Python for Finance

Time-Series Analysis
Tests of normality
In finance, knowledge about normal distribution is very important for two reasons.
First, stock returns are assumed to follow a normal distribution. Second, the error
terms from a good econometric model should follow a normal distribution with a
zero mean. However, in the real world, this might not be true for stocks. On the other
hand, whether stocks or portfolios follow a normal distribution could be tested by
various so-called normality tests. The Shapiro-Wilk test is one of them. For the first
example, random numbers are drawn from a normal distribution. As a consequence,
the test should confirm that those observations follow a normal distribution:
from scipy import stats
import scipy as sp
sp.random.seed(12345)
mean=0.1
std=0.2
n=5000
ret=sp.random.normal(loc=0,scale=std,size=n)
print 'W-test, and P-value'
print(stats.shapiro(ret))
W-test, and P-value
(0.9995986223220825, 0.4129064679145813)
Assume that our confidence level is 95%, that is, alpha=0.05. The first value of the
result is the test statistic, and the second one is its corresponding P-value. Since
the P-value is so big, much bigger than 0.05, we accept the null hypothesis that the
returns follow a normal distribution. For the second example, random numbers are
drawn from a uniform distribution:
from scipy import stats
import scipy as sp
sp.random.seed(12345)
n=5000
ret=sp.random.uniform(size=n)
print 'W-test, and P-value'
print(stats.shapiro(ret))
W-test, and P-value
(0.9537619352340698, 4.078975800593137e-37)
Since the P-value is close to zero, we reject the null hypothesis. In other words, those
observations do not follow a normal distribution. The third example verifies whether
IBM's returns follow a normal distribution. The last five year's daily data from
Yahoo! Finance is used for the test. The null hypothesis is that IBM's daily returns are
drawn from a normal distribution:
from scipy import stats
from matplotlib.finance import quotes_historical_yahoo_ochl as getData
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