[Core] Return params of distributions
Description
Currently, statsforecast can generate mean forecasts and prediction intervals. However, it could be more beneficial to provide the option of returning the forecast distribution for each timestamp within the forecast horizon. This functionality will only apply to models that assume normality.
The first step involves identifying the models compatible with this feature. Subsequently, we should incorporate an option to return the parameters in the following manner:
auto_arima = AutoARIMA()
auto_arima.forecast(y=y, h=12, return_params=True)
The output should include the parameters of the distribution. Following that, this feature should be integrated into the StatsForecast class in the following way:
sf = StatsForecast(models=[AutoETS()], ....)
sf.forecast(Y_df, h=12, return_params=True)
The result of the final function call should be a dataframe that includes the mean and variance (or standard deviation) for each timestamp in the forecast horizon.
Use case
No response