Implement forecast decomposition for ARIMA-like models

[alex-hse-repository]

🚀 Feature Request

Implement forecast decomposition for AutoARIMAModel and SARIMAXModel

Proposal

In _SARIMAXBaseAdapter implement methods:

def predict_components(df: pd.DataFrame) -> pd.DataFrame
def forcast_components(df: pd.DataFrame) -> pd.DataFrame

Details:

• implement in-sample decomposition in predict_components using ARIMAResults
• implement out-of-sample decomposition in forcast_components using PredictionResults.results
• estimate components using state-space representation of SARIMAX
• decompose prediction to SARIMA and exogenious contributions
• use obs_intercept to estimate exog components when mle_regresion is set
• name for SARIMA component in SARIMAXModel: sarima(p={},d={},q={},P={},D={},Q={})
• name for ARIMA component in AutoARIMAModel: arima(p={},d={},q={})
• exogenious components should be pefixed with target_component_

Test cases

For AutoARIMAModel and SARIMAXModel

• Test that components sum up to target
• Test that the components names are correct for all possible parameters combination

Additional context

See implementation in ETNA-1480 folder