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jumps.py
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jumps.py
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import numpy as np
from stock import Stock
from scipy.special import gamma
from scipy import stats
class JumpStatistics(object):
def __init__(self,stock):
self.stock = stock
class BarndorffNielsen(JumpStatistics):
# An implementation of the Barnforff-Nielsen test statistic used for detecting "jumps"
# (or "suprises") in stock price data. The mathematics for this test statistic can be
# found at the following two resources:
#
# Michael William Schwert. 2008. "Problems in the Application of Jump Detection Tests
# to Stock Price Data". Duke University.
#
# "Some Like it Smooth, and Some Like it Rough: Untangling Continuous and Jump
# Components in Measuring, Modeling, and Forecasting Asset Return Volatility".
# Torben G. Andersen, Tim Bollerslev and Francis X. Diebold. September 2003.
#
# The following is an example of how to apply the Barnforff-Nielsen statistic to detect
# surprises in Microsoft stock data:
# if True:
# # Observe a trend in Microsoft stock prices where a jump occurs.
# stock = Stock("MSFT",{"start" : "2013-02-14","end" : "2014-02-14"})
# else:
# # Otherwise, view a sequence of stock prices where no jump was detected.
# stock = Stock("MSFT",{"start" : "2013-03-01","end" : "2013-04-01"})
# stock.display_price()
# bn = BarndorffNielsen(stock)
# bn.barndorff_nielsen_test()
def __init__(self,stock):
super(BarndorffNielsen,self).__init__(stock)
self.n = len(self.stock.statistics["log_returns"])
self.realized_variance = self.calculate_realized_variance()
self.bipower_variance = self.calculate_bipower_variance()
self.relative_jump = np.float(self.realized_variance - self.bipower_variance) / self.realized_variance
self.tripower_quarticity = self.calculate_tripower_quarticity()
self.statistic = self.barndorff_nielsen_statistic()
def calculate_realized_variance(self):
log_returns = self.stock.statistics["log_returns"]
variance = np.sum(np.power(log_returns,2))
return variance
def calculate_bipower_variance(self):
n = self.n
log_returns = np.absolute(self.stock.statistics["log_returns"])
variance = (np.pi / 2.0) * (np.float(n) / (n - 1.0)) * np.sum(log_returns[1:] * log_returns[:-1])
return variance
def calculate_tripower_quarticity(self):
n = self.n
# Notice that the absolute value of the log returns is calculated in this step. This is to
# prevent numerical nan's from being produced. This also seems to be consistent with the
# notation specified by Michael Schwert and Torben G. Andersen et al.
log_returns = np.absolute(self.stock.statistics["log_returns"])
mu = np.power(np.power(2.0,2.0 / 3) * gamma(7.0 / 6.0) * np.power(gamma(1.0 / 2.0),-1),-3)
tripower = np.sum(np.power(log_returns[2:],4.0 / 3) *
np.power(log_returns[1:-1],4.0 / 3) * np.power(log_returns[:-2],4.0 / 3))
quarticity = n * mu * (np.float(n) / (n - 2.0)) * tripower
return quarticity
def barndorff_nielsen_statistic(self):
n = self.n
pi = np.pi
relative_jump = self.relative_jump
tripower = self.tripower_quarticity
bipower = self.bipower_variance
statistic = relative_jump / np.sqrt(((pi / 2) ** 2 + pi - 5) * (1.0 / n) * max(1,tripower / (bipower ** 2)))
return statistic
def barndorff_nielsen_test(self,alpha = .01):
quantile = stats.norm.ppf(1 - alpha)
print_string = ""
if self.statistic > quantile:
print_string += "\tThe Barndorff-Nielsen Test reports that there was a jump in asset price.\n"
else:
print_string += "\tThe Barndorff-Nielsen Test reports that there was not a jump in asset price.\n"
print_string += "\tThe significance level of the test: %.2f\n" % alpha
print self.stock
print print_string
if True:
# Observe a trend in Microsoft stock prices where a jump occurs.
stock = Stock("MSFT",{"start" : "2013-02-14","end" : "2014-02-14"})
else:
# Otherwise, view a sequence of stock prices where no jump was detected.
stock = Stock("MSFT",{"start" : "2013-03-01","end" : "2013-04-01"})
stock.display_price()
bn = BarndorffNielsen(stock)
bn.barndorff_nielsen_test()