environmentaltools.temporal.nonstationary_analysis

environmentaltools.temporal.nonstationary_analysis(df: DataFrame, param: dict)

Perform non-stationary probability analysis with time-varying parameters.

Conducts non-stationary analysis where distribution parameters vary over time using Fourier expansions or other basis functions. Automatically selects the best model based on BIC or negative log-likelihood criteria.

Parameters:

• df (pd.DataFrame) – Time series data containing the variable and time information

• param (dict) –

  Configuration dictionary containing:

  • ’var’str

    Variable name to analyze

  • ’basis_function’dict

    Basis function specification with ‘order’ key

  • ’bic’bool

    If True, use BIC for model selection; else use NLLF

  • ’no_fun’int

    Number of distribution functions

  • ’initial_parameters’dict

    Contains ‘make’ (bool) and ‘mode’ (list) for custom initialization

Returns:

Updated param dictionary with fitted results:

• ’par’list

  Fitted parameters for the selected model

• ’mode’list

  Selected Fourier mode orders for each parameter

• ’all’list

  All tested models with [mode_str, bic, parameters]

Return type:

dict

Notes

The function tests multiple Fourier expansion modes and selects the best one based on either Bayesian Information Criterion (BIC) or negative log-likelihood (NLLF). Lower values indicate better fit.

For stationary cases (order=0), mode is set to zeros.

Model selection prioritizes: 1. BIC if param[‘bic’] is True (penalizes complexity) 2. NLLF otherwise (pure likelihood fit)

See also

nonst_fit

Core fitting function called internally

stationary_analysis

For time-invariant parameter fitting

Examples

>>> param = {
...     'var': 'Hs',
...     'basis_function': {'order': 2},
...     'bic': True,
...     'no_fun': 1,
...     'initial_parameters': {'make': False}
... }
>>> param = nonstationary_analysis(df, param)
>>> print(f"Selected mode: {param['mode']}")
>>> print(f"Parameters: {param['par']}")