Machine Learning for Trading--1-6 Histograms and Scatter Plots

• 生成柱状统计图–Plot a histogram
• 柱状图统计分析–Computing Histogram Statistics
• 同时plot两个柱状图–Plot Two Histograms together
• 散点图–Scatterplots

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生成柱状统计图–Plot a histogram

• 日回报率 – daily_returns[1:] = (df[1:] / df[:-1].values) - 1
• 生成柱状图 – daily_returns.hist(bins=20)

Example:

import pandas as pd
import matplotlib.pyplot as plt

from util import get_data, plot_data

def compute_daily_returns(df):
    """Compute and return the daily return values."""
    daily_returns = df.copy()
    daily_returns[1:] = (df[1:] / df[:-1].values) - 1
    daily_returns.ix[0, :] = 0 # set daily returns for row 0 to 0
    return daily_returns

def test_run():
    # Read data
    dates = pd.date_range('2009-01-01', '2012-12-31')
    symbols = ['SPY']
    df = get_data(symbols, dates)
    plot_data(df)
    
    # Compute daily returns
    daily_returns = compute_daily_returns(df)
    plot_data(daily_returns, title="Daily returns", ylabel="Daily returns")
    
    # Plot a histogram
    daily_returns.hist()  # default number of bins, 10
    daily_returns.hist(bins=20)  # changing no. of bins to 20
    plt.show()
    
if __name__ == "__main__":
    test_run()

柱状图统计分析–Computing Histogram Statistics

• 计算均值 – mean = daily_returns[‘SPY’].mean()
• 计算方差 – std = daily_returns[‘SPY’].std()
• 添加垂线 – plt.axvline(mean)
• 计算样本峰度kurtosis – daily_returns.kurtosis() 注：表征概率密度分布曲线在平均值处峰值的高低，数值越大越瘦长。

Example:

import pandas as pd
import matplotlib.pyplot as plt

from util import get_data, plot_data

def compute_daily_returns(df):
    """Compute and return the daily return values."""
    daily_returns = df.copy()
    daily_returns[1:] = (df[1:] / df[:-1].values) - 1
    daily_returns.ix[0, :] = 0 # set daily returns for row 0 to 0
    return daily_returns

def test_run():
    # Read data
    dates = pd.date_range('2009-01-01', '2012-12-31')
    symbols = ['SPY']
    df = get_data(symbols, dates)
    plot_data(df)
    
    # Compute daily returns
    daily_returns = compute_daily_returns(df)
    plot_data(daily_returns, title="Daily returns", ylabel="Daily returns")
    
    # Plot a histogram
    daily_returns.hist(bins=20)  # changing no. of bins to 20
    
    # Get mean and standard deviation
    mean = daily_returns['SPY'].mean()
    print ("mean=", mean)
    std = daily_returns['SPY'].std()
    print ("std=", std)
    
    plt.axvline(mean, color='w', linestyle='dashed', linewidth=2)
    plt.axvline(std, color='r', linestyle='dashed', linewidth=2)
    plt.axvline(-std, color='r', linestyle='dashed', linewidth=2)
    plt.show()
    
    # Compute kurtosis
    print (daily_returns.kurtosis())

if __name__ == "__main__":
    test_run()

同时plot两个柱状图–Plot Two Histograms together

• 两张图分开左右显示 – plot_data(daily_returns) 注：daily_returns 为包含两列不同数据的表格
• 两张图同时显示 – daily_returns[‘SPY’].hist(bins=20, label=”SPY”) daily_returns[‘XOM’].hist(bins=20, label=”XOM”)

Example:

import pandas as pd
import matplotlib.pyplot as plt

from util import get_data, plot_data

def compute_daily_returns(df):
    """Compute and return the daily return values."""
    daily_returns = df.copy()
    daily_returns[1:] = (df[1:] / df[:-1].values) - 1
    daily_returns.ix[0, :] = 0 # set daily returns for row 0 to 0
    return daily_returns
    
def test_run():
    # Read data
    dates = pd.date_range('2009-01-01', '2012-12-31')
    symbols = ['SPY', 'XOM']
    df = get_data(symbols, dates)
    plot_data(df)
    
    """ Two separate histograms ==========="""
    # Compute daily returns
    daily_returns = compute_daily_returns(df)
    plot_data(daily_returns, title="Daily returns", ylabel="Daily returns")
    
    # Plot a histogram
    daily_returns.hist(bins=20) 
    plt.show()

    """ Histograms on the same graph ======"""
    # Compute daily returns
    daily_returns = compute_daily_returns(df)
    
    # Compute and plot both histograms on the same chart
    daily_returns['SPY'].hist(bins=20, label="SPY")
    daily_returns['XOM'].hist(bins=20, label="XOM")
    plt.legend(loc='upper right')
    plt.show()
    
if __name__ == "__main__":
    test_run()

散点图–Scatterplots

• 生成散点图 – daily_returns.plot(kind=’scatter’, x=’SPY’, y=’XOM’)
• 数据拟合(线性) – beta_XOM, alpha_XOM= np.polyfit(daily_returns[‘SPY’], daily_returns[‘XOM’], 1)

Example:

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np

from util import get_data, plot_data

def compute_daily_returns(df):
    """Compute and return the daily return values."""
    daily_returns = df.copy()
    daily_returns[1:] = (df[1:] / df[:-1].values) - 1
    daily_returns.ix[0, :] = 0 # set daily returns for row 0 to 0
    return daily_returns
    
def test_run():
    # Read data
    dates = pd.date_range('2009-01-01', '2012-12-31')
    symbols = ['SPY', 'XOM', 'GLD']
    df = get_data(symbols, dates)
    
    # Compute daily returns
    daily_returns = compute_daily_returns(df)
    
    # Scatterplot SPY vs XOM
    daily_returns.plot(kind='scatter', x='SPY', y='XOM')
    beta_XOM, alpha_XOM= np.polyfit(daily_returns['SPY'], daily_returns['XOM'], 1)
    print ("beta_XOM= ", beta_XOM)
    print ("alpha_XOM=", alpha_XOM)
    plt.plot(daily_returns['SPY'], beta_XOM*daily_returns['SPY'] + alpha_XOM, '-',color='r')
    plt.show()
    
    # Scatterplot SPY vs GLD
    daily_returns.plot(kind='scatter', x='SPY', y='GLD')
    beta_GLD, alpha_GLD= np.polyfit(daily_returns['SPY'], daily_returns['GLD'], 1)
    print ("beta_GLD= ", beta_GLD)
    print ("alpha_GLD=", alpha_GLD)
    plt.plot(daily_returns['SPY'], beta_GLD*daily_returns['SPY'] + alpha_GLD, '-',color='r')
    plt.show()
    
    
if __name__ == "__main__":
    test_run()