The Multi-Sample Block-Scalar Sphericity Test: Exact and Near-Exact Distributions for Its Likelihood Ratio Test Statistic

In this article the authors show how by adequately decomposing the null hypothesis of the multi-sample block-scalar sphericity test it is possible to obtain the likelihood ratio test statistic as well as a different look over its exact distribution. This enables the construction of well-performing near-exact approximations for the distribution of the test statistic, whose exact distribution is quite elaborate and non-manageable. The near-exact distributions obtained are manageable and perform much better than the available asymptotic distributions, even for small sample sizes, and they show a good asymptotic behavior for increasing sample sizes as well as for increasing number of variables and/or populations involved.     

Automatic Specification Testing for Vector Autoregressions and Multivariate Nonlinear Time Series Models

This article introduces an automatic test for the correct specification of a vector autoregression (VAR) model. The proposed test statistic is a Portmanteau statistic with an automatic selection of the order of the residual serial correlation tested. The test presents several attractive characteristics: simplicity, robustness, and high power in finite samples. The test is simple to implement since the researcher does not need to specify the order of the autocorrelation tested and the proposed critical values are simple to approximate, without resorting to bootstrap procedures. In addition, the test is robust to the presence of conditional heteroscedasticity of unknown form and accounts for estimation uncertainty without requiring the computation of large-dimensional inverses of near-to-singularity covariance matrices. The basic methodology is extended to general nonlinear multivariate time series models. Simulations show that the proposed test presents higher power than the existing ones for models commonly employed in empirical macroeconomics and empirical finance. Finally, the test is applied to the classical bivariate VAR model for GNP (gross national product) and unemployment of Blanchard and Quah (1989 Blanchard, O. and Quah, D. 1989. “The Dynamic Effects of Aggregate Demand and Supply Disturbances,”. The American Economic Review, 79: 655–673. [Web of Science ®] , [Google Scholar]) and Evans (1989 Evans, G. W. 1989. “Output and Unemployment Dynamics in the United States: 1950–1985,”. Journal of Applied Econometrics, 4: 213–238. [Crossref], [Web of Science ®] , [Google Scholar]). Online supplementary material includes proofs and additional details.     

Canonical correlation analysis in the definition of weight restrictions for data envelopment analysis

This work investigates the use of canonical correlation analysis (CCA) in the definition of weight restrictions for data envelopment analysis (DEA). With this purpose, CCA limits are introduced into Wong and Beasley's DEA model. An application of the method is made over data from hospitals in 27 Brazilian cities, producing as outputs average payment (average admission values) and percentage of hospital admissions according to disease groups (International Classification of Diseases, 9th Edition), and having as inputs mortality rates and average stay (length of stay after admission (days)). In this application, performance scores were calculated for both the (CCA) restricted and unrestricted DEA models. It can be concluded that the use of CCA-based weight limits for DEA models increases the consistency of the estimated DEA scores (more homogenous weights) and that these limits do not present mathematical infeasibility problems while avoiding the need for subjectively restricting weight variation in DEA.     

On Random and Gibbsian Particle Motions for Point Processes Evolving in Space and Time

This article presents an analysis of space-time interdependencies of spatial point processes considering random and deterministic Gibbsian point motions caused by repulsion effects between particles. Two deterministic models of Gibbsian motions are considered by formulating a constant (i.e., Strauss-like) and a linear interaction motion functions. Given that theoretical development of continuous space-time stochastic processes are mathematically intractable, we have mainly based our analysis on numerical simulations. Our results suggest that to fully understand such complex dynamics, the analysis of purely spatial patterns should be combined with their interactions in the space-time domain. Otherwise, analysis of pure spacial patterns may not fully explain the real mechanism generating such dynamical configurations. We highlight that adding movement to sedentary points opens new areas of application and research to study biological phenomena, where particles not only evolve through time but also can change spatial positions in terms of their neighbor locations.     

Consistent Testing of Cointegrating Relationships

In this paper we investigate methods for testing the existence of a cointegration relationship among the components of a nonstationary fractionally integrated (NFI) vector time series. Our framework generalizes previous studies restricted to unit root integrated processes and permits simultaneous analysis of spurious and cointegrated NFI vectors. We propose a modified F‐statistic, based on a particular studentization, which converges weakly under both hypotheses, despite the fact that OLS estimates are only consistent under cointegration. This statistic leads to a Wald‐type test of cointegration when combined with a narrow band GLS‐type estimate. Our semiparametric methodology allows consistent testing of the spurious regression hypothesis against the alternative of fractional cointegration without prior knowledge on the memory of the original series, their short run properties, the cointegrating vector, or the degree of cointegration. This semiparametric aspect of the modelization does not lead to an asymptotic loss of power, permitting the Wald statistic to diverge faster under the alternative of cointegration than when testing for a hypothesized cointegration vector. In our simulations we show that the method has comparable power to customary procedures under the unit root cointegration setup, and maintains good properties in a general framework where other methods may fail. We illustrate our method testing the cointegration hypothesis of nominal GNP and simple‐sum (M1, M2, M3) monetary aggregates.