Python for Finance

Time-Series Analysis
The output for those five values, including the number of observations, is given here:
This result is very close to the result in the paper titled Study of Fat Tail Risk by
Cook Pine Capital (2008). Using the same argument, we conclude that the SP500
daily returns are skewed to the left, that is, a negative skewness, and have fat tails
(kurtosis is 20.81 instead of zero).
T-test and F-test
In finance, a T-test could be viewed as one of the most widely used statistical
hypothesis tests in which the test statistic follows a student's t distribution if the null
hypothesis is supported. We know that the mean for a standard normal distribution
is zero. In the following program, we generate 1,000 random numbers from a
standard normal distribution. Then, we conduct two tests: test whether the mean is
0.5, and test whether the mean is zero:
>>>from scipy import stats
>>>import numpy as np
>>>np.random.seed(1235)
>>>x = stats.norm.rvs(size=10000)
>>>print("T-value P-value (two-tail)")
>>>print(stats.ttest_1samp(x,0.5))
>>>print(stats.ttest_1samp(x,0))
T-value P-value (two-tail)
Ttest_1sampResult(statistic=-49.763471231428966, pvalue=0.0)
Ttest_1sampResult(statistic=-0.26310321925083019,
pvalue=0.79247644375164861)
For the first test, in which we test whether the time-series has a mean of 0.5, we reject
the null hypothesis since the T-value is 49.76 and the P-value is 0. For the second test,
we accept the null hypothesis since the T-value is close to -0.26 and the P-value is
0.79. In the following program, we test whether the mean of the daily returns from
IBM in 2013 is zero:
from scipy import stats
import scipy as sp
from matplotlib.finance import quotes_historical_yahoo_ochl as getData
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