Confidence intervals from error estimation from backtest

[martins0n]

🚀 Feature Request

We can build confidence intervals for generative models or models like Arima out of the box.
But we miss this opportunity for Regression models.
We should build intervals from backtest results for such models.

Motivation

Confidence intervals are helpfull for risk estimation.

Proposal

• Pipeline method forecast has parameter confidence_interval by default False
• Pipeline __init__ has parameters interval_width by default 0.95 and confidence_interval_cv by default 3
• While forecast -- default implementation of confidence intervals is used, if it's not available -- we use another procedure
  • Estimating errors on crossvalidation results using backtest
  • confidence interva is given by (y_{i} - t_{\alpha} * SE, y_{i} + t_{\alpha} * SE) - SE -- standart error estimation

Test cases

No response

Alternatives

No response

Additional context

No response

Checklist

• Added feature request
• Added motivation
• Added proposal

[iKintosh]

If model already has confidence interval support then use model's method, otherwise use Pipeline's