A simple regression approach to HAC and LRV estimation is suggested. The method exploits the fact that the quantities of interest relate to only one point of the spectrum (the origin). The new estimator is simply the explained sum of squares in a linear regression whose regressors are a set of trend basis functions. Positive definiteness in the estimate is therefore automatically enforced, and the technique can be implemented with standard regression packages. No kernel choice is needed in practical implementation, but basis functions need to be chosen and a smoothing parameter corresponding to the number of basis functions needs to be selected. An automated approach to making this selection based on optimizing the asymptotic mean squared error is derived. The limit theory of the new estimator shows that its properties, including the convergence rate, are comparable to those of conventional HAC estimates constructed from quadratic kernels.My thanks go to Bruce Hansen, Guido Kuersteiner, and two referees for comments on an earlier version of the paper. NSF research support under grant SES 00-92509 is acknowledged.

When Stephen Perez and I first began our Monte Carlo studies of the efficacy of general-to-specific search methodologies in 1995, we were keenly aware of our limited ability to capture the tacit knowledge of the skilled time-series econometrician operating in the London School of Economics (LSE) tradition (Hoover and Perez, 1999a, 1999b). Econometrics, we believed, was an art, and our algorithm was not intended to replace the artist. David Hendry and Hans-Martin Krolzig's subsequent development of PcGets did not, in fact, eliminate the art of econometrics. Power tools did not eliminate the art of the cabinetmaker but changed where his value added lay and—importantly—made new things possible. PcGets is likewise a new, powerful tool, useful in the hands of a skilled craftsman.I thank Peter Phillips, Selva Demiralp, Stephen Perez, and an anonymous referee for helpful comments on an earlier draft.

We propose a new diagnostic test for linear and nonlinear time series models, using a generalized spectral approach. Under a wide class of time series models that includes autoregressive conditional heteroskedasticity (ARCH) and autoregressive conditional duration (ACD) models, the proposed test enjoys the appealing “nuisance-parameter-free” property in the sense that model parameter estimation uncertainty has no impact on the limit distribution of the test statistic. It is consistent against any type of pairwise serial dependence in the model standardized residuals and allows the choice of a proper lag order via data-driven methods. Moreover, the new test is asymptotically more efficient than the correlation integral–based test of Brock, Hsieh, and LeBaron (1991, Nonlinear Dynamics, Chaos, and Instability: Statistical Theory and Economic Evidence) and Brock, Dechert, Scheinkman, and LeBaron (1996, Econometric Reviews 15, 197–235), the well-known BDS test, against a class of plausible local alternatives (not including ARCH). A simulation study compares the finite-sample performance of the proposed test and the tests of BDS, Box and Pierce (1970, Journal of the American Statistical Association 65, 1509–1527), Ljung and Box (1978, Biometrika 65, 297–303), McLeod and Li (1983, Journal of Time Series Analysis 4, 269–273), and Li and Mak (1994, Journal of Time Series Analysis 15, 627–636). The new test has good power against a wide variety of stochastic and chaotic alternatives to the null models for conditional mean and conditional variance. It can play a valuable role in evaluating adequacy of linear and nonlinear time series models. An empirical application to the daily S&P 500 price index highlights the merits of our approach.We thank the co-editor (Don Andrews) and two referees for careful and constructive comments that have lead to significant improvement over an earlier version. We also thank C.W.J. Granger, D. Tjøstheim, and Z. Xiao for helpful comments. Hong's participation is supported by the National Science Foundation via NSF grant SES–0111769. Lee thanks the UCR Academic Senate for research support.

This paper considers unit root tests based on M estimators. The asymptotic theory for these tests is developed. It is shown how the asymptotic distributions of the tests depend on nuisance parameters and how tests can be constructed that are invariant to these parameters. It is also shown that a particular linear combination of a unit root test based on the ordinary least-squares (OLS) estimator and on an M estimator converges to a normal random variate. The interpretation of this result is discussed. A simulation experiment is described, illustrating the level and power of different unit root tests for several sample sizes and data generating processes. The tests based on M estimators turn out to be more powerful than the OLS-based tests if the innovations are fat-tailed.

I provide a systematic treatment of the asymptotic properties of weighted M-estimators under standard stratified sampling. Simple, consistent asymptotic variance matrix estimators are proposed for a broad class of problems. When stratification is based on exogenous variables, I show that the usual, unweighted M-estimator is more efficient than the weighted estimator under a generalized conditional information matrix equality. Hausman tests for the exogeneity of the sampling scheme, including fully robust forms, are derived.

