------------------------------------------------------------------------ source ### pesh ``` python def pesh( models:dict, # A dictionary of model instances to be used for forecasting. The keys should be string names for each model. weighting_scheme:Optional[Dict[str, float]]=None, # Optional dictionary specifying weights for each model's forecast. Default is None, which means equal weighting. )->None: ``` *Initialize the pesh model with the specified parameters for hybrid forecasting that combines forecasts from multiple models.*

	Type	Default	Details
models	dict		A dictionary of model instances to be used for forecasting. The keys should be string names for each model.
weighting_scheme	Optional[Dict[str, float]]	None	Optional dictionary specifying weights for each model’s forecast. Default is None, which means equal weighting.
Returns	None

------------------------------------------------------------------------ source ### pesh.fit ``` python def fit( df:pd.DataFrame, # Training DataFrame containing the target and any feature columns. )->None: ``` *Fit the specified models to the training data.*

	Type	Details
df	pd.DataFrame	Training DataFrame containing the target and any feature columns.
Returns	None

------------------------------------------------------------------------ source ### pesh.forecast ``` python def forecast( H:int, # Forecast horizon. exog:Optional[pd.DataFrame]=None, # Optional dataframe of future regressors. Must have the same columns as the exogenous variables used during training and at least `H` rows. )->np.ndarray: # Forecast values of length `H`. ``` *Recursive multi-step forecast.*

	Type	Default	Details
H	int		Forecast horizon.
exog	Optional[pd.DataFrame]	None	Optional dataframe of future regressors. Must have the same columns as the exogenous variables used during training and at least H rows.
Returns	np.ndarray		Forecast values of length H.

------------------------------------------------------------------------ source ### pesh.cross_validate ``` python def cross_validate( df:pd.DataFrame, # The input DataFrame containing the target and any feature columns. cv_split:int, # The number of cross-validation splits. test_size:int, # The size of the test set for each split. metrics:List[Callable], # Metric functions (e.g. ``[MAE, RMSE]``) used to evaluate forecast accuracy across folds. Call ``.cv_summary()`` after cross-validation to retrieve the aggregated scores. step_size:int=1, # The step size for rolling the forecasting origin. metric_to_opt:Optional[Callable]=None, # An optional metric function to optimize when weighting_scheme is set to "optimize". If None, it defaults to the first metric in the metrics list. weighting_scheme:Optional[Union[Dict[str, float], str]]=None, # None: equal weights across models. dict: user-provided weights (must sum to 1). "optimize": optimize weights to minimize MSE via `scipy.optimize.minimize`. optimizer:str='SLSQP', # Optimization method to use when weighting_scheme is set to "optimize". Passed to `scipy.optimize.minimize`. Refer to SciPy documentation for available methods. )->pd.DataFrame: # A DataFrame containing the performance metrics for each model and the combined forecast across all cross-validation splits. Also, optimized weights are stored in `self.optimal_weights_` if `weighting_scheme` is "optimize". ``` *Perform cross-validation for the pesh model using a rolling forecasting origin approach.*

	Type	Default	Details
df	pd.DataFrame		The input DataFrame containing the target and any feature columns.
cv_split	int		The number of cross-validation splits.
test_size	int		The size of the test set for each split.
metrics	List[Callable]		Metric functions (e.g. [MAE, RMSE]) used to evaluate forecast accuracy across folds. Call .cv_summary() after cross-validation to retrieve the aggregated scores.
step_size	int	1	The step size for rolling the forecasting origin.
metric_to_opt	Optional[Callable]	None	An optional metric function to optimize when weighting_scheme is set to “optimize”. If None, it defaults to the first metric in the metrics list.
weighting_scheme	Optional[Union[Dict[str, float], str]]	None	None: equal weights across models. dict: user-provided weights (must sum to 1). “optimize”: optimize weights to minimize MSE via scipy.optimize.minimize.
optimizer	str	SLSQP	Optimization method to use when weighting_scheme is set to “optimize”. Passed to scipy.optimize.minimize. Refer to SciPy documentation for available methods.
Returns	pd.DataFrame		A DataFrame containing the performance metrics for each model and the combined forecast across all cross-validation splits. Also, optimized weights are stored in self.optimal_weights_ if weighting_scheme is “optimize”.