https://www.quantopian.com/lectures/statistical-moments
This lecture corresponds to the Statistical Moments and Normality Testing lecture, which is part of the Quantopian lecture series. This homework expects you to rely heavily on the code presented in the corresponding lecture. Please copy and paste regularly from that lecture when starting to work on the problems, as trying to do them from scratch will likely be too difficult.
Part of the Quantopian Lecture Series:
# Useful Libraries
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import scipy.stats as stats
from statsmodels.stats.stattools import jarque_bera
xs2 = np.linspace(stats.gamma.ppf(0.01, 0.7, loc=-1), stats.gamma.ppf(0.99, 0.7, loc=-1), 150) + 1
X = stats.gamma.pdf(xs2, 1.5)
#Your code goes here
Use the results from the stats.skew function to determine the skew of the returns of NFLX and use it to make a conclusion about the symmetry of the stock's returns.
start = '2015-01-01'
end = '2016-01-01'
pricing = get_pricing('NFLX', fields='price', start_date=start, end_date=end)
returns = pricing.pct_change()[1:]
#Your code goes here
xs = np.linspace(-6,6, 300) + 2
Y = stats.cosine.pdf(xs)
#Your code goes here
Use the results from the stats.kurtosis function to determine the kurtosis of the returns of NFLX and use it to make a conclusion about the volatility of the stock's price.
start = '2015-01-01'
end = '2016-01-01'
pricing = get_pricing('NFLX', fields='price', start_date=start, end_date=end)
returns = pricing.pct_change()[1:]
#Your code goes here
xs2 = np.linspace(stats.lognorm.ppf(0.01, 0.7, loc=-.1), stats.lognorm.ppf(0.99, 0.7, loc=-.1), 150)
lognorm = stats.lognorm.pdf(xs2, 0.4)
Z = lognorm/2 + lognorm[::-1]
#Your code goes here
Ensure that the jarque-bera function is calibrated by running it on many trials of simulated data and ensuring that the sample probability that the test returns a result under the p-value is equal to the p-value.
N = 1000
M = 1000
pvalues = np.ndarray((N))
for i in range(N):
# Draw M samples from a normal distribution
X = np.random.normal(0, 1, M);
_, pvalue, _, _ = jarque_bera(X)
pvalues[i] = pvalue
num_significant = len(pvalues[pvalues < 0.05])
#Your code goes here
Use the Jarque-Bera function to determine the normality of Z.
#Your code goes here
Plot Z and observe that skewness is not informative unless the underlying distribution is somewhat normal.
#Your code goes here
start = '2014-01-01'
end = '2016-01-01'
pricing = get_pricing('AMC', fields='price', start_date=start, end_date=end)
returns = pricing.pct_change()[1:]
#Your code goes here
Find the skew of the historical returns of AMC between 2014 to 2016.
start = '2014-01-01'
end = '2016-01-01'
pricing = get_pricing('AMC', fields='price', start_date=start, end_date=end)
returns = pricing.pct_change()[1:]
#Your code goes here
Find the skew of the historical retunrs of AMC from the first half of 2016 to determine if the skew from part b holds outside of the original sample.
start = '2016-01-01'
end = '2016-07-01'
out_pricing = get_pricing('AMC', fields='price', start_date=start, end_date=end)
out_returns = out_pricing.pct_change()[1:]
#Your code goes here
Plot the rolling skew of AMC using the pd.rolling_skew function.
AMC = get_pricing('AMC', fields='price', start_date='2015-01-01', end_date='2017-01-01')
#Your code goes here
Congratulations on completing the Statistical Moments and Normality Testing exercises!
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