Spatial weights : constructing weight-compatible exchange matrices from proximity matrices

Exchange matrices represent spatial weights as symmetric probability distributions on pairs of regions, whose margins yield regional weights, generally well-specified and known in most contexts. This contribution proposes a mechanism for constructing exchange matrices, derived from quite general symmetric proximity matrices, in such a way that the margin of the exchange matrix coincides with the regional weights. Exchange matrices generate in turn diffusive squared Euclidean dissimilarities, measuring spatial remoteness between pairs of regions. Unweighted and weighted spatial frameworks are reviewed and compared, regarding in particular their impact on permutation and normal tests of spatial autocorrelation. Applications include tests of spatial autocorrelation with diagonal weights, factorial visualization of the network of regions, multivariate generalizations of Moran's I, as well as "landscape clustering", aimed at creating regional aggregates both spatially contiguous and endowed with similar features

Short-Run Regional Forecasts: Spatial Models through Varying Cross-Sectional and Temporal Dimensions

In any economic analysis, regions or municipalities should not be regarded as isolated spatial units, but rather as highly interrelated small open economies. These spatial interrelations must be considered also when the aim is to forecast economic variables. For example, policy makers need accurate forecasts of the unemployment evolution in order to design short- or long-run local welfare policies. These predictions should then consider the spatial interrelations and dynamics of regional unemployment. In addition, a number of papers have demonstrated the improvement in the reliability of long-run forecasts when spatial dependence is accounted for. We estimate a heterogeneouscoefficients dynamic panel model employing a spatial filter in order to account for spatial heterogeneity and/or spatial autocorrelation in both the levels and the dynamics of unemployment, as well as a spatial vector-autoregressive (SVAR) model. We compare the short-run forecasting performance of these methods, and in particular, we carry out a sensitivity analysis in order to investigate if different number and size of the administrative regions influence their relative forecasting performance. We compute short-run unemployment forecasts in two countries with different administrative territorial divisions and data frequency: Switzerland (26 regions, monthly data for 34 years) and Spain (47 regions, quarterly data for 32 years)

Tree diversity and above-ground biomass in the South America Cerrado biome and their conservation implications

Less than half of the original two million square kilometers of the Cerrado vegetation remains standing, and there are still many uncertainties as to how to conserve and prioritize remaining areas effectively. A key limitation is the continuing lack of geographically-extensive evaluation of ecosystem-level properties across the biome. Here we sought to address this gap by comparing the woody vegetation of the typical cerrado of the Cerrado–Amazonia Transition with that of the core area of the Cerrado in terms of both tree diversity and vegetation biomass. We used 21 one-hectare plots in the transition and 18 in the core to compare key structural parameters (tree height, basal area, and above-ground biomass), and diversity metrics between the regions. We also evaluated the effects of temperature and precipitation on biomass, as well as explored the species diversity versus biomass relationship. We found, for the first time, both that the typical cerrado at the transition holds substantially more biomass than at the core, and that higher temperature and greater precipitation can explain this difference. By contrast, plot-level alpha diversity was almost identical in the two regions. Finally, contrary to some theoretical expectations, we found no positive relationship between species diversity and biomass for the Cerrado woody vegetation. This has implications for the development of effective conservation measures, given that areas with high biomass and importance for the compensation of greenhouse gas emissions are often not those with the greatest diversity

The exact distribution of Moran's I

In analogy to the exact distribution of the Durbin - Watson d statistic for serial auto-correlation of regression residuals, the exact small sample distribution of Moran's I statistic (or alternatively Geary's c ) can be derived. Use of algebraic results by Koerts and Abrahamse and theoretical results by Inthof, allows the authors to determine by numerical integration the exact distribution function of Moran's I for normally distributed variables. For the case in which the explanatory variables have been neglected, an upper and a lower bound can be given within which the exact distribution of Moran's I for regression residuals will lie. Furthermore, the proposed methodology is flexible enough to investigate related topics such as the characteristics of the exact distribution for distinct spatial structures as well as their different specifications, the exact power function under different spatial autocorrelation levels, and the distribution of Moran's I for nonnormal random variables.

Spatial Filtering Methods for Tracing Space-Time Developments in an Open Regional System: Experiments with German Unemployment Data

Socio-economic interrelationships among regions can be measured in terms of economic flows, migration, or physical geographically-based measures, such as distance or length of shared areal unit boundaries. In general, proximity and openness tend to favour a similar economic performance among adjacent regions. Therefore, proper forecasting of socio-economic variables, such as employment, requires an understanding of spatial (or spatio-temporal) autocorrelation effects associated with a particular geographic configuration of a system of regions. Several spatial econometric techniques have been developed in recent years to identify spatial interaction effects within a parametric framework. Alternatively, newly devised spatial filtering techniques aim to achieve this end as well through the use of a semi-parametric approach. The experiments presented in this paper deal with the analysis of and accounting for spatial autocorrelation by means of spatial filtering techniques for data pertaining to regional unemployment in Germany. The available dataset comprises information about the share of unemployed workers in 439 German districts (the NUTS-III regional aggregation level). In this paper, various results based upon an eigenvector spatial filter model formulation (that is, the use of orthogonal map pattern components), constructed for the 439 German districts, are presented, with an emphasis on their consistency over several observation years. New insights obtained by applying spatial filtering to the database about the German regional labour markets also are discussed