Supplement 1. MATLAB and R code for performing ARMA(p,q) model fitting.

File List ARMApqREMLfunct.m -- Matlab code for the ARMA likelihood function for REML and ML estimation ARMApq_ME_REMLfunct.m -- Matlab code for the ARMA likelihood function for pseudo-REML and pseudo_ML estimation ARMApqREMLfunct_R.txt -- R code for the ARMA likelihood function for REML and ML estimation Description The ARMApqREMLfunct.m matlab program gives the negative log likelihood function and restricted likelihood function for an ARMA(p,q) model that can be used with a minimization program such as fminsearch.m. The ARMApqREMLfunct.m matlab program similarly gives the negative log likelihood function and restricted likelihood function for an ARMA(p,q) model for pseudo-ML and pseudo-REML estimation in which the standard error of the estimates is provided by the user. ARMApqREMLfunct_R.txt gives a version of ARMApqREMLfunct.m translated from matlab into R. The derivations of the code are given in Appendix A.