def hurst(prices, plot=False):
"""
Hurst exponent test
"""
prices = np.log(prices)
lags = range(1, 100)
# Variance of differences for each lag tau
variances = [((prices.shift(-lag) - prices)**2).mean() for lag in lags]
loglags = np.log(lags)
logvars = np.log(variances)
# Fit a straight line
b, a = np.polyfit(loglags, logvars, 1)
if plot:
fig, ax = plt.subplots()
plt.scatter(loglags, logvars)
plt.plot(loglags, a + b * loglags, lw=2, color='orange')
plotting.style_default(ax, fig,
xlabel='log(Lag)', ylabel='log(Variance)')
plt.show()
# Gradient is 2H
hurst = b / 2
return hurst
def plot_scatter(prices):
assert len(prices.columns) == 2
xprices = prices.iloc[:, 0]
yprices = prices.iloc[:, 1]
fig, ax = plt.subplots()
ax.scatter(xprices, yprices, label=None)
b, a = ols(prices).beta
#print sm.ols(formula='{} ~ {}'.format(*reversed(prices.columns)),
# data=prices).fit().summary()
xmin, xmax = xprices.min(), xprices.max()
axrange = np.arange(xmin, xmax, 0.01 * (xmax - xmin))
ax.plot(axrange, a + b * axrange,
lw=4, color='orange',
label='y = {:.2f}x + {:.2f}'.format(b, a))
axlabel = 'Price of {}'
plotting.style_default(ax, fig,
xlabel=axlabel.format(prices.columns[0]),
ylabel=axlabel.format(prices.columns[1]))
plt.show()
def plot_time_series(prices, *names):
fig, ax = plt.subplots()
prices.plot(ax=ax)
plotting.style_default(ax, fig, ylabel='Price')
plt.show()
def hurst(prices, plot=False):
"""
Hurst exponent test
"""
prices = np.log(prices)
lags = range(1, 100)
# Variance of differences for each lag tau
variances = [((prices.shift(-lag) - prices)**2).mean() for lag in lags]
loglags = np.log(lags)
logvars = np.log(variances)
# Fit a straight line
b, a = np.polyfit(loglags, logvars, 1)
if plot:
fig, ax = plt.subplots()
plt.scatter(loglags, logvars)
plt.plot(loglags, a + b * loglags, lw=2, color='orange')
plotting.style_default(ax,
fig,
xlabel='log(Lag)',
ylabel='log(Variance)')
plt.show()
# Gradient is 2H
hurst = b / 2
return hurst
def plot_scatter(prices):
assert len(prices.columns) == 2
xprices = prices.iloc[:, 0]
yprices = prices.iloc[:, 1]
fig, ax = plt.subplots()
ax.scatter(xprices, yprices, label=None)
b, a = ols(prices).beta
#print sm.ols(formula='{} ~ {}'.format(*reversed(prices.columns)),
# data=prices).fit().summary()
xmin, xmax = xprices.min(), xprices.max()
axrange = np.arange(xmin, xmax, 0.01 * (xmax - xmin))
ax.plot(axrange,
a + b * axrange,
lw=4,
color='orange',
label='y = {:.2f}x + {:.2f}'.format(b, a))
axlabel = 'Price of {}'
plotting.style_default(ax,
fig,
xlabel=axlabel.format(prices.columns[0]),
ylabel=axlabel.format(prices.columns[1]))
plt.show()
def plot_time_series(prices, *names):
fig, ax = plt.subplots()
prices.plot(ax=ax)
plotting.style_default(ax, fig, ylabel='Price')
plt.show()
def plot_residuals(prices):
fig, ax = plt.subplots()
#residuals(prices).plot()
ax.plot(residuals(prices))
plotting.style_default(ax, fig, ylabel='Residual')
plt.show()
def plot_residuals(prices):
fig, ax = plt.subplots()
#residuals(prices).plot()
ax.plot(residuals(prices))
plotting.style_default(ax, fig, ylabel='Residual')
plt.show()
