Maximum entropy bootstrap for time series the meboot R package.pdf

JSS Journal of Statistical Software January 2009, Volume 29, Issue 5. / Maximum Entropy Bootstrap for Time Series: The mebootRPackage Hrishikesh D. Vinod Fordham University Javier L′opez-de-Lacalle Universidad del Pa′?s Vasco Abstract The maximum entropy bootstrap is an algorithm that creates an ensemble for time series inference. Stationarity is not required and the ensemble satis?es the ergodic theorem and the central limit theorem. ThemebootRpackage implements such algorithm. This document introduces the procedure and illustrates its scope by means of several guided applications. Keywords: time series, dependent data, bootstrap,R. 1. Introduction This paper illustrates the use of themebootRpackage forR(RDevelopment Core Team 2008). The packagemebootimplements the maximum entropy bootstrap algorithm for time series described in Vinod(2004,2006). The package can be obtained from prehensive work at-/package=meboot. In the traditional theory, an ensemble ? represents the population from which the observed time series is drawn. The maximum entropy (ME) bootstrap constructs a large number of replicates (J= 999, say) as elements of ? for inference using a seven-step algorithm designed to satisfy the ergodic theorem (the grand mean of all ensembles is close to the sample mean). The algorithm’s practical appeal is that it avoids all structural change and unit root type testing plicated asymptotics and all shape-destroying transformations like de- trending or di?erencing to achieve stationarity. The constructed ensemble elements retain the basic shape and time dependence structure of the autocorrelation function (ACF) and the partial autocorrelation function (PACF) of the original time series. This discussion collects relevant portions of Vinod(2004,2006) as templates for users of the mebootpackage. Let us begin with some motivation. Wiener, Kolmogorov and Khintchine 2 meboot: Max