[BUG] Prophet with logistic growth does not work

Describe the bug It is not compatible with the case that the growth parameter of prophet is equal to ‘logistic‘

To Reproduce

from sktime.datasets import load_airline
y = load_airline()
y = y.to_timestamp(freq="M")
y_train, y_test = temporal_train_test_split(y, test_size=36)

y_train_df = pd.DataFrame(y_train,index = y_train.index,columns=['y'])
y_train_df["cap"] = max(y_train_df["y"])
y_train_df['floor'] = 0

forecaster = Prophet(
    growth = 'logistic'
)

forecaster.fit(y_train_df)

Expected behavior

The growth parameter compatible with prophet is equal to ‘logistic‘ Additional context

Versions

from sktime import show_versions; show_versions()

System: python: 3.8.3 (default, Jul 2 2020, 11:26:31) [Clang 10.0.0 ] executable: /Users/baixiaotiao/opt/anaconda3/bin/python machine: macOS-10.16-x86_64-i386-64bit

Python dependencies: pip: 20.1.1 setuptools: 49.2.0.post20200714 sklearn: 0.24.2 sktime: 0.6.1 statsmodels: 0.12.2 numpy: 1.20.3 scipy: 1.5.0 Cython: 0.29.21 pandas: 1.2.5 matplotlib: 3.2.2 joblib: 0.16.0 numba: 0.50.1 pmdarima: 1.8.2 tsfresh: None

[fkiraly]

@fkiraly How would your framework deal with a class in which the inner-type depends on user-input?

Assuming that “user input” means behaviour controlled by hyper-parameters set in construction, the paradigm would be reading that hyper-parameter in _fit and dealing with any additional conversion or input logic there. fit would be set up to pass through the supported inner types and otherwise convert to them.

Generally, implementers can do whatever they want in _fit in addition to the “generic” conversions which only take over if nothing smarter is specified.

[fkiraly]

Report of closely related behaviour by @ohbtorres here: https://github.com/alan-turing-institute/sktime/issues/2444