We consider the problem of identifying the parameters of a time-homogeneous bivariate Markov chain when only one of the two variables is observable. We show that, subject to conditions that we spell out, the transition kernel and the distribution of the initial condition are uniquely recoverable (up to an arbitrary relabelling of the state space of the latent variable) from the joint distribution of four (or more) consecutive time-series observations. The result is, therefore, applicable to (short) panel data as well as to (stationary) time series data.

We propose a family of weighted statistics based on the CUSUM process of the WLS residuals for the online detection of changepoints in a Random Coefficient Autoregressive model, using both the standard CUSUM and the Page-CUSUM process. We derive the asymptotics under the null of no changepoint for all possible weighing schemes, including the case of the standardized CUSUM, for which we derive a Darling–Erdös-type limit theorem; our results guarantee the procedure-wise size control under both an open-ended and a closed-ended monitoring. In addition to considering the standard RCA model with no covariates, we also extend our results to the case of exogenous regressors. Our results can be applied irrespective of (and with no prior knowledge required as to) whether the observations are stationary or not, and irrespective of whether they change into a stationary or nonstationary regime. Hence, our methodology is particularly suited to detect the onset, or the collapse, of a bubble or an epidemic. Our simulations show that our procedures, especially when standardising the CUSUM process, can ensure very good size control and short detection delays. We complement our theory by studying the online detection of breaks in epidemiological and housing prices series.

This study proposes two novel time-varying model-averaging methods for time-varying parameter regression models. When the number of predictors is small, we propose a novel time-varying complete subset-averaging (TVCSA) procedure, where the optimal time-varying subset size is obtained by minimizing the local leave-h-out cross-validation criterion. The TVCSA method is asymptotically optimal for achieving the lowest possible local mean squared error. When the number of predictors is relatively large, we propose a factor TVCSA method to reduce the computational burden by first reducing the dimension of predictors by extracting a few factors using principal component analysis and then obtaining the TVCSA forecasts from time-varying models with the generated factors. We show that the TVCSA estimator remains asymptotically optimal in the presence of generated factors. Monte Carlo simulation studies have provided favorable evidence for the TVCSA methods relative to the popular model-averaging methods in the literature. Empirical applications to equity premiums and inflation forecasting highlight the practical merits of the proposed methods.

This article extends the validity of the conditional likelihood ratio (CLR) test developed by Moreira (2003, Econometrica 71(4), 1027-–1048) to instrumental variable regression models with unknown homoskedastic error variance and many weak instruments. We argue that the conventional CLR test with estimated error variance loses exact similarity and is asymptotically invalid in this setting. We propose a modified critical value function for the likelihood ratio (LR) statistic with estimated error variance, and prove that our modified test achieves asymptotic validity under many weak instruments asymptotics. Our critical value function is constructed by representing the LR using four statistics, instead of two as in Moreira (2003, Econometrica 71(4), 1027-–1048). A simulation study illustrates the desirable finite sample properties of our test.

We study the uniform convergence rates of nonparametric estimators for a probability density function and its derivatives when the density has a known pole. Such situations arise in some structural microeconometric models, for example, in auction, labor, and consumer search, where uniform convergence rates of density functions are important for nonparametric and semiparametric estimation. Existing uniform convergence rates based on Rosenblatt’s kernel estimator are derived under the assumption that the density is bounded. They are not applicable when there is a pole in the density. We treat the pole nonparametrically and show various kernel-based estimators can attain any convergence rate that is slower than the optimal rate when the density is bounded uniformly over an appropriately expanding support under mild conditions.

This article considers a general class of varying coefficient models defined by a set of moment equalities and/or inequalities, where unknown functional parameters are not necessarily point-identified. We propose an inferential procedure for a subvector of the varying parameters and establish the asymptotic validity of the resulting confidence sets uniformly over a broad family of data-generating processes. We also propose a practical specification test for a set of necessary conditions of our model. Monte Carlo studies show that the proposed methods have good finite sample properties. We apply our method to estimate the return to education in China using its 1%-population census data from 2005.

This article studies estimation and inference in the autoregressive (AR) models with unspecified and heavy-tailed heteroskedastic noises. A piece-wise locally stationary structure of the noise is constructed to capture various forms of heterogeneity, without imposing any restrictions on the tail index. The new nonstationary AR model allows for not only time-varying conditional features but also unconditional variance and tail index. This makes it appealing in practice, with wide applications in economics and finance. To obtain a feasible inference, we investigate the self-weighted least absolute deviation estimator and derive its asymptotic normality. Since the asymptotic variance relies on an unobserved density, a bootstrap method is proposed to approximate the limiting distribution. Based on the conditional moment condition, a portmanteau test from residuals is further proposed to detect misspecifications in the proposed model. A simulation study and two applications to time series illustrate our inference procedures.

We study minimax regret treatment rules under matched treatment assignment in a setup where a policymaker, informed by a sample of size N, needs to decide between T different treatments for a $T\geq 2$. Randomized rules are allowed for. We show that the generalization of the minimax regret rule derived in Schlag (2006, ELEVEN—Tests needed for a recommendation, EUI working paper) and Stoye (2009, Journal of Econometrics 151, 70–81) for the case $T=2$ is minimax regret for general finite $T>2$ and also that the proof structure via the Nash equilibrium and the “coarsening” approaches generalizes as well. We also show by example, that in the case of random assignment the generalization of the minimax rule in Stoye (2009, Journal of Econometrics 151, 70–81) to the case $T>2$ is not necessarily minimax regret and derive minimax regret rules for a few small sample cases, e.g., for $N=2$ when $T=3.$

In the case where a covariate x is included, it is shown that a minimax regret rule is obtained by using minimax regret rules in the “conditional-on-x” problem if the latter are obtained as Nash equilibria.