Bootstrap Procedure for Correlation Model of Random Design Under Strong Dependence

This paper investigates the validity of a bootstrap least square estimate of a polynomial correlation model whose error terms are an autoregressive fractionally integrated moving average ARFIMA (p,d,q) strongly dependent time series. For an (r + 1)*1 vector B of unknown parameters, ^Ba an 'adjusted' least square estimate of B, ^B* a bootstrap estimate of B, it is shown that the distribution of ✓n(^ B*- ^Ba) converges to that of ✓n (^Ba - B), where n is the sample size. The result in this paper extends the correlation part of the results obtained by [9] and [6] to the case where the error term exhibits a long memory time series.