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.     

Temporal Disaggregation: Methods,Information Loss,and Diagnostics

This research provides a generalized framework to disaggregate lower-frequency time series and evaluate the disaggregation performance. The proposed framework combines two models in separate stages: a linear regression model to exploit related independent variables in the first stage and a state–space model to disaggregate the residual from the regression in the second stage. For the purpose of providing a set of practical criteria for assessing the disaggregation performance, we measure the information loss that occurs during temporal aggregation while examining what effects take place when aggregating data. To validate the proposed framework, we implement Monte Carlo simulations and provide two empirical studies. Supplementary materials for this article are available online.     

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.     

Local influence diagnostics for incomplete overdispersed longitudinal counts

We develop local influence diagnostics to detect influential subjects when generalized linear mixed models are fitted to incomplete longitudinal overdispersed count data. The focus is on the influence stemming from the dropout model specification. In particular, the effect of small perturbations around an MAR specification are examined. The method is applied to data from a longitudinal clinical trial in epileptic patients. The effect on models allowing for overdispersion is contrasted with that on models that do not.     

Some maximum-indifference estimators for the slope of a univariate linear model

As known, the least-squares estimator of the slope of a univariate linear model sets to zero the covariance between the regression residuals and the values of the explanatory variable. To prevent the estimation process from being influenced by outliers, which can be theoretically modelled by a heavy-tailed distribution for the error term, one can substitute covariance with some robust measures of association, for example Kendall's tau in the popular Theil–Sen estimator. In a scarcely known Italian paper, Cifarelli [(1978), ‘La Stima del Coefficiente di Regressione Mediante l'Indice di Cograduazione di Gini’, Rivista di matematica per le scienze economiche e sociali, 1, 7–38. A translation into English is available at http://arxiv.org/abs/1411.4809 and will appear in Decisions in Economics and Finance] shows that a gain of efficiency can be obtained by using Gini's cograduation index instead of Kendall's tau. This paper introduces a new estimator, derived from another association measure recently proposed. Such a measure is strongly related to Gini's cograduation index, as they are both built to vanish in the general framework of indifference. The newly proposed estimator is shown to be unbiased and asymptotically normally distributed. Moreover, all considered estimators are compared via their asymptotic relative efficiency and a small simulation study. Finally, some indications about the performance of the considered estimators in the presence of contaminated normal data are provided.     

On approximations via convolution-defined mixture models

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture distribution is sufficiently complex. This fact is often not made concrete. We investigate and review theorems that provide approximation bounds for mixing distributions. Connections between the approximation bounds of mixing distributions and estimation bounds for the maximum likelihood estimator of finite mixtures of location-scale distributions are reviewed.     

A new estimator of Kullback–Leibler information and its application in goodness of fit tests*

We propose here a general statistic for the goodness of fit test of statistical distributions. The proposed statistic is constructed based on an estimate of Kullback–Leibler information. The proposed test is consistent and the limiting distribution of the test statistic is derived. Then, the established results are used to introduce goodness of fit tests for the normal, exponential, Laplace and Weibull distributions. A simulation study is carried out for examining the power of the proposed test and to compare it with those of some existing procedures. Finally, some illustrative examples are presented and analysed, and concluding comments are made.     

An omnibus two-sample test for ranked-set sampling data

We develop an omnibus two-sample test for ranked-set sampling (RSS) data. The test statistic is the conditional probability of seeing the observed sequence of ranks in the combined sample, given the observed sequences within the separate samples. We compare the test to existing tests under perfect rankings, finding that it can outperform existing tests in terms of power, particularly when the set size is large. The test does not maintain its level under imperfect rankings. However, one can create a permutation version of the test that is comparable in power to the basic test under perfect rankings and also maintains its level under imperfect rankings. Both tests extend naturally to judgment post-stratification, unbalanced RSS, and even RSS with multiple set sizes. Interestingly, the tests have no simple random sampling analog.