RO Types#

The CRO framework supports a total of 24 model configurations, constructed by combining four key design choices:

  • deterministic terms: linear or nonlinear dynamics

  • noise coefficient: additive or multiplicative

  • noise color: white or red noise

  • seasonality: time-invariant or seasonally modulated parameters

Together, these choices define a flexible hierarchy of RO model variants spanning increasing physical complexity. The default parameter estimation method depends on the selected RO formulation.

Default fitting methods by RO type#

RO Type

Default Fitting Method

Linear-White-Additive

LR-F

Linear-White-Multi

MLE

Linear-White-Multi-H

MLE

Linear-Red-Additive

LR-F

Linear-Red-Multi

LR-F-MAC

Linear-Red-Multi-H

LR-F

Nonlinear-White-Additive

LR-F

Nonlinear-White-Multi

LR-F-MAC

Nonlinear-White-Multi-H

MLE

Nonlinear-Red-Additive

LR-F

Nonlinear-Red-Multi

LR-F-MAC

Nonlinear-Red-Multi-H

LR-F

Seasonal-Linear-White-Additive

LR-F

Seasonal-Linear-White-Multi

MLE

Seasonal-Linear-White-Multi-H

MLE

Seasonal-Linear-Red-Additive

LR-F

Seasonal-Linear-Red-Multi

LR-F-MAC

Seasonal-Linear-Red-Multi-H

LR-F

Seasonal-Nonlinear-White-Additive

LR-F

Seasonal-Nonlinear-White-Multi

LR-F-MAC

Seasonal-Nonlinear-White-Multi-H

MLE

Seasonal-Nonlinear-Red-Additive

LR-F

Seasonal-Nonlinear-Red-Multi

LR-F-MAC

Seasonal-Nonlinear-Red-Multi-H

LR-F

Note

  • LR-F: Linear regression with forward differencing

  • MLE: Maximum likelihood estimation

  • LR-F-MAC: LR-F combined with Moment Analytical Constraint (MAC)