Numerical Simulations of Random Phase Sine-Gordon Model and Renormalization Group Predictions

Numerical Simulations of the random phase sine-Gordon model suffer from strong finite size effects preventing the non-Gaussian $\log^2 r$ component of the spatial correlator from following the universal infinite volume prediction. We show that a finite size prediction based on perturbative Renormalisation Group (RG) arguments agrees well with new high precision simulations for small coupling and close to the critical temperature.Comment: 13 pages, 3 ps figures. Extensive new numerical simulation

Which univariate time series model predicts quicker a crisis? The Iberia case

In this paper four univariate models are fitted to monthly observations of the number of passengers in the Spanish airline IBERIA from January 1985 to October 1994. During the first part of the sample, the series shows an upward trend which has a rupture during 1990 with the slope changing to be negative. The series is also characterized by having seasonal variations. We fit a deterministic components model, the Holt-Winters algorithm, an ARIMA model and a structural time series model to the observations up to December 1992. Then we predict with each ofthe models and compare predicted with observed values. As expected, the results show that the detenninistic model is too rigid in this situation even if the within-sample fit is even better than for any of the other models considered. With respect to Holt-Winters predictions, they faH because they are not able to accornmodate outliers. Finally, ARIMA and structural models are shown to have very similar prediction performance, being flexible enough to predict reasonably well when there are changes in trend

Bootstraping financial time series

It is well known that time series of returns are characterized by volatility clustering and excess kurtosis. Therefore, when modelling the dynamic behavior of returns, inference and prediction methods, based on independent and/or Gaussian observations may be inadequate. As bootstrap methods are not, in general, based on any particular assumption on the distribution of the data, they are well suited for the analysis of returns. This paper reviews the application of bootstrap procedures for inference and prediction of financial time series. In relation to inference, bootstrap techniques have been applied to obtain the sample distribution of statistics for testing, for example, autoregressive dynamics in the conditional mean and variance, unit roots in the mean, fractional integration in volatility and the predictive ability of technical trading rules. On the other hand, bootstrap procedures have been used to estimate the distribution of returns which is of interest, for example, for Value at Risk (VaR) models or for prediction purposes. Although the application of bootstrap techniques to the empirical analysis of financial time series is very broad, there are few analytical results on the statistical properties of these techniques when applied to heteroscedastic time series. Furthermore, there are quite a few papers where the bootstrap procedures used are not adequate.Publicad

Prediction with univariate time series models: The Iberia case

In this paper we model the monthly number of passengers flying with the Spanish airline IBERIA from January 1985 to December 1992 and predict future values of the series up to October 1994. This series is characterized by strong seasonal variations and by having an upward trend which has a rupture during 1990 with the slope changing to be negative. We compare observed values with predictions made by a deterministic components model, the Holt-Winters exponential smoothing filter, an ARIMA model and a structural time series model. As expected, we show that the deterministic components model is too rigid in the presence fo breaks in trends although surprisingly the within-sample fit is better than for any of the other models considered. With respect to Holt-Winters predictions, they fail because they are not able to acommodate outliers. Finally, ARIMA and structural models are shown to have very similar prediction performance, being very flexible to predict reasonably well when there are changes in trend and outliers.ARIMA models, Breaks in trends, Deterministic components, Holt-Winters algorithm, Outliers, Intervention analysis, Structural time series models, Unobserved components models.

The relation between the level and uncertainty of inflation

This paper focus on the problems faced in the empirical investigation of the relation between the level and volatility of inflation. Monthly inflation series seem to be affected by both the presence of outliers and conditional heteroscedasticity. First, the paper illustrates the implications that the presence of outliers and conditional heteroscedasticity have on the usual residual diagnostics. Then, estimates of the level and volatility of inflation are obtained for each of the countries of the G-7 group. Empirical evidence for the majority of the inflation series for these countries indicates both the presence of outliers and conditional heteroscedasticity, and that estimates of the latter are sensitive to the presence of outliers. Finally, the temporal dependence found in the conditional variance is enduring.Conditional Heteroscedasticity, Diagnostic, Inflation, Outlier, Stochastic Volatility.

Bootstrap predictive inference for ARIMA processes

In this study, we propose a new bootstrap strategy to obtain prediction intervals for autoregressive integrated moving-average processes. Its main advantage over other bootstrap methods previously proposed for autoregressive integrated processes is that variability due to parameter estimation can be incorporated into prediction intervals without requiring the backward representation of the process. Consequently, the procedure is very flexible and can be extended to processes even if their backward representation is not available. Furthermore, its implementation is very simple. The asymptotic properties of the bootstrap prediction densities are obtained. Extensive finite-sample Monte Carlo experiments are carried out to compare the performance of the proposed strategy vs. alternative procedures. The behaviour of our proposal equals or outperforms the alternatives in most of the cases. Furthermore, our bootstrap strategy is also applied for the first time to obtain the prediction density of processes with moving-average components.Publicad

Bootstrap prediction intervals for power-transformed time series

In this paper we propose a bootstrap resampling scheme to construct prediction intervals for future values of a variable after a linear ARIMA model has been fitted to a power transformation of it. The advantages over existing methods for computing prediction intervals of power transformed time series are that the proposed bootstrap intervals incorporate the variability due to parameter estimation, and do not rely on distributional assumptions neither on the original variable nor on the transformed one. We show the good behavior of the bootstrap approach versus alternative procedures by means of Monte Carlo experiments. Finally, the procedure is illustrated by analysing three real time series data sets

Scaling above the upper critical dimension in Ising Models

We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our numerical data are in a good agreement with the Mean Field theoretical predictions, in particular, with the finite size exponent of the connected susceptibility and with the value of the Binder cumulant.Comment: 9 pages and 3 figures, available at http://chimera.roma1.infn.it/index_papers_complex.htm

3D numerical modelling of twisting cracks under bending and torsion of skew notched beams

The testing of mode III and mixed mode failure is every so often encountered in the dedicated literature of mechanical characterization of brittle and quasi-brittle materials. In this work, the application of the mixed strain displacement e-ue-u finite element formulation to three examples involving skew notched beams is presented. The use of this FE technology is effective in problems involving localization of strains in softening materials. The objectives of the paper are: (i) to test the mixed formulation in mode III and mixed mode failure and (ii) to present an enhancement in terms of computational time given by the kinematic compatibility between irreducible displacement-based and the mixed strain-displacement elements. Three tests of skew-notched beams are presented: firstly, a three point bending test of a PolyMethyl MethaAcrylate beam; secondly, a torsion test of a plain concrete prismatic beam with square base; finally, a torsion test of a cylindrical beam made of plain concrete as well. To describe the mechanical behavior of the material in the inelastic range, Rankine and Drucker-Prager failure criteria are used in both plasticity and isotropic continuum damage formats. The proposed mixed formulation is capable of yielding results close to the experimental ones in terms of fracture surface, peak load and global loss of carrying capability. In addition, the symmetric secant formulation and the compatibility condition between the standard irreducible method and the strain-displacement one is exploited, resulting in a significant speedup of the computational procedure.Peer ReviewedPostprint (author's final draft