Projection Methods for some Constrained Systems

This article is concerned with a geometric tool given by a pair of projector operators defined by almost product structures on finite dimensional manifolds, polarized by a distribution of constant rank and also endowed with some geometric structures (Riemann,resp.Poisson,resp.symplectic).The work is motivated by non-holonomic and sub-Riemannian geometry of mechanical systems on finite dimensional manifolds.Two examples are given

Calendar effects in daily ATM withdrawals

This paper analyses the calendar effects present in Automated Teller Machines (ATM) withdrawals of residents, using daily data for Portugal for the period from January 1st 2001 to December 31st 2008. The results presented may allow for a better understanding of consumer habits and for adjusting the original series for calendar effects. Considering the Quarterly National Accounts' procedure of adjusting data for seasonality and working days effects, this correction is important to ensure the use of the ATM series as an instrument to nowcast private consumption.Calendar Effects, ATM, Nowcasting, private consumption

Local up-down asymmetrically shaped equilibrium model for tokamak plasmas

A local magnetic equilibrium model is presented, with finite aspect ratio and up-down asymmetrically shaped cross section, that depends on eight free parameters. In contrast with other local equilibria, which provide simple magnetic-surface parametrizations at the cost of complex poloidal-field flux descriptions, the proposed model is intentionally built to afford analytically tractable magnetic-field components. Therefore, it is particularly suitable for analytical assessments of equilibrium-shaping effects on a variety of tokamak-plasma phenomena.Comment: 6 pages, 3 figure

Calendar Effects in Daily ATM Withdrawals

This paper analyses the calendar effects present in Automated Teller Machines (ATM) withdrawals of residents, using daily data for Portugal for the period from January 1st 2001 to December 31st 2008. The results presented may allow for a better understanding of consumer habits and for adjusting the original series for calendar effects. Considering the Quarterly National Accounts’ procedure of adjusting data for seasonality and working days effects, this correction is important to ensure the use of the ATM series as an instrument to nowcast private consumption.

A family of rotation numbers for discrete random dynamics on the circle

We revisit the problem of well-defining rotation numbers for discrete random dynamical systems on the circle. We show that, contrasting with deterministic systems, the topological (i.e. based on Poincar\'{e} lifts) approach does depend on the choice of lifts (e.g. continuously for nonatomic randomness). Furthermore, the winding orbit rotation number does not agree with the topological rotation number. Existence and conversion formulae between these distinct numbers are presented. Finally, we prove a sampling in time theorem which recover the rotation number of continuous Stratonovich stochastic dynamical systems on $S^1$ out of its time discretisation of the flow.Comment: 15 page

The Effects of Additive Outliers and Measurement Errors when Testing for Structural Breaks in Variance

This paper discusses the asymptotic and finite-sample properties of CUSUM-based tests for detecting structural breaks in volatility in the presence of stochastic contamination, such as additive outliers or measurement errors. This analysis is particularly relevant for financial data, on which these tests are commonly used to detect variance breaks. In particular, we focus on the tests by Inclán and Tiao [IT] (1994) and Kokoszka and Leipus [KL] (1998, 2000), which have been intensively used in the applied literature. Our results are extensible to related procedures. We show that the asymptotic distribution of the IT test can largely be affected by sample contamination, whereas the distribution of the KL test remains invariant. Furthermore, the break-point estimator of the KL test renders consistent estimates. In spite of the good large-sample properties of this test, large additive outliers tend to generate power distortions or wrong break-date estimates in small samples.