of Leipus and Viano (2003, Statistics and Probability Letters 61, 177 190).

THE IMPOSSIBILITY OF CONSISTENT DISCRIMINATION BETWEEN I(0) AND I(1) PROCESSES

Research Articles
Ulrich K. MÜller,
Econometric Theory, Volume 24 Issue 03 , pp 616-630

Abstract
An I(0) process is commonly defined as a process that satisfies a functional central limit theorem, i.e., whose scaled partial sums converge weakly to a Wiener process, and an I(1) process as a process whose first differences are I(0). This paper establishes that with this definition, it is impossible to consistently discriminate between I(0) and I(1) processes. At the same time, on a more constructive note, there exist consistent unit root tests and also nontrivial inconsistent stationarity tests with correct asymptotic size.

GAUSSIAN INFERENCE IN AR(1) TIME SERIES WITH OR WITHOUT A UNIT ROOT

Research Articles
Peter C.B. Phillips, Chirok Han,
Econometric Theory, Volume 24 Issue 03 , pp 631-650

Abstract
This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform rate of convergence. En route, a useful central limit theorem (CLT) for sample covariances of linear processes is given, following Phillips and Solo (1992, Annals of Statistics, 20, 971 1001). The approach also has useful extensions to dynamic panels.

A REPRESENTATION THEORY FOR A CLASS OF VECTOR AUTOREGRESSIVE MODELS FOR FRACTIONAL PROCESSES

Research Articles
SØren Johansen,
Econometric Theory, Volume 24 Issue 03 , pp 651-676

Abstract
Based on an idea of Granger (1986, Oxford Bulletin of Economics and Statistics 48, 213 (1 so that Xt is fractional of order d d. We find a representation of the solution that demonstrates the fractional properties. Finally we suggest a model that allows for a polynomial fractional vector, that is, the process Xt is fractional of order d, Xt is fractional of order d bXt is fractional of order d 2b. The representations and conditions are analogous to the well-known conditions for I(0), I(1), and I(2) variables.

MULTIVARIATE AUTOREGRESSION OF ORDER ONE WITH INFINITE VARIANCE INNOVATIONS

Research Articles
M. Zarepour, S.M. Roknossadati,
Econometric Theory, Volume 24 Issue 03 , pp 677-695

Abstract
We consider the limiting behavior of a vector autoregressive model of order one (VAR(1)) with independent and identically distributed (i.i.d.) innovations vector with dependent components in the domain of attraction of a multivariate stable law with possibly different indices of stability. It is shown that in some cases the ordinary least squares (OLS) estimates are inconsistent. This inconsistency basically originates from the fact that each coordinate of the partial sum processes of dependent i.i.d. vectors of innovations in the domain of attraction of stable laws needs a different normalizer to converge to a limiting process. It is also revealed that certain M-estimates, with some regularity conditions, as an appropriate alternative, not only resolve inconsistency of the OLS estimates but also give higher consistency rates in all cases.

KERNEL ESTIMATION WHEN DENSITY MAY NOT EXIST

Research Articles
Victoria Zinde-Walsh,
Econometric Theory, Volume 24 Issue 03 , pp 696-725

Abstract
Nonparametric kernel estimation of density and conditional mean is widely used, but many of the pointwise and global asymptotic results for the estimators are not available unless the density is continuous and appropriately smooth; in kernel estimation for discrete-continuous cases smoothness is required for the continuous variables. Nonsmooth density and mass points in distributions arise in various situations that are examined in empirical studies; some examples and explanations are discussed in the paper. Generally, any distribution function consists of absolutely continuous, discrete, and singular components, but only a few special cases of nonparametric estimation involving singularity have been examined in the literature, and asymptotic theory under the general setup has not been developed. In this paper the asymptotic process for the kernel estimator is examined by means of the generalized functions and generalized random processes approach; it provides a unified theory because density and its derivatives can be defined as generalized functions for any distribution, including cases with singular components. The limit process for the kernel estimator of density is fully characterized in terms of a generalized Gaussian process. Asymptotic results for the Nadaraya Watson conditional mean estimator are also provided.

