修心问道

Machine Learning for Trading--1-4 Statistical Analysis and Stock Basics

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本篇将介绍股市中的一些基本概念以及如何使用pandas和matplotlib库来对股票信息进行统计分析。

  • 对全局数据进行统计分析–Compute Global Statistics
  • 计算滚动的统计数据–Computing Rolling Statistics
  • 布林带–Bollinger Bands
  • 计算单日回报率-Compute daily returns

对全局数据进行统计分析–Compute Global Statistics

  • 将DataFrame中的所有列数据plot在同一个表格中 – df.plot()
  • 计算所有列的平均数，中位数和方差 – df.mean(), de.median(), df.std()

Example:

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import os
import pandas as pd
import matplotlib.pyplot as plt

def symbol_to_path(symbol, base_dir="data"):
    """Return CSV file path given ticker symbol."""
    return os.path.join(base_dir, "{}.csv".format(str(symbol)))

def get_data(symbols, dates):
    """Read stock data (adjusted close) for given symbols from CSV files."""
    df = pd.DataFrame(index=dates)
    if 'SPY' not in symbols:  # add SPY for reference, if absent
        symbols.insert(0, 'SPY')

    for symbol in symbols:
        df_temp = pd.read_csv(symbol_to_path(symbol), index_col='Date',
                parse_dates=True, usecols=['Date', 'Adj Close'], na_values=['nan'])
        df_temp = df_temp.rename(columns={'Adj Close': symbol})
        df = df.join(df_temp)
        if symbol == 'SPY':  # drop dates SPY did not trade
            df = df.dropna(subset=["SPY"])
    return df
  
def plot_data(df, title="Stock prices"):
    """Plot stock prices with a custom title and meaningful axis labels."""
    ax = df.plot(title=title, fontsize=12)
    ax.set_xlabel("Date")
    ax.set_ylabel("Price")
    plt.show()

def test_run():
  # Read data
  dates = pd.date_range('2010-01-01', '2012-12-31')
  symbols = ['SPY', 'XOM', 'GOOG', 'GLD']
  df = get_data(symbols, dates)
  plot_data(df)
  
  # Compute global statistics for each stock
  print (df.mean())
  print (df.median())
  print (df.std())

if __name__ == "__main__":
    test_run()

计算滚动的统计数据–Computing Rolling Statistics

  • 以20天的window计算滚动平均值 – rm_SPY=df[‘SPY’].rolling( window=20).mean()
  • 将rolling mean添加到现有数据的图中 – rm_SPY.plot()

Example:

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import os
import pandas as pd
import matplotlib.pyplot as plt
  
def symbol_to_path(symbol, base_dir="data"):
    """Return CSV file path given ticker symbol."""
    return os.path.join(base_dir, "{}.csv".format(str(symbol)))

def get_data(symbols, dates):
    """Read stock data (adjusted close) for given symbols from CSV files."""
    df = pd.DataFrame(index=dates)
    if 'SPY' not in symbols:  # add SPY for reference, if absent
        symbols.insert(0, 'SPY')

    for symbol in symbols:
        df_temp = pd.read_csv(symbol_to_path(symbol), index_col='Date',
                parse_dates=True, usecols=['Date', 'Adj Close'], na_values=['nan'])
        df_temp = df_temp.rename(columns={'Adj Close': symbol})
        df = df.join(df_temp)
        if symbol == 'SPY':  # drop dates SPY did not trade
            df = df.dropna(subset=["SPY"])
    return df 

def test_run():
  # Read data
  dates = pd.date_range('2010-01-01', '2012-12-31')
  symbols = ['SPY', 'XOM', 'GOOG', 'GLD']
  df = get_data(symbols, dates)
  
  # Plot SPY, retain matplotlib axis object
  ax = df['SPY'].plot(title="SPY rolling mean", label='SPY')
  
  # Compute rolling mean using a 20-day window
  rm_SPY = df['SPY'].rolling( window=20).mean()
  
  # Add rolling mean to same plot
  rm_SPY.plot(label='Rolling mean', ax=ax)
  
  # Add axis labels and legend
  ax.set_xlabel("Date")
  ax.set_ylabel("Price")
  ax.legend(loc='upper left')
  plt.show()
  
if __name__ == "__main__":
    test_run()

布林带–Bollinger Bands

  • 布林带 – 其基本的型态是由三条轨道线组成的带状通道（中轨和上、下轨各一条）。“中轨”为股价的平均成本，“上轨”和“下轨”可分别视为股价的压力线和支撑线。
  • 布林带中轨 – 滚动平均值 rolling mean
  • 布林带上轨和下轨 – 平均值+/-二倍方差 rolling mean +/- rstd * 2

Example:

