Four such directions are identified: (a) empirical time series prediction with nonlinear autoregressive moving-average (ARMA) models, for which an example is given in terms of a geosynchronous electron flux index model.
In particular, we consider (i) the theoretical foundations of ridge regression, (ii) its link to commonly used methods in animal breeding, (iii) the computational feasibility, and (iv) the scope for constructing prediction models with nonlinear effects (e.g., dominance and epistasis).
We find a small performance increase for long-term predictions (>40 days) with nonlinear models, indicating that nonlinear effects expose themselves for larger prediction horizons, and no significant difference between nonrecurrent and recurrent methods meaning that the effects of dependencies spanning several days are of no importance.
These uncertainties can cause discrepancies mainly in the prediction by models with nonlinear behavior and they can be the source of confusion in the design of chemical reactors and consequently also in the safety and operability analysis.
VanRaden et al. [ 7] showed that combined predictions (PA and genomic predictions) were more accurate than PA (0.22 to 0.62 greater with nonlinear genomic predictions) in North American Holstein bulls.
In particular, the recorded time series are evaluated with nonlinear prediction error to unveil deterministic dynamics, cross-prediction error to determine the stationarity of the signal, and surrogate data testing to verify the existence of nonlinear components in the underlying system.
Besides, the control algorithm is gathering the direct estimation technique, with the covariance resetting procedure based on the weighted prediction error, to deal with nonlinear plants.
Parameter uncertainty leading to inaccurate predictions is often present when kinetic models with nonlinear rate equations are considered.
Comparisons of numerical predictions with experiments show that the nonlinear elastic approach is not very suitable for fibre composite confinement.
The results demonstrated that, for the two nonlinear static analysis methods used in this study, different predictions of nonlinear response occurred with neither method being regarded as producing correct results due to a number of simplifications inherent in the methods.
