This paper introduces a new test statistic for the null hypothesis of short memory against long memory alternatives. The novelty of our statistic is that it is based on only high-order sample autocovariances and by construction eliminates the effects of nuisance parameters typically induced by short memory autocorrelation. For practically relevant situations where the short memory process is not directly observed, but instead appears as the disturbance term in a deterministic linear regression model, we are able to demonstrate that our residual-based statistic has an asymptotic standard normal distribution under the null hypothesis. We also establish consistency of the statistic under long memory alternatives. The finite-sample properties of our procedure are compared to other well-known tests in the literature via Monte Carlo simulations. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.We thank the associate editor and two anonymous referees for their valuable comments on an earlier draft of this paper.

In this paper, we consider a nonparametric model with a time-varying regression function and locally stationary regressors. We are interested in the question whether the regression function has the same shape over a given time span. To tackle this testing problem, we propose a kernel-based L2-test statistic. We derive the asymptotic distribution of the statistic both under the null and under fixed and local alternatives. To improve the small sample behavior of the test, we set up a wild bootstrap procedure and derive the asymptotic properties thereof. The theoretical analysis of the paper is complemented by a simulation study and a real data example.

Under more general assumptions than those usually made in the sequential analysis literature, a variable-sample-size-sequential probability ratio test (VPRT) of two simple hypotheses is found that maximizes the expected net gain over all sequential decision procedures. In contrast, Wald and Wolfowitz [25] developed the sequential probability ratio test (SPRT) to minimize expected sample size, but their assumptions on the parameters of the decision problem were restrictive. In this article we show that the expected net-gain-maximizing VPRT also minimizes the expected (with respect to both data and prior) total sampling cost and that, under slightly more general conditions than those imposed by Wald and Wolfowitz, it reduces to the one-observation-at-a-time sequential probability ratio test (SPRT). The ways in which the size and power of the VPRT depend upon the parameters of the decision problem are also examined.

This paper offers a perspective on A.R. Bergstrom’s contribution to continuous-time modeling, focusing on his preferred method of estimating the parameters of a structural continuous-time model using an exact discrete-time analog. Some inherent difficulties in this approach are discussed, which help to explain why, in spite of his prescience, the methods around his time were not universally adopted as he had hoped. Even so, it is argued that Bergstrom’s contribution and legacy is secure and retains some relevance today for the analysis of macroeconomic and financial time series.

This article studies two-step sieve M estimation of general semi/nonparametric models, where the second step involves sieve estimation of unknown functions that may use the nonparametric estimates from the first step as inputs, and the parameters of interest are functionals of unknown functions estimated in both steps. We establish the asymptotic normality of the plug-in two-step sieve M estimate of a functional that could be root-n estimable. The asymptotic variance may not have a closed form expression, but can be approximated by a sieve variance that characterizes the effect of the first-step estimation on the second-step estimates. We provide a simple consistent estimate of the sieve variance, thereby facilitating Wald type inferences based on the Gaussian approximation. The finite sample performance of the two-step estimator and the proposed inference procedure are investigated in a simulation study.

This article proposes a small sample bounds test for equality between sets of coefficients in two linear regressions with unequal disturbance variances. The probability that our test is inconclusive is given under the null hypothesis. It is also shown that our test is more powerful than the Jayatissa test when the regression coefficients differ substantially.

A well known result is that many of the tests used in econometrics, such as the Rao score (RS) test, may not be robust to misspecified alternatives, that is, when the alternative model does not correspond to the underlying data generating process. Under this scenario, these tests spuriously reject the null hypothesis too often. We generalize this result to generalized method of moments–based (GMM-based) tests. We also extend the method proposed in Bera and Yoon (1993, Econometric Theory 9, 649–658) for constructing RS tests that are robust to local misspecification to GMM-based tests. Finally, a further generalization for general estimating and testing functions is developed. This framework encompasses both likelihood and GMM-based results.

