The three de-trended series are then simulated. Correlation is
captured by substituting the Gaussian pseudorandom vector
normally used for ε in Eq. (4) with the covariance matrix of the
three de-trended series. The determination of AR coefficients and
model generation is implemented using the ARfit algorithm in
MATLAB developed by Neumaier and Schneider (2001). Order is
chosen by optimising Schwarz's Bayesian Criterion and coefficients
using stepwise least squares estimation process. The simulation
methodology maintains persistence characteristics, seasonality
and correlation between wind speed, wave height, and wave
period time series of the observed site.