如何检测时间序列中的异方差（Heteroskedasticity）

 import pandas as pd
 import statsmodels.stats.api as sms
 from statsmodels.formula.api import ols
 
 TEST_NAMES = ['White', 'Breusch-Pagan', 'Goldfeld-Quandt']
 FORMULA = 'value ~ time'
 
 
 class Heteroskedasticity:
 
     @staticmethod
     def het_tests(series: pd.Series, test: str) -> float:
         """
         Testing for heteroskedasticity
 
         :param series: Univariate time series as pd.Series
         :param test: String denoting the test. One of 'white','goldfeldquandt', or 'breuschpagan'
 
         :return: p-value as a float.
 
         If the p-value is high, we accept the null hypothesis that the data is homoskedastic
         """
         assert test in TEST_NAMES, 'Unknown test'
 
         series = series.reset_index(drop=True).reset_index()
         series.columns = ['time', 'value']
         series['time'] += 1
 
         olsr = ols(FORMULA, series).fit()
 
         if test == 'White':
             _, p_value, _, _ = sms.het_white(olsr.resid, olsr.model.exog)
         elif test == 'Goldfeld-Quandt':
             _, p_value, _ = sms.het_goldfeldquandt(olsr.resid, olsr.model.exog, alternative='two-sided')
         else:
             _, p_value, _, _ = sms.het_breuschpagan(olsr.resid, olsr.model.exog)
 
         return p_value
 
     @classmethod
     def run_all_tests(cls, series: pd.Series):
 
         test_results = {k: cls.het_tests(series, k) for k in TEST_NAMES}
 
         return test_results

 from pmdarima.datasets import load_airpassengers
 
 # https://github.com/vcerqueira/blog/blob/main/src/heteroskedasticity.py
 from src.heteroskedasticity import Heteroskedasticity
 
 series = load_airpassengers(True)
 
 test_results = Heteroskedasticity.run_all_tests(series)
 
 # {'Breusch-Pagan': 4.55e-07,
 # 'Goldfeld-Quandt': 8.81e-13,
 # 'White': 4.34e-07}

 import numpy as np
 
 test_results = Heteroskedasticity.run_all_tests(np.log(series))
 
 # {'Breusch-Pagan': 0.033,
 # 'Goldfeld-Quandt': 0.18,
 # 'White': 0.10}

 import numpy as np
 from pmdarima.datasets import load_airpassengers
 from pmdarima.arima import auto_arima
 from sklearn.model_selection import train_test_split
 
 series = load_airpassengers(True)
 
 # leaving the last 12 points for testing
 train, test = train_test_split(series, test_size=12, shuffle=False)
 # stabilizing the variance in the train
 log_train = np.log(train)
 
 # building an arima model, m is the seasonal period (monthly)
 mod = auto_arima(log_train, seasonal=True, m=12)
 
 # getting the log forecasts
 log_forecasts = mod.predict(12)
 
 # reverting the forecasts
 forecasts = np.exp(log_forecasts)