A classification of spherical conjugacy classes

Let G be a simple algebraic group over an algebraically closed field k. We classify the spherical conjugacy classes of G.Comment: 36 page

Local automorphisms of finite dimensional simple Lie algebras

Let ${\mathfrak g}$ be a finite dimensional simple Lie algebra over an algebraically closed field $K$ of characteristic $0$. A linear map $\varphi:{\mathfrak g}\to {\mathfrak g}$ is called a local automorphism if for every $x$ in ${\mathfrak g}$ there is an automorphism $\varphi_x$ of ${\mathfrak g}$ such that $\varphi(x)=\varphi_x(x)$. We prove that a linear map $\varphi:{\mathfrak g}\to {\mathfrak g}$ is local automorphism if and only if it is an automorphism or an anti-automorphism.Comment: 14 page

On Lusztig's map for spherical unipotent conjugacy classes

We provide an alternative description of the restriction to spherical unipotent conjugacy classes, of Lusztig's map Psi from the set of unipotent conjugacy classes in a connected reductive algebraic group to the set of conjugacy classes of its Weyl group. For irreducible root systems, we analyze the image of this restricted map and we prove that a conjugacy class in a finite Weyl group has a unique maximal length element if and only if it has a maximum.Comment: Refereed version, one reference added. The final version will appear in the Bulletin of the London Mathematical Societ

Combination of Forecast Methods Using Encompassing Tests. An Algorithm-Based Procedure ; For the revised version of this paper, see Working Paper 240, Economics Series, June 2009, which includes some changes. The most important change regards the reference of Kisinbay (2007), which was not reported in the previous version. The hierarchical procedure proposed in the paper is based on the approach of Kisinbay (2007), but some modifications of that approach are provided.

This paper proposes a strategy to increase the efficiency of forecast combining methods. Given the availability of a wide range of forecasting models for the same variable of interest, our goal is to apply combining methods to a restricted set of models. To this aim, an algorithm procedure based on a widely used encompassing test (Harvey, Leybourne, Newbold, 1998) is developed. First, forecasting models are ranked according to a measure of predictive accuracy (RMSFE) and, in a consecutive step, each prediction is chosen for combining only if it is not encompassed by the competing models. To assess the robustness of this procedure, an empirical application to Italian monthly industrial production using ISAE short-term forecasting models is provided.Combining forecasts, Econometric models, Evaluating forecasts, Models selection, Time series

Asymptotic convergence of weighted random matrices: nonparametric cointegration analysis for I(2) processes.

The aim of this paper is to provide a new perspective on the nonparametric co-integration analysis for integrated processes of the second order. Our analysis focus on a pair of random matrices related to such integrated process. Such matrices are constructed by introducing some weight functions. Under asymptotic conditions on such weights, convergence results in distribution are obtained. Therefore, a generalized eigenvalue problem is solved. Differential equations and stochastic calculus theory are used.Co-integration, Nonparametric, Differential equations, Asymptotic properties.

A Hierarchical Procedure for the Combination of Forecasts ; This is a revised version of Working Paper 228, Economics Series, October 2008, which includes some changes. The most important change regards the reference of Kisinbay (2007), which was not reported in the previous version. The hierarchical procedure proposed in the paper is based on the approach of Kisinbay (2007), but some modifications of that approach are provided.

This paper proposes a strategy to increase the efficiency of forecast combination. Given the availability of a wide range of forecasts for the same variable of interest, our goal is to apply combining methods to a restricted set of models. To this aim, a hierarchical procedure based on an encompassing test is developed. Firstly, forecasting models are ranked according to a measure of predictive accuracy (RMSFE). The models are then selected for combination such that each forecast is not encompassed by any of the competing forecasts. Thus, the procedure aims to unit model selection and model averaging methods. The robustness of the procedure is investigated in terms of the relative RMSFE using ISAE (Institute for Studies and Economic Analyses) short-term forecasting models for monthly industrial production in Italy.Combining forecasts, Econometric models, Evaluating forecasts, Models selection, Time series

A Simple Panel-CADF Test for Unit Roots

In this paper we propose a simple extension to the panel case of the covariate-augmented Dickey Fuller (CADF) test for unit roots developed in Hansen (1995). The extension we propose is based on a p-values combination approach that takes into account cross-section dependence. We show that the test is easy to compute, has good size properties and gives power gains with respect to other popular panel approaches. A procedure to compute the asymptotic p-values of Hansen’s CADF test is also a side-contribution of the paper. We also complement Hansen (1995) and Caporale and Pittis (1999) with some new theoretical results. Two empirical applications are carried out for illustration purposes on international data to test the PPP hypothesis and the presence of a unit root in international industrial production indices.Unit root, panel data, approximate p-values, Monte Carlo

Stochastic convergence among European economies

The aim of this paper is to test the stochastic convergence in real per capita GDP for 15 European countries using non-stationary panel data approaches over the period 1950-2003. Cross-sectional dependence is assumed due to the existence of strong linkages among European economies. However, tests derived under the assumption of cross-sectional independence are also carried out for completeness and comparison. We also split the whole sample into two sub-periods (1950-1976, 1977-2003) in order to take into account the effects of the first oil crisis (1973-1974) and to evaluate the robustness of the statistical analysis. Our results offer little support to the stochastic convergence hypothesis for the whole period, while suggest the presence of convergence in the first sub-period.Convergence