時系列モデルの当てはめ

Pythonで学ぶARIMAモデル

James Fulton

Climate informatics researcher

モデルの作成

from statsmodels.tsa.arima.model import ARIMA

# これは ARMA(p,q) モデルです
model = ARIMA(timeseries, order=(p,0,q))

ARモデルとMAモデルの作成

ar_model = ARIMA(timeseries, order=(p,0,0))

ma_model = ARIMA(timeseries, order=(0,0,q))

当てはめと要約の表示

model = ARIMA(timeseries, order=(2,0,1))

results = model.fit()

print(results.summary())

当てはめ結果の要約

                             SARIMAX Results                                                  
 ==============================================================================
 Dep. Variable:                      y   No. Observations:                 1000
 Model:                     ARMA(2, 1)   Log Likelihood                 148.580
 Date:                Thu, 25 Apr 2022   AIC                           -287.159
 Time:                        22:57:00   BIC                           -262.621
 Sample:                             0   HQIC                          -277.833
 Covariance Type:                    opg                                       
 ==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
 ------------------------------------------------------------------------------
 const         -0.0017      0.012     -0.147      0.883      -0.025       0.021
 ar.L1.y        0.5253      0.054      9.807      0.000       0.420       0.630
 ar.L2.y       -0.2909      0.042     -6.850      0.000      -0.374      -0.208
 ma.L1.y        0.3679      0.052      7.100      0.000       0.266       0.469

当てはめ結果の要約

                            SARIMAX Results                           
==============================================================================
Dep. Variable:                      y   No. Observations:                 1000
Model:                     ARMA(2, 1)   Log Likelihood                 148.580
Date:                Thu, 25 Apr 2022   AIC                           -287.159
Time:                        22:57:00   BIC                           -262.621
Sample:                             0   HQIC                          -277.833
Covariance Type:                    opg

当てはめ結果の要約

 ==============================================================================
                  coef    std err          z      P>|z|      [0.025      0.975]
 ------------------------------------------------------------------------------
 const         -0.0017      0.012     -0.147      0.883      -0.025       0.021
 ar.L1.y        0.5253      0.054      9.807      0.000       0.420       0.630
 ar.L2.y       -0.2909      0.042     -6.850      0.000      -0.374      -0.208
 ma.L1.y        0.3679      0.052      7.100      0.000       0.266       0.469

 sigma2         1.6306      0.339      6.938      0.000       0.583       1.943

ARMAXモデル入門

外生変数ありのARMA
時系列に加え外部変数を使用
ARMAX = ARMA + 線形回帰

ARMAXの式

ARMA(1,1) モデル：$$y_t = a_1 y_{t-1} + m_1 \epsilon_{t-1} + \epsilon_t$$

ARMAX(1,1) モデル：$$y_t = x_1 z_t + a_1 y_{t-1} + m_1 \epsilon_{t-1} + \epsilon_t$$

ARMAXの例

ARMAXの当てはめ

# モデルを生成
model = ARIMA(df['productivity'], order=(2,0,1), exog=df['hours_sleep'])


# モデルを当てはめ
results = model.fit()

ARMAXの要約

 ==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
 -----------------------------------------------------------------------------
 const         -0.1936      0.092     -2.098      0.041      -0.375      -0.013
 x1             0.1131      0.013      8.602      0.000       0.087       0.139
 ar.L1.y        0.1917      0.252      0.760      0.450      -0.302       0.686
 ar.L2.y       -0.3740      0.121     -3.079      0.003      -0.612      -0.136
 ma.L1.y       -0.0740      0.259     -0.286      0.776      -0.581       0.433

¡Vamos a practicar!

Pythonで学ぶARIMAモデル