Add `params_to_tune` for arima models

[Mr-Geekman]

🚀 Feature Request

Add params_to_tune for arima models.

Proposal

Sources for the grid:

• pycaret
  • sktime
  • statsforecast
• kats
  • arima
  • sarima

Suggested grid for SARIMAXModel:

{
    "p": IntUniformDistribution(low=1, high=6, step=1),
    "d": IntUniformDistribution(low=1, high=3, step=1),
    "q": IntUniformDistribution(low=1, high=6, step=1),
    "P": IntUniformDistribution(low=0, high=2, step=1),
    "D": IntUniformDistribution(low=0, high=1, step=1),
    "Q": IntUniformDistribution(low=0, high=1, step=1),
    "trend": CategoricalDistribution(["n", "c", "t", "ct"]),
}

Suggested grid for AutoARIMAModel:

{}

To discuss:

• Can we do something with S parameter in SARIMAXModel (It is the seasonality)? The problem is that it depends on the data. For example, we can just keep the value that was put by the user and don't change it.
• How to generate order for SARIMAXModel from p, d, q (same for seasonal_order)? In pycaret they generate all combinations and put them into CategoricalDistribution.
  • It will be solved in #1201.
• Do we really need the grid for AutoARIMAModel?
  • No, we don't need it.

Test cases

Look at #1184.

Additional context

Is blocked by #1201.

[Mr-Geekman]

Closed by #1206.