UNIFORM CONVERGENCE RATES FOR KERNEL ESTIMATION WITH DEPENDENT DATA

Research Articles
Bruce E. Hansen,
Econometric Theory, Volume 24 Issue 03 , pp 726-748

Abstract
This paper presents a set of rate of uniform consistency results for kernel estimators of density functions and regressions functions. We generalize the existing literature by allowing for stationary strong mixing multivariate data with infinite support, kernels with unbounded support, and general bandwidth sequences. These results are useful for semiparametric estimation based on a first-stage nonparametric estimator.

SEMI-NONPARAMETRIC INTERVAL-CENSORED MIXED PROPORTIONAL HAZARD MODELS: IDENTIFICATION AND CONSISTENCY RESULTS

Research Articles
Herman J. Bierens,
Econometric Theory, Volume 24 Issue 03 , pp 749-794

Abstract
In this paper I propose estimating distributions on the unit interval semi-nonparametrically using orthonormal Legendre polynomials. This approach will be applied to the interval-censored mixed proportional hazard (ICMPH) model, where the distribution of the unobserved heterogeneity is modeled semi-nonparametrically. Various conditions for the nonparametric identification of the ICMPH model are derived. I will prove general consistency results for M-estimators of (partly) non-euclidean parameters under weak and easy-to-verify conditions and specialize these results to sieve estimators. Special attention is paid to the case where the support of the covariates is finite.

A PERMUTATION-BASED ESTIMATOR FOR MONOTONE INDEX MODELS

Research Articles
Debopam Bhattacharya,
Econometric Theory, Volume 24 Issue 03 , pp 795-807

Abstract
This paper shows that the finite-dimensional parameters of a monotone-index model can be estimated by minimizing an objective function based on sorting the data. The key observation guiding this procedure is that the sum of distances between pairs of adjacent observations is minimized (over all possible permutations) when the observations are sorted by their values. The resulting estimator is a generalization of Cavanagh and Sherman's monotone rank estimator (MRE) (Cavanagh and Sherman, 1998, Journal of Econometrics 84, 351 $\sqrt{n}$ ">-consistent and asymptotically normal with a consistently estimable covariance matrix. This least-squares estimator can also be used to estimate monotone-index panel data models. A Monte Carlo study is presented where the proposed estimator is seen to dominate the MRE in terms of mean-squared error and mean absolute deviation.

THE LIMIT DISTRIBUTION OF THE CUSUM OF SQUARES TEST UNDER GENERAL MIXING CONDITIONS

Research Articles
Ai Deng, Pierre Perron,
Econometric Theory, Volume 24 Issue 03 , pp 809-822

Abstract
We consider the cumulative sum (CUSUM) of squares test in a linear regression model with general mixing assumptions on the regressors and the errors. We derive its limit distribution and show how it depends on the nature of the error process. We suggest a corrected version that has a limit distribution free of nuisance parameters. We also discuss how it provides an improvement over the standard approach to testing for a change in the variance in a univariate times series. Simulation evidence is presented to support this.

A NOTE ON INEQUALITY CONSTRAINTS IN THE GARCH MODEL

Research Articles
Henghsiu Tsai, Kung-Sik Chan,
Econometric Theory, Volume 24 Issue 03 , pp 823-828

Abstract
We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH(p,q) model remains nonnegative. Previously, Nelson and Cao (1992, Journal of Business 235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH(p,q) models with p 3. In this paper, we show that the sufficient condition of Nelson and Cao (1992) for p 3 actually is also a necessary condition. In addition, we point out the linkage between the absolute monotonicity of the generalized autoregressive conditional heteroskedastic (GARCH) generating function and the nonnegativity of the GARCH kernel, and we use it to provide examples of sufficient conditions for this nonnegativity property to hold.