We investigate a new separable nonparametric model for time series, which includes many autoregressive conditional heteroskedastic (ARCH) models and autoregressive (AR) models already discussed in the literature. We also propose a new estimation procedure called LIVE, or local instrumental variable estimation, that is based on a localization of the classical instrumental variable method. Our method has considerable computational advantages over the competing marginal integration or projection method. We also consider a more efficient two-step likelihood-based procedure and show that this yields both asymptotic and finite-sample performance gains.This paper is based on Chapter 2 of the first author's Ph.D. dissertation from Yale University. We thank Wolfgang Härdle, Joel Horowitz, Peter Phillips, and Dag Tjøstheim for helpful discussions. We are also grateful to Donald Andrews and two anonymous referees for valuable comments. The second author thanks the National Science Foundation and the ESRC for financial support.

In the context of linear latent-variable models, and a general type of distribution of the data, the asymptotic optimality of a subvector of minimum-distance estimators whose weight matrix uses only second-order moments is investigated. The asymptotic optimality extends to the whole vector of parameter estimators, if additional restrictions on the third-order moments of the variables are imposed. Results related to the optimality of normal (pseudo) maximum likelihood methods are also encompassed. The results derived concern a wide class of latent-variable models and estimation methods used routinely in software for the analysis of latent-variable models such as LISREL, EQS, and CALIS. The general results are specialized to the context of multivariate regression and simultaneous equations with errors in variables.

The problem of statistical inference for the mean of a time series with possibly heavy tails is considered. We first show that the self-normalized sample mean has a well-defined asymptotic distribution. Subsampling theory is then used to develop asymptotically correct confidence intervals for the mean without knowledge (or explicit estimation) either of the dependence characteristics, or of the tail index. Using a symmetrization technique, we also construct a distribution estimator that combines robustness and accuracy: it is higher-order accurate in the regular case, while remaining consistent in the heavy tailed case. Some finite-sample simulations confirm the practicality of the proposed methods.

We construct properly scaled functions of Rp-valued partial sums of demeaned data and derive bounds via the functional law of the iterated logarithm for strong mixing processes. If we obtain a value below or equal to the bound we decide in favor of I(0); otherwise we decide in favor of I(1). This provides a consistent rule for classifying time series as being I(1) or I(0). The nice feature of the procedure lies in the almost sure nature of the bound, guaranteeing a lim sup–type result. We finally provide conditions for the strong consistency of estimators of the variance in the dependent and heterogeneous case.

This paper examines the effects of temporal aggregation on the asymptotic variances of estimators in cointegrated systems. Two important findings are obtained. First, estimators based on flow data alone are more efficient than when the data are all stocks or a mixture of stocks and flows. Second, estimators based on flow data are as efficient as when the data are recorded continuously. A method of improving efficiency with stock variables is also proposed, and an empirical illustration of the method is provided in the context of long-run money demand regressions.I thank Roy Bailey, Rex Bergstrom, Roderick McCrorie, a co-editor, and two anonymous referees for helpful comments. I also thank Katsumi Shimotsu for help with some data issues. None of these individuals are implicated, however, in any possible shortcomings of this paper. The financial support provided by the ESRC under grant R000221818 is gratefully acknowledged.

The finite sample distributions of estimators and test statistics in ARMA time series models are generally unknown. For typical sample sizes, the approximations provided by asymptotic distributions are often unsatisfactory. Hence simulation or numerical integration methods are used to investigate the distributions. In practice only a limited part of the parameter space is examined using these methods. Thus any results which allow us to infer properties from one portion of the parameter space to another or to establish symmetry are most welcome.

For the ARMA model estimated with no intercept term, we show that the least-squares and maximum likelihood estimators have mirror-image invariant or symmetric distributions. The F, t, likelihood ratio, Wald, and Lagrange multiplier statistics are also shown to have distributions with certain mirror-image invariant or symmetry properties. The analysis is extended to misspecified models as well as to ARMA spectral densities.

