予測

Pythonで学ぶARIMAモデル

James Fulton

Climate informatics researcher

次の値を予測する

AR(1)モデルを考えます

$y_t = a_1 y_{t-1} + \epsilon_t$

次の値を予測

$y_t = 0.6\; \text{x} \; 10 + \epsilon_t$

$y_t = 6.0 + \epsilon_t$

予測の不確実性

$ 5.0 < y_t < 7.0$

1期先予測

1期先予測を作成する

# Make predictions for last 25 values
results = model.fit()

# Make in-sample prediction
forecast = results.get_prediction(start=-25)

1期先予測を作成する

# Make predictions for last 25 values
results = model.fit()

# Make in-sample prediction
forecast = results.get_prediction(start=-25)

# forecast mean
mean_forecast = forecast.predicted_mean

予測平均は pandas の Series です

2013-10-28    1.519368
2013-10-29    1.351082
2013-10-30    1.218016

信頼区間

# Get confidence intervals of forecasts
confidence_intervals = forecast.conf_int()

信頼区間メソッドは pandas の DataFrame を返します

                                 lower y                       upper y
2013-09-28                     -4.720471                     -0.815384
2013-09-29                     -5.069875                      0.112505
2013-09-30                     -5.232837                      0.766300
2013-10-01                     -5.305814                      1.282935
2013-10-02                     -5.326956                      1.703974

予測のプロット

plt.figure()

# Plot prediction
plt.plot(dates, 
         mean_forecast.values, 
         color='red', 
         label='forecast')

# Shade uncertainty area
plt.fill_between(dates, lower_limits, upper_limits, color='pink')

plt.show()

予測のプロット

動的予測

動的予測を作成する

results = model.fit()
forecast = results.get_prediction(start=-25, dynamic=True)

# forecast mean
mean_forecast = forecast.predicted_mean

# Get confidence intervals of forecasts
confidence_intervals = forecast.conf_int()

サンプル外の予測

forecast = results.get_forecast(steps=20)

# forecast mean
mean_forecast = forecast.predicted_mean

# Get confidence intervals of forecasts
confidence_intervals = forecast.conf_int()

サンプル外の予測

forecast = results.get_forecast(steps=20)

Ayo berlatih!

Pythonで学ぶARIMAモデル