[time-series]
지수 평활
import pandas as pd
df = pd.read_excel('ausvisitor.xlsx')
y = df.visitor
y.plot()
y.ewm(alpha=0.1).mean().plot()
:::note[output]
<Axes: >
<Figure size 640x480 with 1 Axes>
:::
단순지수평활 ETS(A, N, N)
from statsmodels.tsa.api import ETSModel
ets_ann = ETSModel(y).fit()
ets_ann.summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
ETS Results
==============================================================================
Dep. Variable: visitor No. Observations: 68
Model: ETS(ANN) Log Likelihood -240.535
Date: Thu, 08 Aug 2024 AIC 487.070
Time: 17:25:13 BIC 493.729
Sample: 0 HQIC 489.709
- 68 Scale 69.178
Covariance Type: approx
===================================================================================
coef std err z P>|z| [0.025 0.975]
-----------------------------------------------------------------------------------
smoothing_level 0.1964 0.048 4.101 0.000 0.103 0.290
initial_level 27.5115 4.976 5.529 0.000 17.758 37.265
===================================================================================
Ljung-Box (Q): 10.91 Jarque-Bera (JB): 1.20
Prob(Q): 0.00 Prob(JB): 0.55
Heteroskedasticity (H): 2.57 Skew: -0.00
Prob(H) (two-sided): 0.03 Kurtosis: 2.35
===================================================================================
Warnings:
[1] Covariance matrix calculated using numerical (complex-step) differentiation.
"""
:::
import matplotlib.pyplot as plt
y.plot(label='y')
ets_ann.predict(start=0, end=100).plot(label='ETS(A, N, N)')
plt.legend();
:::note[output]
<Figure size 640x480 with 1 Axes>
:::
홀트의 선형 추세 기법 ETS(A, A, N)
ets_aan = ETSModel(y, trend='add').fit()
ets_aan.summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
ETS Results
==============================================================================
Dep. Variable: visitor No. Observations: 68
Model: ETS(AAN) Log Likelihood -231.928
Date: Thu, 08 Aug 2024 AIC 473.856
Time: 17:25:37 BIC 484.954
Sample: 0 HQIC 478.254
- 68 Scale 53.707
Covariance Type: approx
===================================================================================
coef std err z P>|z| [0.025 0.975]
-----------------------------------------------------------------------------------
smoothing_level 0.0097 nan nan nan nan nan
smoothing_trend 0.0097 0.006 1.680 0.093 -0.002 0.021
initial_level 25.1272 1.738 14.461 0.000 21.722 28.533
initial_trend 0.1841 0.169 1.089 0.276 -0.147 0.516
===================================================================================
Ljung-Box (Q): 11.15 Jarque-Bera (JB): 0.85
Prob(Q): 0.00 Prob(JB): 0.65
Heteroskedasticity (H): 2.53 Skew: 0.01
Prob(H) (two-sided): 0.03 Kurtosis: 2.45
===================================================================================
Warnings:
[1] Covariance matrix calculated using numerical (complex-step) differentiation.
"""
:::
예측
y.plot(label='y')
ets_aan.predict(start=0, end=100).plot(label='ETS(A, A, N)')
plt.legend();
:::note[output]
<Figure size 640x480 with 1 Axes>
:::
감쇠 추세 기법 ETS(A, Ad, N)
ets_aadn = ETSModel(y, trend='add', damped_trend=True).fit()
ets_aadn.summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
ETS Results
==============================================================================
Dep. Variable: visitor No. Observations: 68
Model: ETS(AAdN) Log Likelihood -232.737
Date: Thu, 08 Aug 2024 AIC 477.473
Time: 17:26:12 BIC 490.790
Sample: 0 HQIC 482.750
- 68 Scale 54.999
Covariance Type: approx
===================================================================================
coef std err z P>|z| [0.025 0.975]
-----------------------------------------------------------------------------------
smoothing_level 0.0164 0.089 0.185 0.853 -0.158 0.191
smoothing_trend 0.0164 0.023 0.730 0.466 -0.028 0.061
damping_trend 0.9800 0.069 14.112 0.000 0.844 1.116
initial_level 26.2533 3.205 8.192 0.000 19.972 32.535
initial_trend 0.1244 0.318 0.392 0.695 -0.498 0.747
===================================================================================
Ljung-Box (Q): 10.90 Jarque-Bera (JB): 0.91
Prob(Q): 0.00 Prob(JB): 0.63
Heteroskedasticity (H): 2.59 Skew: 0.02
Prob(H) (two-sided): 0.03 Kurtosis: 2.43
===================================================================================
Warnings:
[1] Covariance matrix calculated using numerical (complex-step) differentiation.
"""
:::
예측
y.plot(label='y')
ets_aadn.predict(start=0, end=100).plot(label='ETS(A, Ad, N)')
plt.legend();
:::note[output]
<Figure size 640x480 with 1 Axes>
:::
홀트-윈터스의 계절성 기법 ETS(A, A, A)
ets_aaa = ETSModel(y, trend='add', seasonal='add', seasonal_periods=4).fit()
ets_aaa.summary()
:::note[output]
<class 'statsmodels.iolib.summary.Summary'>
"""
ETS Results
==============================================================================
Dep. Variable: visitor No. Observations: 68
Model: ETS(AAA) Log Likelihood -150.480
Date: Thu, 08 Aug 2024 AIC 320.960
Time: 17:26:47 BIC 343.155
Sample: 0 HQIC 329.754
- 68 Scale 4.894
Covariance Type: approx
======================================================================================
coef std err z P>|z| [0.025 0.975]
--------------------------------------------------------------------------------------
smoothing_level 0.3042 0.099 3.075 0.002 0.110 0.498
smoothing_trend 3.042e-05 nan nan nan nan nan
smoothing_seasonal 0.4154 0.082 5.057 0.000 0.254 0.576
initial_level 29.4939 nan nan nan nan nan
initial_trend 0.5711 0.113 5.076 0.000 0.351 0.792
initial_seasonal.0 -3.4686 nan nan nan nan nan
initial_seasonal.1 -5.9855 nan nan nan nan nan
initial_seasonal.2 -11.4778 nan nan nan nan nan
initial_seasonal.3 0 nan nan nan nan nan
===================================================================================
Ljung-Box (Q): 5.11 Jarque-Bera (JB): 8.62
Prob(Q): 0.75 Prob(JB): 0.01
Heteroskedasticity (H): 0.48 Skew: -0.68
Prob(H) (two-sided): 0.08 Kurtosis: 4.10
===================================================================================
Warnings:
[1] Covariance matrix calculated using numerical (complex-step) differentiation.
"""
:::
예측
y.plot(label='y')
ets_aaa.predict(start=0, end=100).plot(label='ETS(A, A, A)')
plt.legend();
:::note[output]
<Figure size 640x480 with 1 Axes>
:::