StatsModels 偏峰与峰态

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偏峰（Skewness）

一个对称的分布偏峰（skewness）的值为 0.
正倾斜偏峰分布意味 mean > median > mode。
负倾斜偏峰分布意味 mean < median < mode.

import tushare as ts
import pandas as pd
import scipy.stats as stats
import matplotlib.pyplot as plt
import numpy as np

s是指shape=sigma, loc是mu。
lognorm.pdf(x, s, loc, scale)

# Generate xvalues for which we will plot the distribution
#Percent point function (inverse of cdf - percentiles)
x = np.linspace(stats.lognorm.ppf(0.01, .7, loc=-.1), stats.lognorm.ppf(0.99, .7, loc=-.1), 150)
# Negatively skewed distribution
lognormal = stats.lognorm.pdf(x, .7)
plt.plot(x, lognormal, label='Skew < 0')
# Positively skewed distribution
plt.plot(x, lognormal[::-1], label='Skew > 0')
plt.legend()
plt.show()

读取000001股票的skewnes值

data = ts.get_k_data('000001', start='2016-01-01', end='2016-12-31', ktype='D',autype='qfq')
data.index = pd.to_datetime(data['date'],format='%Y-%m-%d')
data['returns'] = data['close'].pct_change()[1:]
returns = data['returns'].dropna()
print 'Skew:', stats.skew(returns)
print 'Mean:', np.mean(returns)
print 'Median:', np.median(returns)
plt.hist(returns, 30)
plt.show()

Skew: -0.589166660049
Mean: -1.11957279761e-05
Median: 0.000939739222366

Kurtosis

xs = np.linspace(-6,6,300)
normal = stats.norm.pdf(xs)
# Plot some example distributions
plt.plot(xs, stats.laplace.pdf(xs), label='Leptokurtic')
print 'Excess kurtosis of leptokurtic distribution:', (stats.laplace.stats(moments='k'))
plt.plot(xs, normal, label='Mesokurtic (normal)')
print 'Excess kurtosis of mesokurtic distribution:', (stats.norm.stats(moments='k'))
plt.plot(xs,stats.cosine.pdf(xs), label='Platykurtic')
print 'Excess kurtosis of platykurtic distribution:', (stats.cosine.stats(moments='k'))
plt.legend()
plt.show()

Excess kurtosis of leptokurtic distribution: 3.0
Excess kurtosis of mesokurtic distribution: 0.0
Excess kurtosis of platykurtic distribution: -0.593762875598

获取000001股票的超值峰度

print "Excess kurtosis of returns: ", stats.kurtosis(returns)

Excess kurtosis of returns: 3.95204544689
'''大于三属于尖顶峰度'''

用JarqueBera检验是否正态分布

return (JB, JBpv, skew, kurtosis)

data = ts.get_k_data('000001', start='2016-01-01', end='2016-12-31', ktype='D',autype='qfq')
data.index = pd.to_datetime(data['date'],format='%Y-%m-%d')
data['percentage']=data['close'].pct_change()
returns = data['percentage'][1:]
_, pvalue, _, _ = jarque_bera(returns)
if pvalue > 0.05:
    print 'The returns are likely normal.'
else:
    print 'The returns are likely not normal.'

The returns are likely not normal.

一个正收益的策略收益率峰度计算

例子对000001股票从12年到16年的15分钟数据，用均线交叉的策略，获取了收益数据。
数据可从微云下载：

import pandas as pd
import scipy.stats as stats
import matplotlib.pyplot as plt
import numpy as np
r = pd.read_excel('performance.xls')
r.index = r[u'最后成交时间']
r = r[r[u'买卖'] == u'卖']
r['equity'] = r[u'累积盈利']+100000
returns = r[u'盈利']/r['equity']
print(returns)
plt.hist(returns)
print 'Skew:', stats.skew(returns)
print 'Mean:', np.mean(returns)
print 'Median:', np.median(returns)
print 'kurtosis:', stats.kurtosis(returns)
plt.show()

Skew: 2.98409620906
Mean: 0.00258093135289
Median: -0.00318133586001
kurtosis: 12.7743488626