Testing for a unit root in the moving average model is discussed. First, for the stationary MA(1) model, we suggest a score type test which is locally best invariant and unbiased. Performance of the test for finite samples is compared with the most powerful test. The asymptotic behavior of the test is also considered by computing the limiting power under a sequence of local alternatives. We then extend the model to an infinite order MA and suggest a test for this extended case.

We consider the local power of the cusum and cusum of squares tests for structural change in the linear regression model. We show that the local power of the cusum of squares test equals its size for a wide class of structural changes, as compared to a nontrivial local power for the cusum test. The conventional ranking of these procedures is thus reversed.

The Cox-Ingersoll-Ross model is a diffusion process suitable for modeling the term structure of interest rates. In this paper, we consider estimation of the parameters of this process from observations at equidistant time points. We study two estimators based on conditional least squares as well as a one-step improvement of these, two weighted conditional least-squares estimators, and the maximum likelihood estimator. Asymptotic properties of the various estimators are discussed, and we also compare their performance in a simulation study.

This paper derives the limiting distributions of alternative jackknife instrumental variables (JIV) estimators and gives formulas for accompanying consistent standard errors in the presence of heteroskedasticity and many instruments. The asymptotic framework includes the many instrument sequence of Bekker (1994, Econometrica 62, 657–681) and the many weak instrument sequence of Chao and Swanson (2005, Econometrica 73, 1673–1691). We show that JIV estimators are asymptotically normal and that standard errors are consistent provided that as n→∞, where Kn and rn denote, respectively, the number of instruments and the concentration parameter. This is in contrast to the asymptotic behavior of such classical instrumental variables estimators as limited information maximum likelihood, bias-corrected two-stage least squares, and two-stage least squares, all of which are inconsistent in the presence of heteroskedasticity, unless Kn/rn→0. We also show that the rate of convergence and the form of the asymptotic covariance matrix of the JIV estimators will in general depend on the strength of the instruments as measured by the relative orders of magnitude of rn and Kn.

Because the empirical characteristic function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for strictly stationary processes. Under some regularity conditions, the resulting estimators are shown to be consistent and asymptotically normal. The method is applied to estimate the stable autoregressive moving average (ARMA) models. For the general stable ARMA model for which the maximum likelihood approach is not feasible, Monte Carlo evidence shows that the ECF method is a viable estimation method for all the parameters of interest. For the Gaussian ARMA model, a particular stable ARMA model, the optimal weight functions and estimating equations are given. Monte Carlo studies highlight the finite sample performances of the ECF method relative to the exact and conditional maximum likelihood methods.

Using generalized functions of random variables and generalized Taylor series expansions, we provide quick demonstrations of the asymptotic theory for the LAD estimator in a regression model setting. The approach is justified by the smoothing that is delivered in the limit by the asymptotics, whereby the generalized functions are forced to appear as linear functionals wherein they become real valued. Models with fixed and random regressors, and autoregressions with infinite variance errors are studied. Some new analytic results are obtained including an asymptotic expansion of the distribution of the LAD estimator.

This paper is concerned with derivation of a new efficient algorithm for computing the exact Gaussian likelihood for structural parameters in nonstationary higher-order continuous-time dynamic models and with its application in the estimation of these parameters. The algorithm completely avoids the computation of the covariance matrix of the observations and is applicable to a system of any order with mixed stock and flow data. It is used as the basis for an iterative procedure in which the structural parameters and the initial state vector are estimated alternately.

In this paper we propose a bootstrap method for panel data linear regression models with individual fixed effects. The method consists of applying the standard moving blocks bootstrap of Künsch (1989, Annals of Statistics 17, 1217–1241) and Liu and Singh (1992, in R. LePage & L. Billiard (eds.), Exploring the Limits of the Bootstrap) to the vector containing all the individual observations at each point in time. We show that this bootstrap is robust to serial and cross-sectional dependence of unknown form under the assumption that n (the cross-sectional dimension) is an arbitrary nondecreasing function of T (the time series dimension), where T → ∞, thus allowing for the possibility that both n and T diverge to infinity. The time series dependence is assumed to be weak (of the mixing type), but we allow the cross-sectional dependence to be either strong or weak (including the case where it is absent). Under appropriate conditions, we show that the fixed effects estimator (and also its bootstrap analogue) has a convergence rate that depends on the degree of cross-section dependence in the panel. Despite this, the same studentized test statistics can be computed without reference to the degree of cross-section dependence. Our simulation results show that the moving blocks bootstrap percentile-t intervals have very good coverage properties even when the degree of serial and cross-sectional correlation is large, provided the block size is appropriately chosen.

