시계열 회귀
import pandas as pd
df = pd.read_excel('uschange.xlsx')
df.Consumption.plot(legend=True)
df.Income.plot(legend=True)
output
<Axes: >
<Figure size 640x480 with 1 Axes>
from statsmodels.formula.api import ols
ols('Consumption ~ Income', df).fit().summary()
output
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: Consumption R-squared: 0.159
Model: OLS Adj. R-squared: 0.154
Method: Least Squares F-statistic: 34.98
Date: Thu, 08 Aug 2024 Prob (F-statistic): 1.58e-08
Time: 14:48:02 Log-Likelihood: -169.62
No. Observations: 187 AIC: 343.2
Df Residuals: 185 BIC: 349.7
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 0.5451 0.056 9.789 0.000 0.435 0.655
Income 0.2806 0.047 5.915 0.000 0.187 0.374
==============================================================================
Omnibus: 16.528 Durbin-Watson: 1.696
Prob(Omnibus): 0.000 Jarque-Bera (JB): 29.145
Skew: -0.454 Prob(JB): 4.69e-07
Kurtosis: 4.707 Cond. No. 2.08
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
ols('Consumption ~ Income + Production + Unemployment + Savings', df).fit().summary()
output
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: Consumption R-squared: 0.754
Model: OLS Adj. R-squared: 0.749
Method: Least Squares F-statistic: 139.5
Date: Thu, 08 Aug 2024 Prob (F-statistic): 2.62e-54
Time: 14:48:45 Log-Likelihood: -54.692
No. Observations: 187 AIC: 119.4
Df Residuals: 182 BIC: 135.5
Df Model: 4
Covariance Type: nonrobust
================================================================================
coef std err t P>|t| [0.025 0.975]
--------------------------------------------------------------------------------
Intercept 0.2673 0.037 7.184 0.000 0.194 0.341
Income 0.7145 0.042 16.934 0.000 0.631 0.798
Production 0.0459 0.026 1.773 0.078 -0.005 0.097
Unemployment -0.2048 0.106 -1.941 0.054 -0.413 0.003
Savings -0.0453 0.003 -16.287 0.000 -0.051 -0.040
==============================================================================
Omnibus: 18.566 Durbin-Watson: 2.169
Prob(Omnibus): 0.000 Jarque-Bera (JB): 28.796
Skew: 0.564 Prob(JB): 5.58e-07
Kurtosis: 4.556 Cond. No. 61.9
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
추세
n = len(df)
n
output
187
df['t'] = np.arange(n)
ols('Consumption ~ t', df).fit().summary()
output
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: Consumption R-squared: 0.025
Model: OLS Adj. R-squared: 0.020
Method: Least Squares F-statistic: 4.726
Date: Thu, 08 Aug 2024 Prob (F-statistic): 0.0310
Time: 15:03:24 Log-Likelihood: -183.46
No. Observations: 187 AIC: 370.9
Df Residuals: 185 BIC: 377.4
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 0.9242 0.095 9.777 0.000 0.738 1.111
t -0.0019 0.001 -2.174 0.031 -0.004 -0.000
==============================================================================
Omnibus: 46.181 Durbin-Watson: 1.333
Prob(Omnibus): 0.000 Jarque-Bera (JB): 115.917
Skew: -1.058 Prob(JB): 6.74e-26
Kurtosis: 6.225 Cond. No. 214.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
계절성
year = n // 4 # 몫
df['season'] = np.tile([1,2,3,4], year + 1)[:n]
ols('Consumption ~ C(season)', df).fit().summary()
output
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: Consumption R-squared: 0.009
Model: OLS Adj. R-squared: -0.007
Method: Least Squares F-statistic: 0.5513
Date: Thu, 08 Aug 2024 Prob (F-statistic): 0.648
Time: 15:11:51 Log-Likelihood: -184.97
No. Observations: 187 AIC: 377.9
Df Residuals: 183 BIC: 390.9
Df Model: 3
Covariance Type: nonrobust
==================================================================================
coef std err t P>|t| [0.025 0.975]
----------------------------------------------------------------------------------
Intercept 0.7356 0.096 7.667 0.000 0.546 0.925
C(season)[T.2] -0.0296 0.136 -0.218 0.828 -0.297 0.238
C(season)[T.3] 0.1143 0.136 0.842 0.401 -0.153 0.382
C(season)[T.4] -0.0424 0.136 -0.311 0.756 -0.312 0.227
==============================================================================
Omnibus: 29.475 Durbin-Watson: 1.283
Prob(Omnibus): 0.000 Jarque-Bera (JB): 63.812
Skew: -0.718 Prob(JB): 1.39e-14
Kurtosis: 5.476 Cond. No. 4.78
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
p가 모두 0.05보다 크기 때문에 계절성이 없다는 것을 기 각할 수 없다
계절성이 있을 수는 있지만 없을 가능성을 배제 못함