Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Forecasting time series combining Holt-Winters and bootstrap approaches

Publicado em "AIP Conference Proceedings", Vol. 1648

Specification and testing of multiplicative time-varying GARCH models with applications

In this article, we develop a specification technique for building multiplicative time-varying GARCH models of Amado and Teräsvirta (2008, 2013). The variance is decomposed into an unconditional and a conditional component such that the unconditional variance component is allowed to evolve smoothly over time. This nonstationary component is defined as a linear combination of logistic transition functions with time as the transition variable. The appropriate number of transition functions is determined by a sequence of specification tests. For that purpose, a coherent modelling strategy based on statistical inference is presented. It is heavily dependent on Lagrange multiplier type misspecification tests. The tests are easily implemented as they are entirely based on auxiliary regressions. Finite-sample properties of the strategy and tests are examined by simulation. The modelling strategy is illustrated in practice with two real examples: an empirical application to daily exchange rate returns and another one to daily coffee futures returns.

Predicting SO2 pollution incidents by means of additive models with optimum variable selection

The aim of this paper is to predict time series of SO2 concentrations emitted by coal-fired power stations in order to estimate in advance emission episodes and analyze the influence of some meteorological variables in the prediction. An emission episode is said to occur when the series of bi-hourly means of SO2 is greater than a specific level. For coal-fired power stations it is essential to predict emission epi- sodes sufficiently in advance so appropriate preventive measures can be taken. We proposed a meth- odology to predict SO2 emission episodes based on using an additive model and an algorithm for variable selection. The methodology was applied to the estimation of SO2 emissions registered in sampling lo- cations near a coal-fired power station located in Northern Spain. The results obtained indicate a good performance of the model considering only two terms of the time series and that the inclusion of the meteorological variables in the model is not significant.

Blow-up and finite time extinction for p(x, t)-curl systems arising in electromagnetism

"Available online 22 March 2016"