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

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

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

Numerical Simulations of Spin Glass Systems

We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass systems. After a short historical note and a brief theoretical introduction we start by discussing the (crucial) 3D case: the warm phase, the critical point and the cold phase, the ultrametric structure and the out of equilibrium dynamics. With the same style we discuss the cases of 4D and 2D. In a few appendices we give some details about the definition of states and about the tempering Monte Carlo approach.Comment: Contribution to the volume: "Spin Glasses and Random Fields", edited by P. Young. 40 pages including 13 figure

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.

Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the right information in the known cases (diluted ferromagnets and random field Ising model far from the critical point) and we used it to obtain more convincing results on the frozen phase of finite-dimensional spin glasses. Moreover we used it to study the Griffiths phase of the diluted and the random field Ising models.Comment: 20 pages, 10 figures, uses epsfig.sty. Partially presented at StatPhys XX in a talk by one of the authors (FRT). Added 1 reference in the new versio

Forecasting returns and volatilities in GARCH processes using the bootstrap

We propose a new bootstrap resampling scheme to obtain prediction densities of levels and volatilities of time series generated by GARCH processes. The main advantage over other bootstrap methods previously proposed for GARCH processes, is that the procedure incorpora tes the variability due to parameter estimation and, consequently, it is possible to obtain bootstrap prediction densities for the volatility process. The asymptotic properties of the procedure are derived and the finite sample properties are analysed by means of Monte CarIo experiments, showing its good behaviour versus altemative procedures. Finally, the procedure is applied to estimate prediction densities of retums and volatilities of the Madrid Stock Market index, IBEX-35

Bootstrap prediction for returns and volatilities in GARCH models.

A new bootstrap procedure to obtain prediction densities of returns and volatilities of GARCH processes is proposed. Financial market participants have shown an increasing interest in prediction intervals as measures of uncertainty. Furthermore, accurate predictions of volatilities are critical for many financial models. The advantages of the proposed method are that it allows incorporation of parameter uncertainty and does not rely on distributional assumptions. The finite sample properties are analyzed by an extensive Monte Carlo simulation. Finally, the technique is applied to the Madrid Stock Market index, IBEX-35.Acknowledgements: We are very grateful for their helpful comments by three anonymous referees, the editor Stephen Pollock and seminar participants at the Universities of Valladolid, New South Wales and Canterbury and the June 2001 Time Series Workshop of Arrabida, the September 2001 International Conference on Modelling Volatility (Perth) and the June 2002 International Symposium on Forecasting (Dublin). We are also grateful to Gregorio Serna for providing the data set analyzed in this paper and to Dolores Redondas for helping us with the figures. Financial support was provided by projects DGES PB96-0111 and BEC2002-03720 from the Spanish Government and Cátedra de Calidad from BBVAPublicad