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D. Politis and J. Romano, “A General Resampling Scheme for Triangular Arrays of α-Mixing Random Variables with Applications to the Problem of Spectral Density Estimation,” The Annals of Statistics, Vol. 20, No. 4, 1992, pp. 1985-2007. doi:10.1214/aos/1176348899

has been cited by the following article:

• TITLE: On the Application of Bootstrap Method to Stationary Time Series Process

  AUTHORS: T. O. Olatayo

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

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.1, March 29, 2013

  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.