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)