Robert M. de Jong

Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices

Conditions are derived for the consistency of kernel estimators of the covariance matrix of a sum of vectors of dependent heterogeneous random variables, which match those of the currently best-known conditions for the central limit theorem, as required for a unified theory of asymptotic inference. These include finite moments of order no more than 2 + for > 0, trending variances, and variables which are near-epoch dependent on a mixing process, but not necessarily mixing. The results are also proved for the case of sample-dependent bandwidths.

The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii

This paper derives a functional central limit theorem for the partial sums of fractionally integrated processes, otherwise known as I(d) processes for |d|

The Bierens Test under Data Dependence

Abstract This paper generalizes the consistent model specification test proposed by Bierens to the framework of time series. The main problem encountered in this generalization is the fact that time series usually are functions of an infinite number of random variables. A simulation procedure that is capable of establishing asymptotically valid critical values for such a test is described.

Dynamic Time Series Binary Choice

This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’s smoothed maximum score estimation of dynamic binary choice models with lags of the dependent variable as regressors. For the semiparametric model, the latent error is explicitly allowed to be correlated. It turns out that no long-run variance estimator is needed for the validity of the smoothed maximum score procedure in the dynamic time series framework.

The functional central limit theorem and weak convergence to stochastic integrals II: fractionally integrated processes

This paper derives a functional central limit theorem for the partial sums of fractionally integrated processes, otherwise known as I ( d ) processes for | d | < 1/2. Such processes have long memory, and the limit distribution is the so-called fractional Brownian motion, having correlated increments even asymptotically. The underlying shock variables may themselves exhibit quite general weak dependence by being near-epoch-dependent functions of mixing processes. Several weak convergence results for stochastic integrals having fractional integrands and weakly dependent integrators are also obtained. Taken together, these results permit I ( p + d ) integrands for any integer p ≥ 1.

Son Targeting Fertility Behavior: Some Consequences and Determinants

This article draws out some implications of son targeting fertility behavior and studies its determinants. We demonstrate that such behavior has two notable implications at the aggregate level: (a) girls have a larger number of siblings (sibling effect), and (b) girls are born at relatively earlier parities within families (birth-order effect). Empirically testing for these effects, we find that both are present in many countries in South Asia, Southeast Asia, and North Africa but are absent in the countries of sub-Saharan Africa. Using maximum likelihood estimation, we study the effect of covariates on son targeting fertility behavior in India, a country that displays significant sibling and birth-order effects. We find that income and geographic location of families significantly affect son targeting behavior.

Consistency of the stationary bootstrap under weak moment conditions

Abstract We prove the first order asymptotic validity of the stationary bootstrap of Politis and Romano [J. Am. Statistics Assoc. 89 (1994) 1303] under the existence of only slightly more than second moments. Our results improve upon previous results in the literature, which assumed finite sixth moments.

A STRONG CONSISTENCY PROOF FOR HETEROSKEDASTICITY AND AUTOCORRELATION CONSISTENT COVARIANCE MATRIX ESTIMATORS

A strong consistency result for heteroskedasticity and autocorrelation consistent covariance matrix estimators is proven in this paper. In addition, an error in a weak consistency proof for such estimators in the econometrics literature and a correction of that result is provided.

Further Results On The Asymptotics For Nonlinear Transformations Of Integrated Time Series

This paper establishes various results involving functions of integrated processes. Two theorems—which improve similar results by Park and Phillips—are proved for averages of functions of an integrated process that has not been rescaled by the square root of sample size. In addition, two results are given that characterize asymptotic behavior of averages of nonintegrable functions of rescaled integrated processes; the observations close to the pole take over asymptotic behavior in that case. Throughout, we make the assumption that the innovations of the integrated process are a linear process.

Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results

This paper surveys recent developments in the strong law of large numbers for dependent heterogeneous processes. We prove a generalised version of a recent strong law for Lz-mixingales, and also a new strong law for Lpmixingales. These results greatly relax the dependence and heterogeneity conditions relative to those currently cited, and introduce explicit trade-offs between dependence and heterogeneity. The results are applied to proving strong laws for near-epoch dependent functions of mixing processes. We contrast several methods for obtaining these results, including mapping directly to the mixingale properties, and applying a truncation argument.