A Bootstrap simulation study in ARMA (p,q) structures

In 1979 Efron proposed a new general statistical procedure known as ‘Bootstrap’, a computer-intensive method used when finite-sample theory is impossible or difficult to derive, or when only asymptotic theory is available. It is recommended in the estmation of measures of both location and scale for any statistical model without making any distributional assumptions about the data. This technique has been successfully used in various applied statistical problems, although not many applications have been reported in the area of time series. This paper presents a new application of Bootstrap to time series. It considers a simulation study where artificial time series corresponding to AR(1), AR(2), MA(1), MA(2) and ARMA(1,1) strucures were generated, covering important regions of the parameter space of each one of them. The conventional Box-Jenkins parametric estimators of the parameters are compared with the corresponding non-parametric Bootstrap estimators, obtained by 500 Bootstrap repetitions for each series.