check_stats on time series differences.

[ngupta23]

Related to #1654

Once this is implemented, add option to run ACF, PACF and Spectral Density and White Noise tests on the differences.

Interface: TBD

# Shows all mentioned differences together with original.
# Trellis with ACF and PACF below the time series in individual rows
plot_model(plot="diff", data_kwargs={'order':[1,2], 'acf': True, 'pacf" True})  

So the above example would have a 3x3 plot

• Row 1: Time Series Plots for [Original, 1st difference, 2nd difference]
• Row 2: ACF for [Original, 1st difference, 2nd difference]
• Row 3: PACF for [Original, 1st difference, 2nd difference]

Other options that could be supported are Spectral Density, FFT, etc. (TBD)

Here is an example, though it is not in the right format. The reason for showing this is to demonstrate its usefulness. It clearly shows that we need to perform the first difference and then either the value of 'p' is 50 or else seasonality is 50.

[ngupta23]

Actually, thinking about this more, the purpose of evaluation would not be to replicate the plotting (#1654), but to do additional tests on the differences for example, run LJung-Box, ADF test, etc. on differences. Hence, this functionality should be limited to check_stats method.

Interface TBD

[ngupta23]

To Test

import pandas as pd
from pycaret.datasets import get_data
from pycaret.internal.pycaret_experiment import TimeSeriesExperiment

data = get_data("airline")

exp = TimeSeriesExperiment()
exp.setup(data=data, fh=12, session_id=42)

# Runs tests on original dataset as well as lagged versions 
# Note order = 2 = lags = [1, 1] (same as d=2 in ARIMA)
exp.check_stats(test=test, data_kwargs={"order_list": [1, 2]})
exp.check_stats(test=test, data_kwargs={"lags_list": [1, [1, 12]]})

model = exp.create_model(arima)
# Runs tests on model residuals as well as lagged versions of the residuals
exp.check_stats(model, test=test, data_kwargs={"order_list": [1, 2]})
exp.check_stats(model, test=test, data_kwargs={"lags_list": [1, [1, 12]]})