When the covariance between the risk factors of asset prices is due to both Brownian and jump components, the realized covariation (RC) approaches the sum of the integrated covariation (IC) with the sum of the co-jumps, as the observation frequency increases to infinity, in a finite and fixed time horizon. In this paper the two components are consistently separately estimated within a semimartingale framework with possibly infinite activity jumps. The threshold (or truncated) estimator is used, which substantially excludes from RC all terms containing jumps. Unlike in Jacod (2007, Universite de Paris-6) and Jacod (2008, Stochastic Processes and Their Applications 118, 517–559), no assumptions on the volatilities’ dynamics are required. In the presence of only finite activity jumps: 1) central limit theorems (CLTs) for and for further measures of dependence between the two Brownian parts are obtained; the estimation error asymptotic variance is shown to be smaller than for the alternative estimators of IC in the literature; 2) by also selecting the observations as in Hayashi and Yoshida (2005, Bernoulli 11, 359–379), robustness to nonsynchronous data is obtained. The proposed estimators are shown to have good finite sample performances in Monte Carlo simulations even with an observation frequency low enough to make microstructure noises’ impact on data negligible.

We consider the issue of testing a time series for a unit root in the possible presence of a break in a linear deterministic trend at an unknown point in the series. We propose a new break fraction estimator which, where a break in trend occurs, is consistent for the true break fraction at rate Op(T−1). Unlike other available estimators, however, when there is no trend break, our estimator converges to zero at rate Op(T−1/2). Used in conjunction with a quasi difference (QD) detrended unit root test that incorporates a trend break regressor, we show that these rates of convergence ensure that known break fraction null critical values are asymptotically valid. Unlike available procedures in the literature, this holds even if there is no break in trend (the break fraction is zero). Here the trend break regressor is dropped from the deterministic component, and standard QD detrended unit root test critical values then apply. We also propose a second procedure that makes use of a formal pretest for a trend break in the series, including a trend break regressor only where the pretest rejects the null of no break. Both procedures ensure that the correctly sized (near-) efficient unit root test that allows (does not allow) for a break in trend is applied in the limit when a trend break does (does not) occur.

We propose projections as means of identifying and estimating the components (endogenous and exogenous) of an additive nonlinear ARX model. The estimates are nonparametric in nature and involve averaging of kernel-type estimates. Such estimates have recently been treated informally in a univariate time series situation. Here we extend the scope to nonlinear ARX models and present a rigorous theory, including the derivation of asymptotic normality for the projection estimates under a precise set of regularity conditions.

This paper introduces a new estimation method for dynamic panel models with fixed effects and AR(p) idiosyncratic errors. The proposed estimator uses a novel form of systematic differencing, called X-differencing, that eliminates fixed effects and retains information and signal strength in cases where there is a root at or near unity. The resulting “panel fully aggregated” estimator (PFAE) is obtained by pooled least squares on the system of X-differenced equations. The method is simple to implement, consistent for all parameter values, including unit root cases, and has strong asymptotic and finite sample performance characteristics that dominate other procedures, such as bias corrected least squares, generalized method of moments (GMM), and system GMM methods. The asymptotic theory holds as long as the cross section (n) or time series (T) sample size is large, regardless of the n/T ratio, which makes the approach appealing for practical work. In the time series AR(1) case (n = 1), the FAE estimator has a limit distribution with smaller bias and variance than the maximum likelihood estimator (MLE) when the autoregressive coefficient is at or near unity and the same limit distribution as the MLE in the stationary case, so the advantages of the approach continue to hold for fixed and even small n. Some simulation results are reported, giving comparisons with other dynamic panel estimation methods.

For a class of parametric ARCH models, Whittle estimation based on squared observations is shown to be [square root of n]-consistent and asymptotically normal. Our conditions require the squares to have short memory autocorrelation, by comparison with the work of Zaffaroni (1999, “Gaussian Inference on Certain Long-Range Dependent Volatility Models,” Preprint), who established the same properties on the basis of an alternative class of models with martingale difference levels and long memory autocorrelated squares.

When estimating integrated volatilities based on high-frequency data, simplifying assumptions are usually imposed on the relationship between the observation times and the price process. In this paper, we establish a central limit theorem for the realized volatility in a general endogenous time setting. We also establish a central limit theorem for the tricity under the hypothesis that there is no endogeneity, based on which we propose a test and document that this endogeneity is present in financial data.