시계열 데이터의 회귀분석

import pandas as pd
df = pd.read_excel('uschange.xlsx')

df.Consumption.plot(legend=True)
df.Income.plot(legend=True)

<Axes: >

from statsmodels.formula.api import ols
ols('Consumption ~ Income', df).fit().summary()

m = ols('Consumption ~ Income + Production + Unemployment + Savings', df).fit()
m.summary()

y_pred = m.predict(df)
df.Consumption.plot(legend=True)
y_pred.plot(legend=True, label='prediction')

<Axes: >

import matplotlib.pyplot as plt
import numpy as np
plt.plot(df.Consumption, y_pred, '.')
x = np.array(plt.gca().get_xlim())  # 그림의 양쪽끝 x 좌표
plt.plot(x, x, '--')  

[<matplotlib.lines.Line2D at 0x158d851a290>]

m.resid

0      0.168638
1     -0.184591
2     -0.051472
3     -0.070916
4      0.267760
         ...   
182   -0.109993
183   -0.037906
184   -0.113017
185    0.128985
186   -0.046047
Length: 187, dtype: float64

df.Consumption - y_pred

0      0.168638
1     -0.184591
2     -0.051472
3     -0.070916
4      0.267760
         ...   
182   -0.109993
183   -0.037906
184   -0.113017
185    0.128985
186   -0.046047
Length: 187, dtype: float64

m.resid.hist()

<Axes: >

from statsmodels.graphics.tsaplots import plot_acf
plot_acf(m.resid);

import pingouin as pg
pg.corr(df.Income, m.resid)

pg.corr(y_pred, m.resid)

n = len(df)
df['t'] = np.arange(n)
ols('Consumption ~ t', df).fit().summary()

r = (n + 1) // 4
df['season'] = np.tile([1, 2, 3, 4], r)[:187]
ols('Consumption ~ C(season)', df).fit().summary()