Chapter 1. Financial Markets, Prices and Risk

price = read.csv('index.csv')
y=diff(log(price$Index))  # calculate returns
plot(y)             # plot returns

import numpy as np
import matplotlib.pyplot as plt
price = np.loadtxt('index.csv', delimiter = ',', skiprows = 1)
y = np.diff(np.log(price), n=1, axis=0)
plt.plot(y)
plt.title("S&P500 Returns")
plt.show()
plt.close()

library(moments)
library(tseries)
mean(y)
sd(y)
min(y)
max(y)
skewness(y)
kurtosis(y)
jarque.bera.test(y)

from scipy import stats
print (np.mean(y))
print (np.std(y, ddof=1))
print (np.min(y))
print (np.max(y))
print (stats.skew(y))
print (stats.kurtosis(y, fisher = False))
print (stats.jarque_bera(y))

library(MASS)
library(stats)
par(mfrow=c(1,2), pty="s")
q = acf(y,20)
q1 = acf(y^2,20)
Box.test(y, lag = 20, type = c("Ljung-Box"))
Box.test(y^2, lag = 20, type = c("Ljung-Box"))

import statsmodels.api as sm
import matplotlib.pyplot as plt
from statsmodels.stats.diagnostic import acorr_ljungbox
q = sm.tsa.stattools.acf(y, nlags=20)
plt.bar(x = np.arange(1,len(q)), height = q[1:])
plt.title("Autocorrelation of returns")
plt.show()
plt.close()
q = sm.tsa.stattools.acf(np.square(y), nlags=20)
plt.bar(x = np.arange(1,len(q)), height = q[1:])
plt.title("Autocorrelation of returns squared")
plt.show()
plt.close()
print (acorr_ljungbox(y, lags=20))
print (acorr_ljungbox(np.square(y), lags=20))

library(car)
par(mfrow=c(1,2), pty="s")
qqPlot(y)
qqPlot(y,distribution="t",df=5)

from statsmodels.graphics.gofplots import qqplot
fig1 = qqplot(y, line='q', dist = stats.norm, fit = True)               
plt.show()
plt.close()
fig2 = qqplot(y, line='q', dist = stats.t, distargs=(5,), fit = True)
plt.show()
plt.close()

p = read.csv('stocks.csv')
y=apply(log(p),2,diff)
print(cor(y)) # correlation matrix

p = np.loadtxt('stocks.csv',delimiter=',',skiprows = 1)
y = np.diff(np.log(p), n=1, axis=0)
print(np.corrcoef(y, rowvar=False)) # correlation matrix