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import os
import pandas as pd
import matplotlib.pyplot as plt

def symbol_to_path(symbol, base_dir="data"):
    """Return CSV file path given ticker symbol."""
    return os.path.join(base_dir, "{}.csv".format(str(symbol)))

def get_data(symbols, dates):
    """Read stock data (adjusted close) for given symbols from CSV files."""
    df = pd.DataFrame(index=dates)
    if 'SPY' not in symbols:  # add SPY for reference, if absent
        symbols.insert(0, 'SPY')

    for symbol in symbols:
        df_temp = pd.read_csv(symbol_to_path(symbol), index_col='Date',
                parse_dates=True, usecols=['Date', 'Adj Close'], na_values=['nan'])
        df_temp = df_temp.rename(columns={'Adj Close': symbol})
        df = df.join(df_temp)
        if symbol == 'SPY':  # drop dates SPY did not trade
            df = df.dropna(subset=["SPY"])

    return df

def plot_data(df, title="Stock prices"):
    """Plot stock prices with a custom title and meaningful axis labels."""
    ax = df.plot(title=title, fontsize=12)
    ax.set_xlabel("Date")
    ax.set_ylabel("Price")
    plt.show()

def get_rolling_mean(values, windows):
    """Return rolling mean of given values, using specified window size."""
    return values.rolling( window=windows).mean()

def get_rolling_std(values, windows):
    """Return rolling standard deviation of given values, using specified window size."""
    # Quiz: Compute and return rolling standard deviation
    return values.rolling(window=windows).std()

def get_bollinger_bands(rm, rstd):
    """Return upper and lower Bollinger Bands."""
    # Quiz: Compute upper_band and lower_band
    upper_band = rm + rstd * 2
    lower_band = rm - rstd * 2
    return upper_band, lower_band

def test_run():
    # Read data
    dates = pd.date_range('2012-01-01', '2012-12-31')
    symbols = ['SPY']
    df = get_data(symbols, dates)

    # Compute Bollinger Bands
    # 1. Compute rolling mean
    rm_SPY = get_rolling_mean(df['SPY'], windows=20)

    # 2. Compute rolling standard deviation
    rstd_SPY = get_rolling_std(df['SPY'], windows=20)

    # 3. Compute upper and lower bands
    upper_band, lower_band = get_bollinger_bands(rm_SPY, rstd_SPY)
    
    # Plot raw SPY values, rolling mean and Bollinger Bands
    ax = df['SPY'].plot(title="Bollinger Bands", label='SPY')
    rm_SPY.plot(label='Rolling mean', ax=ax)
    upper_band.plot(label='upper band', ax=ax)
    lower_band.plot(label='lower band', ax=ax)

    # Add axis labels and legend
    ax.set_xlabel("Date")
    ax.set_ylabel("Price")
    ax.legend(loc='upper left')
    plt.show()

if __name__ == "__main__":
    test_run()

计算单日回报率-Compute daily returns

  • 回报率计算公式 – daily_ret[t] = (price[t]/prict[t-1]) - 1
  • Pandas有两种方式计算回报率：
    • daily_returns[1:] = (df[1:] / df[:-1].values) - 1
    • daily_returns = (df / df.shift(1)) - 1

Example:

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import os
import pandas as pd
import matplotlib.pyplot as plt

def symbol_to_path(symbol, base_dir="data"):
    """Return CSV file path given ticker symbol."""
    return os.path.join(base_dir, "{}.csv".format(str(symbol)))

def get_data(symbols, dates):
    """Read stock data (adjusted close) for given symbols from CSV files."""
    df = pd.DataFrame(index=dates)
    if 'SPY' not in symbols:  # add SPY for reference, if absent
        symbols.insert(0, 'SPY')

    for symbol in symbols:
        df_temp = pd.read_csv(symbol_to_path(symbol), index_col='Date',
                parse_dates=True, usecols=['Date', 'Adj Close'], na_values=['nan'])
        df_temp = df_temp.rename(columns={'Adj Close': symbol})
        df = df.join(df_temp)
        if symbol == 'SPY':  # drop dates SPY did not trade
            df = df.dropna(subset=["SPY"])

    return df

def plot_data(df, title="Stock prices", xlabel="Date", ylabel="Price"):
    """Plot stock prices with a custom title and meaningful axis labels."""
    ax = df.plot(title=title, fontsize=12)
    ax.set_xlabel(xlabel)
    ax.set_ylabel(ylabel)
    plt.show()

def compute_daily_returns(df):
    """Compute and return the daily return values."""
    # Quiz: Your code here
    # Note: Returned DataFrame must have the same number of rows
    daily_returns = df.copy()
    # daily_returns[1:] = (df[1:] / df[:-1].values) - 1 # compute daily returns for row 1 onwards
    daily_returns = (df / df.shift(1)) - 1 # much easier with Pandas!
    daily_returns.iloc[0, :] = 0 # Pandas leaves the 0th row full of Nans
    return daily_returns

def test_run():
    # Read data
    dates = pd.date_range('2012-07-01', '2012-07-31')  # one month only
    symbols = ['SPY','XOM']
    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")


if __name__ == "__main__":
    test_run()
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