如何自动化 SARIMA 模型进行时间序列预测？

Question

我正在尝试使用 SARIMA 在时间序列预测中为 p、d、q 找到正确的参数。我需要预测 1000 个邮政编码的房价。问题是网格搜索需要太多时间，我无法手动查看每个邮政编码的 ACF/PACF，因为我需要将其自动化。

我尝试使用网格搜索来搜索 8 种不同的参数组合，并使用了基于 AIC 的最佳参数集。

p = d = q = range(0, 2)
#d = range(0, 2)
pdq = list(itertools.product(p, d, q))
seasonal_pdq = [(x[0], x[1], x[2], 12) for x in list(itertools.product(p, d, q))]
parameters = []
for param in pdq:
    for param_seasonal in seasonal_pdq:
        try:
            model = sm.tsa.statespace.SARIMAX(y_new,method='css',
                                            order=param,
                                            seasonal_order=param_seasonal,
                                            enforce_stationarity=False,
                                            enforce_invertibility=False)
            results = model.fit()
            #print('ARIMA{}x{}12 - AIC:{}'.format(param, param_seasonal, results.aic))
        except:
            continue
        aic = results.aic
        parameters.append([param,param_seasonal,aic])
result_table = pd.DataFrame(parameters)
result_table.columns = ['parameters','parameters_seasonal','aic']
    # sorting in ascending order, the lower AIC is - the better
result_table = result_table.sort_values(by='aic', ascending=True).reset_index(drop=True)

我无法得到一个能够超越天真的预测的模型。你能给我一些指导吗？

Answer 1

最好的办法是使用 pyramid 库，它可以自动选择 p、d、q 参数。您需要充分处理数据以便输入 1000 个时间序列，但这里有一个如何在单个时间序列上运行的示例。

假设我们有一个随时间变化的每日最高温度记录数据集，目标是自动选择 ARIMA 的 p、d、q 参数。这可以通过以下方式实现：

from pyramid.arima.stationarity import ADFTest
adf_test = ADFTest(alpha=0.05)
adf_test.is_stationary(series)
train, test = series[1:741], series[742:927]
train.shape
test.shape
plt.plot(train)
plt.plot(test)
plt.title("Training and Test Data")
plt.show()

如您所见，在这种情况下，ARIMA 模型选择本身是基于具有最低 AIC 的配置：

>>> Arima_model=auto_arima(train, start_p=1, start_q=1, max_p=8, max_q=8, start_P=0, start_Q=0, max_P=8, max_Q=8, m=12, seasonal=True, trace=True, d=1, D=1, error_action='warn', suppress_warnings=True, random_state = 20, n_fits=30)
Fit ARIMA: order=(1, 1, 1) seasonal_order=(0, 1, 0, 12); AIC=-667.202, BIC=-648.847, Fit time=3.710 seconds
Fit ARIMA: order=(0, 1, 0) seasonal_order=(0, 1, 0, 12); AIC=-270.700, BIC=-261.522, Fit time=0.354 seconds
Fit ARIMA: order=(1, 1, 0) seasonal_order=(1, 1, 0, 12); AIC=-625.446, BIC=-607.090, Fit time=2.365 seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(0, 1, 1, 12); AIC=-1090.370, BIC=-1072.014, Fit time=7.584 seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(1, 1, 1, 12); AIC=-1088.657, BIC=-1065.712, Fit time=10.024 seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(0, 1, 0, 12); AIC=-653.939, BIC=-640.172, Fit time=1.733 seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(0, 1, 2, 12); AIC=-1087.889, BIC=-1064.944, Fit time=25.853 seconds
Fit ARIMA: order=(0, 1, 1) seasonal_order=(1, 1, 2, 12); AIC=-1087.188, BIC=-1059.655, Fit time=31.205 seconds
Fit ARIMA: order=(1, 1, 1) seasonal_order=(0, 1, 1, 12); AIC=-1105.233, BIC=-1082.288, Fit time=10.266 seconds
Fit ARIMA: order=(1, 1, 0) seasonal_order=(0, 1, 1, 12); AIC=-887.349, BIC=-868.994, Fit time=9.558 seconds
Fit ARIMA: order=(1, 1, 2) seasonal_order=(0, 1, 1, 12); AIC=-1086.931, BIC=-1059.397, Fit time=11.649 seconds
Fit ARIMA: order=(0, 1, 0) seasonal_order=(0, 1, 1, 12); AIC=-724.814, BIC=-711.047, Fit time=4.372 seconds
Fit ARIMA: order=(2, 1, 2) seasonal_order=(0, 1, 1, 12); AIC=-1085.480, BIC=-1053.358, Fit time=17.619 seconds
Fit ARIMA: order=(1, 1, 1) seasonal_order=(1, 1, 1, 12); AIC=-1072.933, BIC=-1045.400, Fit time=13.924 seconds
Fit ARIMA: order=(1, 1, 1) seasonal_order=(0, 1, 2, 12); AIC=-1102.926, BIC=-1075.392, Fit time=28.082 seconds
Fit ARIMA: order=(1, 1, 1) seasonal_order=(1, 1, 2, 12); AIC=-1102.342, BIC=-1070.219, Fit time=35.426 seconds
Fit ARIMA: order=(2, 1, 1) seasonal_order=(0, 1, 1, 12); AIC=-1010.837, BIC=-983.303, Fit time=8.926 seconds
Total fit time: 222.656 seconds
>>> 
>>> Arima_model.summary()
<class 'statsmodels.iolib.summary.Summary'>
"""
                                 Statespace Model Results                                 
==========================================================================================
Dep. Variable:                                  y   No. Observations:                  740
Model:             SARIMAX(1, 1, 1)x(0, 1, 1, 12)   Log Likelihood                 557.617
Date:                            Thu, 14 Mar 2019   AIC                          -1105.233
Time:                                    16:33:59   BIC                          -1082.288
Sample:                                         0   HQIC                         -1096.379
                                            - 740                                         
Covariance Type:                              opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
intercept   1.359e-06   6.75e-06      0.201      0.840   -1.19e-05    1.46e-05
ar.L1          0.1558      0.034      4.575      0.000       0.089       0.223
ma.L1         -0.9847      0.013    -75.250      0.000      -1.010      -0.959
ma.S.L12      -0.9933      0.092    -10.837      0.000      -1.173      -0.814
sigma2         0.0118      0.001     11.259      0.000       0.010       0.014
===================================================================================
Ljung-Box (Q):                       54.38   Jarque-Bera (JB):              3179.66
Prob(Q):                              0.06   Prob(JB):                         0.00
Heteroskedasticity (H):               0.77   Skew:                            -1.46
Prob(H) (two-sided):                  0.04   Kurtosis:                        12.82
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).

如果您熟悉 R，也可以使用 auto.arima 命令。事实上，我建议这样做，因为在某些情况下，它可能会为您提供比 Pyramid（最近开发的）更好的自动化配置。

也就是说，pyramid 将极大地帮助您实现自动化。