Simulation procedures for Box‐Jenkins Models

Abstract

New simulation procedures are presented for generating synthetic data from either a nonseasonal or a seasonal Box‐Jenkins model. The simulation techniques are designed so that random realizations of the underlying stochastic process are employed for starting values. Because fixed beginning values are not utilized, systematic bias is not introduced into the synthetic trace. When the data have been transformed by a Box‐Cox transformation, the inverse transformation can be conveniently incorporated into the simulation process. Also a new algorithm is presented for simulating integrated models. A method is developed for incorporating parameter uncertainty into simulation studies, and it is explained how this technique can be used in the design of reservoirs. Practical applications are presented to demonstrate the efficacy of the aforesaid simulation methods. In addition, the Fortran computer subroutines for the simulation procedures are included in an appendix with the microfiche edition of this paper.Appendix is available with entire article on microfiche. Order from American Geophysical Union, 1909 K Street, N.W., Washington, D.C. 20006. Document W78‐006; $1.00. Payment must accompanyorder.