第1章 時系列分析の基礎概念

In [1]:

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from statsmodels.tsa.stattools import acf
from statsmodels.stats.diagnostic import acorr_ljungbox

import pandas as pd import numpy as np import matplotlib.pyplot as plt from statsmodels.tsa.stattools import acf from statsmodels.stats.diagnostic import acorr_ljungbox

In [2]:

n_data = 100
ts = np.arange(n_data)
mus = [0.0, 2.0, -2.0, 0.0, 0.0, 2.0]
sigmas = [1.0, 1.0, 1.0, 2.0, 3.0, 2.0]
plt.figure(figsize=[10, 12])
for i in range(6):
    yt = mus[i] + sigmas[i] * np.random.randn(n_data)
    plt.subplot(3, 2, i+1)
    plt.title(rf'$\mu={mus[i]}$, $\sigma={sigmas[i]}$')
    plt.plot(ts, yt)

n_data = 100 ts = np.arange(n_data) mus = [0.0, 2.0, -2.0, 0.0, 0.0, 2.0] sigmas = [1.0, 1.0, 1.0, 2.0, 3.0, 2.0] plt.figure(figsize=[10, 12]) for i in range(6): yt = mus[i] + sigmas[i] * np.random.randn(n_data) plt.subplot(3, 2, i+1) plt.title(rf'$\mu={mus[i]}$, $\sigma={sigmas[i]}$') plt.plot(ts, yt)

In [3]:

df = pd.read_excel('data/economicdata.xls').rename(columns={'Unnamed: 0': 'date'}).set_index('date'); df

df = pd.read_excel('data/economicdata.xls').rename(columns={'Unnamed: 0': 'date'}).set_index('date'); df

Out[3]:

	nikkei225	topix	indprod	exrate	cpi	saunemp	intrate
date
1975-01-01	3767.09	276.09	47.33	29.13	52.625	1.7	12.67
1975-02-01	4100.97	299.81	46.86	29.70	52.723	1.8	13.00
1975-03-01	4300.08	313.50	46.24	29.98	53.114	1.8	12.92
1975-04-01	4435.26	320.57	47.33	29.80	54.092	1.8	12.02
1975-05-01	4506.24	329.65	47.33	29.79	54.385	1.8	11.06
...	...	...	...	...	...	...	...
2004-12-01	11061.32	1110.39	99.91	87.46	98.109	4.5	0.00
2005-01-01	11394.84	1144.09	103.41	88.88	97.913	4.5	0.00
2005-02-01	11545.30	1159.71	101.41	87.72	97.620	4.6	0.00
2005-03-01	11809.38	1191.82	101.01	86.78	97.913	4.5	0.00
2005-04-01	11395.64	1158.22	102.71	85.88	98.011	4.5	0.00

364 rows × 7 columns

In [4]:

columns = ['topix', 'exrate', 'indprod', 'cpi', 'saunemp', 'intrate']
plt.figure(figsize=[10, 12])
counter = 0
for col in columns:
    counter += 1
    plt.subplot(3, 2, counter)
    plt.title(col)
    plt.plot(df[col])

columns = ['topix', 'exrate', 'indprod', 'cpi', 'saunemp', 'intrate'] plt.figure(figsize=[10, 12]) counter = 0 for col in columns: counter += 1 plt.subplot(3, 2, counter) plt.title(col) plt.plot(df[col])

In [5]:

plt.figure(figsize=[8, 12])
counter = 0
for col in ['topix', 'exrate', 'indprod']:
    counter += 1
    plt.subplot(3, 1, counter)
    plt.title(col)
    plt.plot(df[col].apply(np.log).diff() * 100)

plt.figure(figsize=[8, 12]) counter = 0 for col in ['topix', 'exrate', 'indprod']: counter += 1 plt.subplot(3, 1, counter) plt.title(col) plt.plot(df[col].apply(np.log).diff() * 100)

In [6]:

n_lag = 20
plt.bar(np.arange(1, n_lag+1), acf(df.indprod.apply(np.log).diff(), missing='drop', nlags=n_lag)[1:])
plt.axhline(0.0, color='gray', lw=0.5)
plt.xlabel('lag')
plt.ylabel('auto corr')

n_lag = 20 plt.bar(np.arange(1, n_lag+1), acf(df.indprod.apply(np.log).diff(), missing='drop', nlags=n_lag)[1:]) plt.axhline(0.0, color='gray', lw=0.5) plt.xlabel('lag') plt.ylabel('auto corr')

Out[6]:

Text(0, 0.5, 'auto corr')

In [7]:

pd.options.display.float_format = '{:.2f}'.format
print('indprod')
acorr_ljungbox(df['indprod'].apply(np.log).replace([np.inf, -np.inf], np.nan).diff().dropna(), lags=10).transpose()

pd.options.display.float_format = '{:.2f}'.format print('indprod') acorr_ljungbox(df['indprod'].apply(np.log).replace([np.inf, -np.inf], np.nan).diff().dropna(), lags=10).transpose()

indprod

Out[7]:

	1	2	3	4	5	6	7	8	9	10
lb_stat	34.20	39.76	50.40	51.80	51.91	54.46	54.46	57.46	57.94	58.84
lb_pvalue	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

In [8]:

pd.options.display.float_format = '{:.2f}'.format
for col in ['topix', 'exrate', 'cpi', 'saunemp']:
    df_tmp = acorr_ljungbox(df[col].apply(np.log).replace([np.inf, -np.inf], np.nan).diff().dropna(), lags=10).transpose()
    print(col)
    display(df_tmp)

pd.options.display.float_format = '{:.2f}'.format for col in ['topix', 'exrate', 'cpi', 'saunemp']: df_tmp = acorr_ljungbox(df[col].apply(np.log).replace([np.inf, -np.inf], np.nan).diff().dropna(), lags=10).transpose() print(col) display(df_tmp)

topix

	1	2	3	4	5	6	7	8	9	10
lb_stat	34.68	36.39	36.84	38.55	38.91	39.87	39.97	40.20	44.42	45.97
lb_pvalue	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

exrate

	1	2	3	4	5	6	7	8	9	10
lb_stat	37.90	38.76	41.79	42.29	42.73	45.26	45.61	49.88	53.74	53.87
lb_pvalue	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

cpi

	1	2	3	4	5	6	7	8	9	10
lb_stat	8.72	17.94	17.98	21.45	41.28	63.63	78.35	81.69	81.71	88.47
lb_pvalue	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

saunemp

	1	2	3	4	5	6	7	8	9	10
lb_stat	7.36	30.54	36.14	43.33	47.33	47.77	50.62	50.74	51.01	57.42
lb_pvalue	0.01	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00

In [ ]: