NumPy Beginner's Guide 2e 带注释源码四、NumPy 便利的函数

# 来源：NumPy Beginner's Guide 2e ch4

交易相关偶对

import numpy as np
from matplotlib.pyplot import plot
from matplotlib.pyplot import show

# 读入 BHP 的收盘价
bhp = np.loadtxt('BHP.csv', delimiter=',', usecols=(6,), unpack=True)

# 计算 BHP 的简单收益
bhp_returns = np.diff(bhp) / bhp[ : -1]

# 读入 VALE 的收盘价
vale = np.loadtxt('VALE.csv', delimiter=',', usecols=(6,), unpack=True)

# 计算 VALE 的简单收益
vale_returns = np.diff(vale) / vale[ : -1]

# 计算协方差
# cov_x_y = ((x - x.mean()) * (y - y.mean())).mean()
# cov 函数返回协方差矩阵
# [[ var_x, cov_x_y],
#  [ cov_y_x, var_y]]
covariance = np.cov(bhp_returns, vale_returns) 
print "Covariance", covariance
'''
Covariance [[ 0.00028179  0.00019766]
           [ 0.00019766  0.00030123]]
'''

# diagonal 获取对角线上的元素
print "Covariance diagonal", covariance.diagonal()
# Covariance diagonal [ 0.00028179  0.00030123]
# trace 计算矩阵的迹（对角线元素和）
print "Covariance trace", covariance.trace()
# Covariance trace 0.00058302354992

print covariance/ (bhp_returns.std() * vale_returns.std())

# corrcoef 计算相关系数
# rho_x_y = cov_x_y / (std_x * std_y)
print "Correlation coefficient", np.corrcoef(bhp_returns, vale_returns)
'''
[[ 1.00173366  0.70264666]
[ 0.70264666  1.0708476 ]]
'''

# 检查两个股票是否同步
# 如果差值最后一项，距离均值大于两个标准差，就认为是不同步的
difference = bhp - vale
avg = np.mean(difference)
dev = np.std(difference)

print "Out of sync", np.abs(difference[-1] - avg) > 2 * dev
# Out of sync False

# 绘制两个股票的收益
t = np.arange(len(bhp_returns))
plot(t, bhp_returns, lw=1)
plot(t, vale_returns, lw=2)
show()

多项式拟合

import numpy as np
import sys
from matplotlib.pyplot import plot
from matplotlib.pyplot import show

# 导入 BHP 和 VALE 的收盘价
bhp=np.loadtxt('BHP.csv', delimiter=',', usecols=(6,), unpack=True)

vale=np.loadtxt('VALE.csv', delimiter=',', usecols=(6,), unpack=True)

# polyfit 用于多项式拟合
# 参数为训练集x，训练集y，最高项次数
# 返回方程的系数数组，高次在前
t = np.arange(len(bhp))
poly = np.polyfit(t, bhp - vale, int(sys.argv[1]))
print "Polynomial fit", poly
# 假设最高项次数为 3：
# Polynomial fit [  1.11655581e-03  -5.28581762e-02   5.80684638e-01   5.79791202e+01]

# polyval 使用拟合结果来预测新的值
# p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]
print "Next value", np.polyval(poly, t[-1] + 1)
# Next value 57.9743076081

# 返回多项式的根
print "Roots", np.roots(poly)
# Roots [ 35.48624287+30.62717062j  35.48624287-30.62717062j -23.63210575 +0.j        ]

# 多项式求导
# (x ** n)' = n * x ** (n - 1)
# (a * u(x) + b * v(x))' = a * u'(x) + b * v'(x)
der = np.polyder(poly)
print "Derivative", der
# Derivative [ 0.00334967 -0.10571635  0.58068464]

# 导数的根（可能）是极值
print "Extremas", np.roots(der)
# Extremas [ 24.47820054   7.08205278]

# 拟合函数的最大值和最小值点
vals = np.polyval(poly, t)
print np.argmax(vals)
# 7
print np.argmin(vals)
# 24

# 绘制原始函数和拟合函数
plot(t, bhp - vale)
plot(t, vals)
show()

平衡成交量

import numpy as np

# 读入收盘价和成交量
c, v=np.loadtxt('BHP.csv', delimiter=',', usecols=(6, 7), unpack=True)

# 获取绝对收益
change = np.diff(c)
print "Change", change
'''
Change [ 1.92 -1.08 -1.26  0.63 -1.54 -0.28  0.25 -0.6   2.15 0.69 -1.33  1.16
  1.59 -0.26 -1.29 -0.13 -2.12 -3.91  1.28 -0.57 -2.07 -2.07 2.5   1.18
-0.88  1.31  1.24 -0.59]
'''

# 计算状态
signs = np.sign(change)
print "Signs", signs
'''
Signs [ 1. -1. -1.  1. -1. -1.  1. -1.  1.  1. -1.  1.  1. -1. -1. -1. -1. -1.
-1. -1. -1.  1.  1.  1. -1.  1.  1. -1.]
'''

# 状态也可以用 piecewise 来计算
# 参数为输入数组 arr、状态数组 condlist 和结果数组 reslist
# 如果满足 condlist[i]，将 arr[i] 变为 reslist[i]
pieces = np.piecewise(change, [change < 0, change > 0], [-1, 1])
print "Pieces", pieces

print "Arrays equal?", np.array_equal(signs, pieces)
# Arrays equal? True

# 平衡成交量是状态乘以成交量
print "On balance volume", v[1:] * signs
'''
[ 2620800. -2461300. -3270900.  2650200. -4667300. -5359800. 7768400.
 -4799100.  3448300.  4719800. -3898900.  3727700.  3379400. -2463900.
 -3590900. -3805000. -3271700. -5507800.  2996800. -3434800. -5008300.
 -7809799.  3947100.  3809700.  3098200. -3500200.  4285600. 3918800.
 -3632200.]
'''

使用向量化来避免循环

# 向量化就是逐元素调用函数

import numpy as np
import sys

# 获取开盘价、最高价、最低价和收盘价
o, h, l, c = np.loadtxt('BHP.csv', delimiter=',', usecols=(3, 4, 5, 6), unpack=True)

# calc_profit 用于计算利润
def calc_profit(open, high, low, close):
   # 以稍低于开盘价的价格买入
   buy = open * float(sys.argv[1])

   if low <  buy < high:
      # 如果这个价格在当天的区间之内
      # 就以收盘价卖掉
      return (close - buy)/buy
   else:
      # 否则就没有收益，返回 0
      return 0

# 创建向量化的 calc_profit
# 也可以使用装饰器 @np.vectorize
func = np.vectorize(calc_profit)
profits = func(o, h, l, c)
print "Profits", profits

# 获取不为零的收益
real_trades = profits[profits != 0]
# 打印概率和平均利润率
print "Number of trades", len(real_trades), round(100.0 * len(real_trades)/len(c), 2), "%"
# Number of trades 28 93.33 %
print "Average profit/loss %", round(np.mean(real_trades) * 100, 2)
# Average profit/loss % 0.02

# 选择获利的交易，计算概率和平均利润率
winning_trades = profits[profits > 0]
print "Number of winning trades", len(winning_trades), round(100.0 * len(winning_trades)/len(c), 2), "%"
Number of winning trades 16 53.33 %
print "Average profit %", round(np.mean(winning_trades) * 100, 2)
# Average profit/loss % 0.72

# 选择亏损的交易，计算概率和平均利润率
losing_trades = profits[profits < 0]
print "Number of losing trades", len(losing_trades), round(100.0 * len(losing_trades)/len(c), 2), "%"
# Number of losing trades 12 40.0 %
print "Average loss %", round(np.mean(losing_trades) * 100, 2)
# Average loss % -0.92

使用海宁函数实现平滑

import numpy as np
import sys
from matplotlib.pyplot import plot
from matplotlib.pyplot import show

# 读取长度 N
N = int(sys.argv[1])

# 使用 hanning 来生成权重
weights = np.hanning(N)
print "Weights", weights
'''
Weights [ 0.          0.1882551   0.61126047  0.95048443  0.95048443  0.61126047
  0.1882551   0.        ]
'''

# 读取 BHP 收盘价
bhp = np.loadtxt('BHP.csv', delimiter=',', usecols=(6,), unpack=True)
# 计算简单收益
bhp_returns = np.diff(bhp) / bhp[ : -1]
# 使用 convolve 函数来使之平滑
smooth_bhp = np.convolve(weights/weights.sum(), bhp_returns)[N-1:-N+1]

# 读取 VALE 收盘价
vale = np.loadtxt('VALE.csv', delimiter=',', usecols=(6,), unpack=True)
# 计算简单收益
vale_returns = np.diff(vale) / vale[ : -1]
# 使用 convolve 函数来使之平滑
smooth_vale = np.convolve(weights/weights.sum(), vale_returns)[N-1:-N+1]

# 读取最高项系数
K = int(sys.argv[1])
# 多项式拟合 BHP 和 VALE 的平滑收益
t = np.arange(N - 1, len(bhp_returns))
poly_bhp = np.polyfit(t, smooth_bhp, K)
poly_vale = np.polyfit(t, smooth_vale, K)

# np.polysub 用于求多项式的差
poly_sub = np.polysub(poly_bhp, poly_vale)
# 差值为 0 的点就是多项式的交点
xpoints = np.roots(poly_sub)
print "Intersection points", xpoints
'''
Intersection points [ 27.73321597+0.j          27.51284094+0.j          24.32064343+0.j
  18.86423973+0.j          12.43797190+1.73218179j  12.43797190-1.73218179j
   6.34613053+0.62519463j   6.34613053-0.62519463j]
'''

# 检查是否是实数值
reals = np.isreal(xpoints)
print "Real number?", reals
# Real number? [ True  True  True  True False False False False]

# 过滤实数值，转成实数
# 其实可以直接使用 xpoints[np.isreal(xpoints)].real
xpoints = np.select([reals], [xpoints])
xpoints = xpoints.real
print "Real intersection points", xpoints
# Real intersection points [ 27.73321597  27.51284094 24.32064343  18.86423973   0.           0.   0.  0.]
# trim_zeros 去除首尾的零元素
print "Sans 0s", np.trim_zeros(xpoints)
# Sans 0s [ 27.73321597  27.51284094  24.32064343  18.86423973]

# 绘制简单收益，以及 N 天的平滑收益
plot(t, bhp_returns[N-1:], lw=1.0)
plot(t, smooth_bhp, lw=2.0)

plot(t, vale_returns[N-1:], lw=1.0)
plot(t, smooth_vale, lw=2.0)
show()

posted @ 2017-06-01 10:34 绝不原创的飞龙阅读(14) 评论(0) 编辑收藏举报来源

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龙哥盟

掠夺·扩张·投机·博弈

NumPy Beginner's Guide 2e 带注释源码四、NumPy 便利的函数

交易相关偶对

多项式拟合

平衡成交量

使用向量化来避免循环

使用海宁函数实现平滑

公告

龙哥盟

掠夺·扩张·投机·博弈

NumPy Beginner's Guide 2e 带注释源码 四、NumPy 便利的函数

交易相关偶对

多项式拟合

平衡成交量

使用向量化来避免循环

使用海宁函数实现平滑

公告

NumPy Beginner's Guide 2e 带注释源码四、NumPy 便利的函数