These properties would have been helpful in either simplifying or extending much earlier work in this area.

We propose an estimation procedure for a semiparametric panel data censored regression model in which the error terms may be subject to general forms of nonstationarity. Specifically, we allow for heteroskedasticity over time and a time varying factor load on the individual specific effect. Empirically, estimation of this model would be of interest to explore how returns to unobserved skills change over time—see, e.g., Chay (1995, manuscript, Princeton University) and Chay and Honoré (1998, Journal of Human Resources 33, 4–38). We adopt a two-stage procedure based on nonparametric median regression, and the proposed estimator is shown to be -consistent and asymptotically normal. The estimation procedure is also useful in the group effect setting, where estimation of the factor load would be empirically relevant in the study of the intergenerational correlation in income, explored in Solon (1992, American Economic Review 82, 393–408; 1999, Handbook of Labor Economics, vol. 3, 1761–1800) and Zimmerman (1992, American Economic Review 82, 409–429).

This paper updates Hall's (1987, Econometric Theory 3, 171–194; 1990, Econometric Theory 6, 1–16) rankings of academic institutions by publication activity in econometrics over the period 1989–1995. Fifteen leading international journals that publish econometrics articles are used to provide the database. The rankings are based on standardized page counts of articles published in these journals over the stated period. Separate rankings are provided for theoretical contributions in econometrics and for all contributions in econometrics. An “Econometricians' Hall of Fame” is developed listing the top 100 individual producers of theoretical econometrics and all contributions in econometrics research in the 15 journals considered. Separate rankings are also provided both for institutions and for individuals according to all econometrics publication activity in Econometrica, Econometric Theory, and Journal of Econometrics.

Motivated by Efron (1992, Journal of the Royal Statistical Society, Series B 54, 83–111), this paper proposes a version of the moving block jackknife as a method of estimating standard errors of block-bootstrap estimators under dependence. As in the case of independent and identically distributed (i.i.d.) observations, the proposed method merely regroups the values of a statistic from different bootstrap replicates to produce an estimate of its standard error. Consistency of the resulting jackknife standard error estimator is proved for block-bootstrap estimators of the bias and the variance of a large class of statistics. Consistency of Efron's method is also established in similar problems for i.i.d. data.

This paper deals with asymptotically efficient estimation in exchangeable nonlinear dynamic panel models with common unobservable factors. These models are relevant for applications to large portfolios of credits, corporate bonds, or life insurance contracts. For instance, the Asymptotic Risk Factor (ARF) model is recommended in the current regulation in Finance (Basel II and Basel III) and Insurance (Solvency II) for risk prediction and computation of the required capital. The specification accounts for both micro- and macrodynamics, induced by the lagged individual observations and the common stochastic factors, respectively. For large cross-sectional and time dimensions n and T, we derive the efficiency bound and introduce computationally simple efficient estimators for both the micro- and macroparameters. The results are based on an asymptotic expansion of the log-likelihood function in powers of 1/n, and are linked to granularity theory. The results are illustrated with the stochastic migration model for credit risk analysis.

We propose an efficient semiparametric estimator for the coefficients of a multivariate linear regression model—with a conditional quantile restriction for each equation—in which the conditional distributions of errors given regressors are unknown. The procedure can be used to estimate multiple conditional quantiles of the same regression relationship. The proposed estimator is asymptotically as efficient as if the true optimal instruments were known. Simulation results suggest that the estimation procedure works well in practice and dominates an equation-by-equation efficiency correction if the errors are dependent conditional on the regressors.

Some key econometric concepts and problems of great importance to Trygve Haavelmo and Ragnar Frisch are discussed within the general framework of a cointegrated VAR. The focus is on problems typical of time-series data such as multicollinearity, spurious correlation and regression, time dependent residuals, model selection, missing simultaneity, autonomy, and identification. The paper argues that the more recent development of unit root econometrics has been instrumental for a solution to the above problems.