Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.     

Unspanned Macroeconomic Factors in the Yield Curve

In this article, we extract common factors from a cross-section of U.S. macro-variables and Treasury zero-coupon yields. We find that two macroeconomic factors have an important predictive content for government bond yields and excess returns. These factors are not spanned by the cross-section of yields and are well proxied by economic growth and real interest rates.     

In-Sample Inference and Forecasting in Misspecified Factor Models

This article considers in-sample prediction and out-of-sample forecasting in regressions with many exogenous predictors. We consider four dimension-reduction devices: principal components, ridge, Landweber Fridman, and partial least squares. We derive rates of convergence for two representative models: an ill-posed model and an approximate factor model. The theory is developed for a large cross-section and a large time-series. As all these methods depend on a tuning parameter to be selected, we also propose data-driven selection methods based on cross-validation and establish their optimality. Monte Carlo simulations and an empirical application to forecasting inflation and output growth in the U.S. show that data-reduction methods outperform conventional methods in several relevant settings, and might effectively guard against instabilities in predictors’ forecasting ability.     

Short-Term GDP Forecasting With a Mixed-Frequency Dynamic Factor Model With Stochastic Volatility

In this article, we develop a mixed frequency dynamic factor model in which the disturbances of both the latent common factor and of the idiosyncratic components have time-varying stochastic volatilities. We use the model to investigate business cycle dynamics in the euro area and present three sets of empirical results. First, we evaluate the impact of macroeconomic releases on point and density forecast accuracy and on the width of forecast intervals. Second, we show how our setup allows to make a probabilistic assessment of the contribution of releases to forecast revisions. Third, we examine point and density out of sample forecast accuracy. We find that introducing stochastic volatility in the model contributes to an improvement in both point and density forecast accuracy. Supplementary materials for this article are available online.     

On the Joint Estimation of Heterogeneous Technologies,Technical, and Allocative Inefficiency

In this article, we provide a semiparametric approach to the joint measurement of technical and allocative inefficiency in a way that the internal consistency of the specification of allocative errors in the objective function (e.g., cost function) and the derivative equations (e.g., share or input demand functions) is assured. We start from the Cobb–Douglas production and shadow cost system. We show that the shadow cost system has a closed-form likelihood function contrary to what was previously thought. In turn, we use the method of local maximum likelihood applied to a system of equations to obtain firm-specific parameter estimates (which reveal heterogeneity in production) as well as measures of technical and allocative inefficiency and its cost. We illustrate its practical application using data on U.S. electric utilities.     

On asymptotic distribution of prediction in functional linear regression

There has been substantial recent attention on problems involving a functional linear regression model with scalar response. Among them, there have been few works dealing with asymptotic distribution of prediction in functional linear regression models. In recent literature, the centeral limit theorem for prediction has been discussed, but the proof and conditions under which the random bias terms for a fixed predictor converge to zero have been ignored so that the impact of these terms on the convergence of the prediction has not been well understood. Clarifying the proof and conditions under which the bias terms converge to zero, we show that the asymptotic distribution of the prediction is normal. Furthermore, we have derived those results related to other terms that already obtained by others, under milder conditions. Finally, we conduct a simulation study to investigate performance of the asymptotic distribution under various parameter settings.     

Power analysis for clustered non-continuous responses in multicenter trials

Power analysis for multi-center randomized control trials is quite difficult to perform for non-continuous responses when site differences are modeled by random effects using the generalized linear mixed-effects model (GLMM). First, it is not possible to construct power functions analytically, because of the extreme complexity of the sampling distribution of parameter estimates. Second, Monte Carlo (MC) simulation, a popular option for estimating power for complex models, does not work within the current context because of a lack of methods and software packages that would provide reliable estimates for fitting such GLMMs. For example, even statistical packages from software giants like SAS do not provide reliable estimates at the time of writing. Another major limitation of MC simulation is the lengthy running time, especially for complex models such as GLMM, especially when estimating power for multiple scenarios of interest. We present a new approach to address such limitations. The proposed approach defines a marginal model to approximate the GLMM and estimates power without relying on MC simulation. The approach is illustrated with both real and simulated data, with the simulation study demonstrating good performance of the method.     

Unified multivariate survival model with a surviving fraction: an application to a Brazilian customer churn data

In this paper we propose a new lifetime model for multivariate survival data in presence of surviving fractions and examine some of its properties. Its genesis is based on situations in which there are m types of unobservable competing causes, where each cause is related to a time of occurrence of an event of interest. Our model is a multivariate extension of the univariate survival cure rate model proposed by Rodrigues et al. [37 J. Rodrigues, V.G. Cancho, M. de Castro, and F. Louzada-Neto, On the unification of long-term survival models, Statist. Probab. Lett. 79 (2009), pp. 753–759. doi: 10.1016/j.spl.2008.10.029[Crossref], [Web of Science ®] , [Google Scholar]]. The inferential approach exploits the maximum likelihood tools. We perform a simulation study in order to verify the asymptotic properties of the maximum likelihood estimators. The simulation study also focus on size and power of the likelihood ratio test. The methodology is illustrated on a real data set on customer churn data.     

Stochastic comparisons on sample extremes of dependent and heterogenous observations

Stochastic comparison on order statistics from heterogeneous-dependent observations has been paid lots of attention recently. This paper devotes to investigating the ordering properties of order statistics from dependent observations. We derive the usual stochastic order for sample minimums and the second smallest order statistic, the dispersive order and the star order for minimums of samples having proportional hazards and Archimedean survival copulas. Similar ordering results are also obtained for maximums and the second largest order statistic of samples having proportional reversed hazards and Archimedean copulas. Several examples illustrating the main results are presented as well.     

Variable selection in additive quantile regression using nonconcave penalty

This paper considers variable selection in additive quantile regression based on group smoothly clipped absolute deviation (gSCAD) penalty. Although shrinkage variable selection in additive models with least-squares loss has been well studied, quantile regression is sufficiently different from mean regression to deserve a separate treatment. It is shown that the gSCAD estimator can correctly identify the significant components and at the same time maintain the usual convergence rates in estimation. Simulation studies are used to illustrate our method.