Change point models and conditionally pure birth processes; an inequality on the stochastic intensity

We analyze several aspects of a class of simple counting processes, that can emerge in some fields of applications where the presence of a change-point occurs. Under simple conditions we, in particular, prove a significant inequality for the stochastic intensity.Comment: 15 page

Bootstrapping confidence intervals for the change-point of time series

We study an AMOC time series model with an abrupt change in the mean and dependent errors that fulfill certain mixing conditions. We obtain confidence intervals for the unknown change-point via bootstrapping methods. Precisely we use a block bootstrap of the estimated centered error sequence. Then we reconstruct a sequence with a change in the mean using the same estimators as before. The difference between the change-point estimator of the resampled sequence and the one for the original sequence can be use as an approximation of the difference between the real change-point and its estimator. This enables us to construct confidence intervals using the empirical distribution of the resampled time series. A simulation study shows that the resampled confidence intervals are usually closer to their target levels and at the same time smaller than the asymptotic intervals.Comment: 25 pages, 25 figure

Forecasting the underlying potential governing the time series of a dynamical system

Copyright © 2013 The Authors. Published by Elsevier B.V. All rights reserved.We introduce a technique of time series analysis, potential forecasting, which is based on dynamical propagation of the probability density of time series. We employ polynomial coefficients of the orthogonal approximation of the empirical probability distribution and extrapolate them in order to forecast the future probability distribution of data. The method is tested on artificial data, used for hindcasting observed climate data, and then applied to forecast Arctic sea-ice time series. The proposed methodology completes a framework for ‘potential analysis’ of tipping points which altogether serves anticipating, detecting and forecasting nonlinear changes including bifurcations using several independent techniques of time series analysis. Although being applied to climatological series in the present paper, the method is very general and can be used to forecast dynamics in time series of any origin.NERCAXA Research FundEuropean Commissio

Review Paper on Road Vehicle Vibration Simulation for Packaging Testing Purposes

Inefficient packaging constitutes a global problem that costs hundreds of billions of dollars, not to mention the additional environmental impacts. An insufficient level of packaging increases the occurrence of product damage, while an excessive level increases the packages' weight and volume, thereby increasing distribution cost. This problem is well known, and for many years, engineers have tried to optimize packaging to protect products from transport hazards for minimum cost. Road vehicle shocks and vibrations, which is one of the primary causes of damage, need to be accurately simulated to achieve optimized product protection. Over the past 50 years, road vehicle vibration physical simulation has progressed significantly from simple mechanical machines to sophisticated computer-driven shaking tables. There now exists a broad variety of different methods used for transport simulation. Each of them addresses different particularities of the road vehicle vibration. Because of the nature of the road and vehicles, different sources and processes are present in the vibration affecting freight. Those processes can be simplified as the vibration generated by the general road surface unevenness, road surface aberrations (cracks, bumps, potholes, etc.) and the vehicle drivetrain system (wheels, drivetrain, engine, etc.). A review of the transport vibration simulation methods is required to identify and critically evaluate the recent developments. This review begins with an overview of the standardized methods followed by the more advanced developments that focus on the different random processes of vehicle vibration by simulating non-Gaussian, non-stationary, transient and harmonic signals. As no ideal method exists yet, the review presented in this paper is a guide for further research and development on the topic