On the Application of Bootstrap Method to Stationary Time Series Process

T. O. Olatayo

Mathematical Sciences Department, Olabisi Onabanjo University, Ago-Iwoye, Nigeria.

DOI: 10.4236/ajcm.2013.31010                

Abstract

This article introduces a resampling procedure called the truncated geometric bootstrap method for stationary time series process. This procedure is based on resampling blocks of random length, where the length of each blocks has a truncated geometric distribution and capable of determining the probability p and number of block b. Special attention is given to problems with dependent data, and application with real data was carried out. Autoregressive model was fitted and the choice of order determined by Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The normality test was carried out on the residual variance of the fitted model using Jargue-Bera statistics, and the best model was determined based on root mean square error of the forecasting values. The bootstrap method gives a better and a reliable model for predictive purposes. All the models for the different block sizes are good. They preserve and maintain stationary data structure of the process and are reliable for predictive purposes, confirming the efficiency of the proposed method.

Keywords

Truncated Geometric Bootstrap Method; Autoregressive Model; Akaike Information Criterion (AIC); Bayesian Information Criterion (BIC); Root Mean Square Error ()

Conflicts of Interest

The authors declare no conflicts of interest.

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