Generalized factor models: a bayesian approach

There is recent interest in the generalization of classical factor models in which the idiosyncratic factors are assumed to be orthogonal and there are identification restrictions on cross-sectional and time dimensions. In this study, we describe and implement a Bayesian approach to generalized factor models. A flexible framework is developed to determine the variations attributed to common and idiosyncratic factors. We also propose a unique methodology to select the (generalized) factor model that best fits a given set of data. Applying the proposed methodology to the simulated data and the foreign exchange rate data, we provide a comparative analysis between the classical and generalized factor models. We find that when there is a shift from classical to generalized, there are significant changes in the estimates of the structures of the covariance and correlation matrices while there are less dramatic changes in the estimates of the factor loadings and the variation attributed to common factors.

Addressing the net balances problem as a prerequisite for EU budget reform: a proposal

Conflict among member states regarding the distribution of net financial burdens has been allowed to contaminate the entire design of the EU budget with very negative consequences in terms of equity, efficiency and transparency. To get around this problem and pave the way for a substantive budget reform, we propose to decouple distributional negotiations from the rest of the budget process by linking member state net balances in a rigid manner to relative prosperity. This would be achieved through the introduction of a system of compensating horizontal transfers that would take to its logical conclusion the Commission's proposal for a generalized compensation mechanism. We discuss the impact of the proposed scheme on member states? incentives and illustrate its financial implications using revenue and expenditure projections for 2013 that are based on the current Financial Perspectives and Own Resources Decision.

Inverse problems for invariant algebraic curves: explicit computations

Given an algebraic curve in the complex affine plane, we describe how to determine all planar polynomial vector fields which leave this curve invariant. If all (finite) singular points of the curve are nondegenerate, we give an explicit expression for these vector fields. In the general setting we provide an algorithmic approach, and as an alternative we discuss sigma processes.

Generalized multiresolution analyses with given multiplicity functions

Generalized multiresolution analyses are increasing sequences of subspaces of a Hilbert space H that fail to be multiresolution analyses in the sense of wavelet theory because the core subspace does not have an orthonormal basis generated by a fixed scaling function. Previous authors have studied a multiplicity function m which, loosely speaking, measures the failure of the GMRA to be an MRA. When the Hilbert space H is L2(Rn), the possible multiplicity functions have been characterized by Baggett and Merrill. Here we start with a function m satisfying a consistency condition which is known to be necessary, and build a GMRA in an abstract Hilbert space with multiplicity function m.