Preservation of the rescaled adjusted range: 2. Simulation studies using Box‐Jenkins Models

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Abstract
It is demonstrated that autoregressive moving average (Arma) models do preserve the rescaled adjusted range (RAR) or equivalently the Hurst coefficientK. Arma models are fit to 23 geophysical time series, and by using Monte Carlo techniques and a specified statistical test it is shown that the observed RAR orKis retained by the models. The empirical cumulative distribution function (ECDF) for these statistics can be calculated as closely as is required to the theoretical distribution. Furthermore, the distribution of the RAR is a function of the time series lengthNand the parameter values of the particular Arma process being considered. Various estimates for the Hurst coefficient are compared for the 23 geophysical data sets.The appendix is available with entire article on microfiche. Order from American Geophysical Union, 1909 K Street, N.W., Washington, D.C. 20006. Document W78‐003; $1.00. Payment must accompany order.