為替操作国日本：ドル円レートとGDPには相関性があるのか？

from pandas import *
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline
plt.rcParams['figure.figsize'] = 20, 12

yen_dollar = 'DEXJPUS.csv'
jp_gdp = 'JPNNGDP.csv'

exchange = read_csv(yen_dollar)
jp_gdp = read_csv(jp_gdp)

new_table = pd.merge(jp_gdp,exchange)

new_table

new_table.columns = ['DATE','JPN_GDP','USD_JPY_EXCHANGE']
new_table.head()

new_table = DataFrame(new_table)
new_table.head()

jp_gdp_exch_scatt = new_table.plot('JPN_GDP','USD_JPY_EXCHANGE',grid=True, kind='scatter', s = 70)

jp_gdp_exch_scatt.set_title('Correlation between Japanese GDP and the Exchange Rate ', fontsize = 20)

jp_gdp_exch_scatt.set_xlabel('Japanese GDP (Billions of Yen)')

jp_gdp_exch_scatt.set_ylabel('Dollar-Yen Exchange Rate (Yen)')

jp_gdp_plot = new_table[['DATE','JPN_GDP']].set_index('DATE').plot()
jp_gdp_plot.set_title('Japanese GDP 1995 - 2018', fontsize =20)
jp_gdp_plot.set_ylabel('Japanese GDP (Billions of Yen)')

exchange_plot = new_table[['DATE','USD_JPY_EXCHANGE']].set_index('DATE').plot()
exchange_plot.set_title('Dollar Yen Exchange Rate 1995 - 2018', fontsize =20)
exchange_plot.set_ylabel('USD-JPY Exchange Rate (Yen)')

from matplotlib.pyplot import *
from matplotlib.font_manager import FontProperties
from matplotlib import rcParams
style.use('ggplot')

rcParams["font.size"] = "17"
fp = FontProperties(fname='/usr/share/fonts/opentype/ipaexfont-gothic/ipaexg.ttf', size=54)
rcParams['font.family'] = fp.get_name()
fig, ax = plt.subplots(figsize=(20,12))
new_table[['DATE','JPN_GDP']].set_index('DATE').plot(ax=ax,color="red")
ax.set_ylabel('GDP (10億円)')
ax.set_title('1995年〜2018のドル円レートとGDPの相関関係 ', fontsize =20)
ax.legend(["GDP"],loc='lower right', prop={'size': 26})
ax2 = ax.twinx()
new_table[['DATE','USD_JPY_EXCHANGE']].set_index('DATE').plot(ax=ax2,color="blue")
ax2.set_ylabel('ドル円レート (円)')
ax2.legend(["ドル円レート"],loc='lower left', prop={'size': 26})
ax2.annotate('リーマンショック', xy=(57,79),  xycoords='data',
             xytext=(-50, -20),textcoords='offset points',
             size=25, ha='right', va="center",
             bbox=dict(boxstyle="round", alpha=0.1),
             arrowprops=dict(arrowstyle="wedge,tail_width=0.5", alpha=0.1))
ax2.annotate('東日本大震災', xy=(64,79),  xycoords='data',
             xytext=(60,280),textcoords='offset points',
             size=25, ha='right', va="center",
             bbox=dict(boxstyle="round", alpha=0.1),
             arrowprops=dict(arrowstyle="wedge,tail_width=0.5", alpha=0.1))
ax2.annotate('異次元緩和', xy=(73,98.681094),  xycoords='data',
             xytext=(145, -100),textcoords='offset points',
             size=25, ha='right', va="center",
             bbox=dict(boxstyle="round", alpha=0.1),
             arrowprops=dict(arrowstyle="wedge,tail_width=0.5", alpha=0.1))
ax2.annotate('消費税増税', xy=(77,102.103906),  xycoords='data',
             xytext=(145, -60),textcoords='offset points',
             size=25, ha='right', va="center",
             bbox=dict(boxstyle="round", alpha=0.1),
             arrowprops=dict(arrowstyle="wedge,tail_width=0.5", alpha=0.1))
ax2.annotate('アジア通貨危機', xy=(10,120),  xycoords='data',
             xytext=(120, -200),textcoords='offset points',
             size=25, ha='right', va="center",
             bbox=dict(boxstyle="round", alpha=0.1),
             arrowprops=dict(arrowstyle="wedge,tail_width=0.5", alpha=0.1))
ax2.annotate('日米協調介入', xy=(14,140),  xycoords='data',
             xytext=(200, -5),textcoords='offset points',
             size=25, ha='right', va="center",
             bbox=dict(boxstyle="round", alpha=0.1),
             arrowprops=dict(arrowstyle="wedge,tail_width=0.5", alpha=0.1))
ax2.annotate('安倍政権誕生', xy=(71,81),  xycoords='data',
             xytext=(200, 5),textcoords='offset points',
             size=25, ha='right', va="center",
             bbox=dict(boxstyle="round", alpha=0.1),
             arrowprops=dict(arrowstyle="wedge,tail_width=0.5", alpha=0.1));

jpn_gdp_Column = new_table['JPN_GDP']
exchange_Column = new_table['USD_JPY_EXCHANGE']

jpn_gdp_Column.describe()

exchange_Column.describe()

#Sum of X

jpn_gdp_Column.sum()

#Sum of Y

exchange_Column.sum()

#Sum of X times Y

x_y = jpn_gdp_Column*exchange_Column
x_y.sum()

#Sum of X squared

jpn_gdp_sq = jpn_gdp_Column**2

jpn_gdp_sq.sum()

#Sum of Y squared

exchange_sq = exchange_Column**2

exchange_sq.sum()

#Set variables

X = new_table.JPN_GDP

X = np.vstack(new_table.JPN_GDP)

Y = new_table.USD_JPY_EXCHANGE

Y = np.vstack(new_table.USD_JPY_EXCHANGE)

X = np.array([ [value,1] for value in X]).astype(np.float32)

#Find Correlation Coefficients with numpy
# [1
# [correlation(y, x)          1]]

corr = np.corrcoef(jpn_gdp_Column,exchange_Column)

print('The correlational coefficient (r) is %.3f' %corr[0]2)

#Use numpy Least Squares (lstsq) to find the Regression Coefficients

regression = np.linalg.lstsq(X,exchange_Column,rcond=-1)
regression

print('The slope is %.4f' %regression[0][0])
print('The y intercept is %.3f' %regression[0]3)

#Get error

total_error = regression[1]
print('The total error was %.3f' %total_error[0])

#Get Root Mean Sqaure Error

rmse = np.sqrt(total_error/len(X))
print('The root mean squared error was %.2f' %rmse)

import scipy 
from scipy import stats
from scipy.stats import t

#find t-statistic
r = 0.681
t = ((r)*np.sqrt((96-2)/(1-(r**2))))
print('The t-statistic is %.3f' %t)

from scipy.stats import t

#pass t statistic and degrees of freedom
#checked by hand
pvalue = t.sf(9.016, 2)
print('The p-value is %f' %pvalue)

m , b = scipy.linalg.lstsq(X,Y)[0]

#Plot centroid using X and Y means

plt.plot([520118.152083], [107.973519], marker='o', markersize=10, color="red")

#Plot best fit line

plt.plot(jpn_gdp_Column,exchange_Column,'o',color='green')

x = new_table.JPN_GDP

plt.plot(x, m*x + b, 'r')

plt.title('USD-JPY Exchange Rate and Japanese GDP Regression Line',fontsize=20)

plt.xlabel('Japanese GDP (Billions of Yen)')

plt.ylabel('USD-Yen Exchange Rate (Yen)');